From d2722d73b400a385b76bfec22618ee1983c57d71 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 2 Nov 2024 17:52:07 +0000 Subject: [PATCH] build based on 627020d --- dev/404.html | 4 +- dev/Combined.html | 6 +- dev/FL.html | 6 +- dev/FW.html | 6 +- dev/ML.html | 6 +- dev/PM.html | 6 +- .../{app.Tf54mOo0.js => app.CqiBGVtm.js} | 2 +- .../chunks/@localSearchIndexroot.CLv1nWPY.js | 1 - .../chunks/@localSearchIndexroot.D-OpUR6n.js | 1 + ...MrclQK.js => VPLocalSearchBox.Bj4jf4Bg.js} | 2 +- .../{theme.Dp6S0rXT.js => theme.BMfR40cz.js} | 4 +- ...cs.md.Cq4wBRKn.js => funcs.md.OMbgMkND.js} | 78 ++++++++--------- ...BRKn.lean.js => funcs.md.OMbgMkND.lean.js} | 2 +- ...es.md.B3bPqqkV.js => types.md.28jHlNVY.js} | 16 ++-- dev/assets/types.md.28jHlNVY.lean.js | 1 + dev/assets/types.md.B3bPqqkV.lean.js | 1 - dev/benchmark.html | 6 +- dev/fetchdata.html | 6 +- dev/funcs.html | 86 +++++++++---------- dev/hashmap.json | 2 +- dev/index.html | 6 +- dev/performance_eval.html | 6 +- dev/python.html | 6 +- dev/refs.html | 6 +- dev/types.html | 22 ++--- 25 files changed, 144 insertions(+), 144 deletions(-) rename dev/assets/{app.Tf54mOo0.js => app.CqiBGVtm.js} (95%) delete mode 100644 dev/assets/chunks/@localSearchIndexroot.CLv1nWPY.js create mode 100644 dev/assets/chunks/@localSearchIndexroot.D-OpUR6n.js rename dev/assets/chunks/{VPLocalSearchBox.RxMrclQK.js => VPLocalSearchBox.Bj4jf4Bg.js} (99%) rename dev/assets/chunks/{theme.Dp6S0rXT.js => theme.BMfR40cz.js} (99%) rename dev/assets/{funcs.md.Cq4wBRKn.js => funcs.md.OMbgMkND.js} (99%) rename dev/assets/{funcs.md.Cq4wBRKn.lean.js => funcs.md.OMbgMkND.lean.js} (99%) rename dev/assets/{types.md.B3bPqqkV.js => types.md.28jHlNVY.js} (87%) create mode 100644 dev/assets/types.md.28jHlNVY.lean.js delete mode 100644 dev/assets/types.md.B3bPqqkV.lean.js diff --git a/dev/404.html b/dev/404.html index 748ef42..e7abe96 100644 --- a/dev/404.html +++ b/dev/404.html @@ -8,14 +8,14 @@ - +
OnlinePortfolioSelection.jl

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404

PAGE NOT FOUND

But if you don't change your direction, and if you keep looking, you may end up where you are heading.
Take me home
- + \ No newline at end of file diff --git a/dev/Combined.html b/dev/Combined.html index da66340..e8f0467 100644 --- a/dev/Combined.html +++ b/dev/Combined.html @@ -8,9 +8,9 @@ - + - + @@ -125,7 +125,7 @@ 0.333333 1.52594e-6 7.35766e-7 0.333333 5.30452e-6 3.90444e-6 0.333333 0.999993 0.999995

You can analyse the algorithm's performance using several metrics that have been provided in this package. Check out the Performance evaluation section for more details.

References ​

Bibliography ​

  1. H. Guan and Z. An. A local adaptive learning system for online portfolio selection. Knowledge-Based Systems 186, 104958 (2019).

  2. H. Lin, Y. Zhang and X. Yang. Online portfolio selection of integrating expert strategies based on mean reversion and trading volume. Expert Systems with Applications 238, 121472 (2024).

  3. H.-L. Dai, C.-X. Liang, H.-M. Dai, C.-Y. Huang and R. M. Adnan. An online portfolio strategy based on trend promote price tracing ensemble learning algorithm. Knowledge-Based Systems 239, 107957 (2022).

- + \ No newline at end of file diff --git a/dev/FL.html b/dev/FL.html index 3eb244a..7d4bb74 100644 --- a/dev/FL.html +++ b/dev/FL.html @@ -8,9 +8,9 @@ - + - + @@ -486,7 +486,7 @@ 0.05 0.0809567 0.0830907 0.0890398 0.0885799 0.7 0.730957 0.756827 0.746137 0.748113 0.2 0.10713 0.0750128 0.0776584 0.0767483

You can analyse the algorithm's performance using several metrics that have been provided in this package. Check out the Performance evaluation section for more details.

References ​

Bibliography ​

  1. A. Borodin, R. El-Yaniv and V. Gogan. Can we learn to beat the best stock. Advances in Neural Information Processing Systems 16 (2003).

  2. Z.-R. Lai, P.-Y. Yang, L. Fang and X. Wu. Reweighted Price Relative Tracking System for Automatic Portfolio Optimization. IEEE Transactions on Systems, Man, and Cybernetics: Systems 50, 4349–4361 (2020).

  3. B. Li and S. C. Hoi. On-Line Portfolio Selection with Moving Average Reversion (2012), arXiv:1206.4626 [cs.CE].

  4. B. Li, S. C. Hoi, D. Sahoo and Z.-Y. Liu. Moving average reversion strategy for on-line portfolio selection. Artificial Intelligence 222, 104–123 (2015).

  5. B. Li, P. Zhao, S. C. Hoi and V. Gopalkrishnan. PAMR: Passive aggressive mean reversion strategy for portfolio selection. Machine Learning 87, 221–258 (2012).

  6. B. Li, S. C. Hoi, P. Zhao and V. Gopalkrishnan. Confidence Weighted Mean Reversion Strategy for Online Portfolio Selection. ACM Trans. Knowl. Discov. Data 7 (2013).

  7. X. Cai and Z. Ye. Gaussian Weighting Reversion Strategy for Accurate Online Portfolio Selection. IEEE Transactions on Signal Processing 67, 5558–5570 (2019).

  8. Y. Zhong, W. Xu, H. Li and W. Zhong. Distributed mean reversion online portfolio strategy with stock network. European Journal of Operational Research (2023).

  9. D. Huang, J. Zhou, B. Li, S. C. Hoi and S. Zhou. Robust Median Reversion Strategy for Online Portfolio Selection. IEEE Transactions on Knowledge and Data Engineering 28, 2480–2493 (2016).

  10. Z.-R. Lai, L. Tan, X. Wu and L. Fang. Loss control with rank-one covariance estimate for short-term portfolio optimization. J. Mach. Learn. Res. 21 (2020).

  11. L. Bin, W. Jialei, H. Dingjiang and S. C. Hoi. Transaction cost optimization for online portfolio selection. Quantitative Finance 18, 1411–1424 (2018).

- + \ No newline at end of file diff --git a/dev/FW.html b/dev/FW.html index 8d89060..fc5f2d2 100644 --- a/dev/FW.html +++ b/dev/FW.html @@ -8,9 +8,9 @@ - + - + @@ -210,7 +210,7 @@ 0.25 0.0 0.0 0.0 0.0 0.25 0.0 0.0 0.0 0.0 0.25 1.0 9.94367e-9 0.0 0.0

You can analyse the algorithm's performance using several metrics that have been provided in this package. Check out the Performance evaluation section for more details.

References ​

Bibliography ​

  1. D. P. Helmbold, R. E. Schapire, Y. Singer and M. K. Warmuth. On-Line Portfolio Selection Using Multiplicative Updates. Mathematical Finance 8, 325–347 (1998).

  2. Z.-R. Lai, D.-Q. Dai, C.-X. Ren and K.-K. Huang. A Peak Price Tracking-Based Learning System for Portfolio Selection. IEEE Transactions on Neural Networks and Learning Systems 29, 2823–2832 (2018).

  3. Z.-R. Lai, D.-Q. Dai, C.-X. Ren and K.-K. Huang. Radial Basis Functions With Adaptive Input and Composite Trend Representation for Portfolio Selection. IEEE Transactions on Neural Networks and Learning Systems 29, 6214–6226 (2018).

  4. Y. Li, X. Zheng, C. Chen, J. Wang and S. Xu. Exponential Gradient with Momentum for Online Portfolio Selection. Expert Systems with Applications 187, 115889 (2022).

  5. Z.-R. Lai, P.-Y. Yang, L. Fang and X. Wu. Short-term Sparse Portfolio Optimization Based on Alternating Direction Method of Multipliers. Journal of Machine Learning Research 19, 1–28 (2018).

- + \ No newline at end of file diff --git a/dev/ML.html b/dev/ML.html index e62a77d..21fb862 100644 --- a/dev/ML.html +++ b/dev/ML.html @@ -8,9 +8,9 @@ - + - + @@ -120,7 +120,7 @@ 0.25 0.249138 0.248921 0.249289 0.250482 0.23192 0.202576 0.179329 0.160005 0.168903 0.25 0.250026 0.250656 0.24931 0.24995 0.226647 0.237694 0.237879 0.216076 0.192437 0.25 0.250528 0.249134 0.249728 0.248744 0.273746 0.245936 0.263367 0.245737 0.211411

One can analyse the algorithm's performance using several metrics that have been provided in this package. Check out the Performance evaluation section for more details.

References ​

Bibliography ​

  1. Y. Zhang, H. Lin, X. Yang and W. Long. Combining expert weights for online portfolio selection based on the gradient descent algorithm. Knowledge-Based Systems 234, 107533 (2021).

  2. J. H. Xingyu Yang and Y. Zhang. Aggregating exponential gradient expert advice for online portfolio selection. Journal of the Operational Research Society 73, 587–597 (2020).

  3. X. Yang, J. He, H. Lin and Y. Zhang. Boosting Exponential Gradient Strategy for Online Portfolio Selection: An Aggregating Experts' Advice Method. Computational Economics 55, 231–251 (2020).

  4. Y. Zhang, H. Lin, L. Zheng and X. Yang. Adaptive online portfolio strategy based on exponential gradient updates. Journal of Combinatorial Optimization 43, 672–696 (2022).

- + \ No newline at end of file diff --git a/dev/PM.html b/dev/PM.html index 832c353..4d55d21 100644 --- a/dev/PM.html +++ b/dev/PM.html @@ -8,9 +8,9 @@ - + - + @@ -201,7 +201,7 @@ 0.9808095798904469 0.984908122467024 0.9830242099475751

You can analyse the algorithm's performance using several metrics that have been provided in this package. Check out the Performance evaluation section for more details.

References ​

Bibliography ​

  1. B. Li, S. C. Hoi and V. Gopalkrishnan. CORN: Correlation-Driven Nonparametric Learning Approach for Portfolio Selection. ACM Trans. Intell. Syst. Technol. 2 (2011).

  2. S. Sooklal, T. L. van Zyl and A. Paskaramoorthy. DRICORN-K: A Dynamic RIsk CORrelation-driven Non-parametric Algorithm for Online Portfolio Selection. In: Artificial Intelligence Research, edited by A. Gerber (Springer International Publishing, Cham, 2020); pp. 183–196.

  3. L. Györfi, G. Lugosi and F. Udina. NONPARAMETRIC KERNEL-BASED SEQUENTIAL INVESTMENT STRATEGIES. Mathematical Finance 16, 337–357 (2006).

  4. M. Khedmati and P. Azin. An online portfolio selection algorithm using clustering approaches and considering transaction costs. Expert Systems with Applications 159, 113546 (2020).

  5. W. Xi, Z. Li, X. Song and H. Ning. Online portfolio selection with predictive instantaneous risk assessment. Pattern Recognition 144, 109872 (2023).

  6. Z.-R. Lai, P.-Y. Yang, X. Wu and L. Fang. A kernel-based trend pattern tracking system for portfolio optimization. Data Mining and Knowledge Discovery 32, 1708–1734 (2018).

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ct(Ve.Layout,null,{})},enhanceApp({app:s,router:t,siteData:e}){Fr(s)}};export{Ur as R,Zn as c,L as u}; diff --git a/dev/assets/funcs.md.Cq4wBRKn.js b/dev/assets/funcs.md.OMbgMkND.js similarity index 99% rename from dev/assets/funcs.md.Cq4wBRKn.js rename to dev/assets/funcs.md.OMbgMkND.js index 4f28661..e4b56d0 100644 --- a/dev/assets/funcs.md.Cq4wBRKn.js +++ b/dev/assets/funcs.md.OMbgMkND.js @@ -39,7 +39,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr 0.1 6.92278e-8 0.0 0.0 0.0 0.1 0.0 0.0 6.95036e-8 1.0 0.1 0.0 0.0 0.0 0.0 - 0.1 0.0 0.0 1.0 6.95537e-8

References

Radial Basis Functions With Adaptive Input and Composite Trend Representation for Portfolio Selection

source

`,14),E={class:"jldocstring custom-block",open:""},c=s("a",{id:"OnlinePortfolioSelection.ann_sharpe-Union{Tuple{T}, Tuple{T, T, T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.ann_sharpe-Union{Tuple{T}, Tuple{T, T, T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ann_sharpe")],-1),F=a('
julia
ann_sharpe(APY::T, Rf::T, sigma_prtf::T) where T<:AbstractFloat

Calculate the Annualized Sharpe Ratio of investment. Also, see sn, mer, ann_std, apy, mdd, calmar, and opsmetrics.

Arguments

',3),y=s("li",null,[s("p",null,[s("code",null,"APY::T"),i(": the APY of investment.")])],-1),C=s("li",null,[s("p",null,[s("code",null,"Rf::T"),i(": the risk-free rate of return.")])],-1),u=s("code",null,"sigma_prtf::T",-1),T={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.65ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.284ex",height:"1.625ex",role:"img",focusable:"false",viewBox:"0 -431 1009.7 718.2","aria-hidden":"true"},m=a('',1),B=[m],b=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"σ"),s("mi",null,"p")])])],-1),_=s("p",null,[s("strong",null,"Returns")],-1),f=s("ul",null,[s("li",null,[s("code",null,"::AbstractFloat"),i(": the Annualized Sharpe Ratio of investment.")])],-1),Q=s("p",null,[s("a",{href:"https://github.com/shayandavoodii/OnlinePortfolioSelection.jl/blob/1b5fd9e184b06b852af2d5317600d283b84d5230/src/Tools/metrics.jl#L234-L246",target:"_blank",rel:"noreferrer"},"source")],-1),D={class:"jldocstring custom-block",open:""},v=s("a",{id:"OnlinePortfolioSelection.ann_std-Tuple{AbstractVector{<:AbstractFloat}}",href:"#OnlinePortfolioSelection.ann_std-Tuple{AbstractVector{<:AbstractFloat}}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ann_std")],-1),j=a('
julia
ann_std(cum_ret::AbstractVector{AbstractFloat}; dpy)
',1),x={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},S={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.65ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.284ex",height:"1.625ex",role:"img",focusable:"false",viewBox:"0 -431 1009.7 718.2","aria-hidden":"true"},w=a('',1),P=[w],O=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"σ"),s("mi",null,"p")])])],-1),M=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.sn-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}} where T<:AbstractFloat"},[s("code",null,"sn")],-1),q=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.mer-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, T}} where T<:AbstractFloat"},[s("code",null,"mer")],-1),R=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.apy-Union{Tuple{S}, Tuple{AbstractFloat, S}} where S<:Int64"},[s("code",null,"apy")],-1),I=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.ann_sharpe-Union{Tuple{T}, Tuple{T, T, T}} where T<:AbstractFloat"},[s("code",null,"ann_sharpe")],-1),V=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.mdd-Union{Tuple{AbstractVector{T}}, Tuple{T}} where T<:AbstractFloat"},[s("code",null,"mdd")],-1),L=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.calmar-Union{Tuple{T}, Tuple{T, T}} where T<:AbstractFloat"},[s("code",null,"calmar")],-1),H=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.opsmetrics-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, AbstractVector{T}}} where {T<:AbstractFloat, S<:Int64}"},[s("code",null,"opsmetrics")],-1),z=s("p",null,[s("strong",null,"Arguments")],-1),N=s("ul",null,[s("li",null,[s("code",null,"cum_ret::AbstractVector{AbstractFloat}"),i(": the cumulative wealth of investment during the investment period.")])],-1),U=s("p",null,[s("strong",null,"Keyword Arguments")],-1),G=s("ul",null,[s("li",null,[s("code",null,"dpy"),i(": the number of days in a year.")])],-1),Z=s("p",null,[s("strong",null,"Returns")],-1),W=s("code",null,"::AbstractFloat",-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.65ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.284ex",height:"1.625ex",role:"img",focusable:"false",viewBox:"0 -431 1009.7 718.2","aria-hidden":"true"},J=a('',1),X=[J],$=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"σ"),s("mi",null,"p")])])],-1),ss=s("p",null,[s("a",{href:"https://github.com/shayandavoodii/OnlinePortfolioSelection.jl/blob/1b5fd9e184b06b852af2d5317600d283b84d5230/src/Tools/metrics.jl#L194-L207",target:"_blank",rel:"noreferrer"},"source")],-1),is={class:"jldocstring custom-block",open:""},as=s("a",{id:"OnlinePortfolioSelection.anticor-Union{Tuple{T}, Tuple{Matrix{T}, Int64}} where T<:Real",href:"#OnlinePortfolioSelection.anticor-Union{Tuple{T}, Tuple{Matrix{T}, Int64}} where T<:Real"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.anticor")],-1),ts=a(`
julia
anticor(adj_close::Matrix{T}, window::Int) where {T<:Real}

Run the Anticor algorithm on adj_close with window sizes window.

Beware!

adj_close should be a matrix of size n_assets × n_periods.

Arguments

  • adj_close::Matrix{T}: matrix of adjusted close prices

  • window::Int: size of the window

Returns

  • ::OPSAlgorithm(n_assets, b, alg): An OPSAlgorithm object.

Example

julia
julia> using OnlinePortfolioSelection
+ 0.1  0.0         0.0         1.0         6.95537e-8

References

Radial Basis Functions With Adaptive Input and Composite Trend Representation for Portfolio Selection

source

`,14),E={class:"jldocstring custom-block",open:""},c=s("a",{id:"OnlinePortfolioSelection.ann_sharpe-Union{Tuple{T}, Tuple{T, T, T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.ann_sharpe-Union{Tuple{T}, Tuple{T, T, T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ann_sharpe")],-1),F=a('
julia
ann_sharpe(APY::T, Rf::T, sigma_prtf::T) where T<:AbstractFloat

Calculate the Annualized Sharpe Ratio of investment. Also, see sn, mer, ann_std, apy, mdd, calmar, and opsmetrics.

Arguments

',3),y=s("li",null,[s("p",null,[s("code",null,"APY::T"),i(": the APY of investment.")])],-1),C=s("li",null,[s("p",null,[s("code",null,"Rf::T"),i(": the risk-free rate of return.")])],-1),u=s("code",null,"sigma_prtf::T",-1),T={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.65ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.284ex",height:"1.625ex",role:"img",focusable:"false",viewBox:"0 -431 1009.7 718.2","aria-hidden":"true"},m=a('',1),B=[m],b=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"σ"),s("mi",null,"p")])])],-1),_=s("p",null,[s("strong",null,"Returns")],-1),f=s("ul",null,[s("li",null,[s("code",null,"::AbstractFloat"),i(": the Annualized Sharpe Ratio of investment.")])],-1),Q=s("p",null,[s("a",{href:"https://github.com/shayandavoodii/OnlinePortfolioSelection.jl/blob/627020d7225a0a3ecc416fd4340a8c6519fe675d/src/Tools/metrics.jl#L234-L246",target:"_blank",rel:"noreferrer"},"source")],-1),D={class:"jldocstring custom-block",open:""},v=s("a",{id:"OnlinePortfolioSelection.ann_std-Tuple{AbstractVector{<:AbstractFloat}}",href:"#OnlinePortfolioSelection.ann_std-Tuple{AbstractVector{<:AbstractFloat}}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ann_std")],-1),j=a('
julia
ann_std(cum_ret::AbstractVector{AbstractFloat}; dpy)
',1),x={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},S={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.65ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.284ex",height:"1.625ex",role:"img",focusable:"false",viewBox:"0 -431 1009.7 718.2","aria-hidden":"true"},w=a('',1),P=[w],O=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"σ"),s("mi",null,"p")])])],-1),M=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.sn-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}} where T<:AbstractFloat"},[s("code",null,"sn")],-1),q=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.mer-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, T}} where T<:AbstractFloat"},[s("code",null,"mer")],-1),R=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.apy-Union{Tuple{S}, Tuple{AbstractFloat, S}} where S<:Int64"},[s("code",null,"apy")],-1),I=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.ann_sharpe-Union{Tuple{T}, Tuple{T, T, T}} where T<:AbstractFloat"},[s("code",null,"ann_sharpe")],-1),V=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.mdd-Union{Tuple{AbstractVector{T}}, Tuple{T}} where T<:AbstractFloat"},[s("code",null,"mdd")],-1),L=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.calmar-Union{Tuple{T}, Tuple{T, T}} where T<:AbstractFloat"},[s("code",null,"calmar")],-1),H=s("a",{href:"/OnlinePortfolioSelection.jl/dev/funcs#OnlinePortfolioSelection.opsmetrics-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, AbstractVector{T}}} where {T<:AbstractFloat, S<:Int64}"},[s("code",null,"opsmetrics")],-1),z=s("p",null,[s("strong",null,"Arguments")],-1),N=s("ul",null,[s("li",null,[s("code",null,"cum_ret::AbstractVector{AbstractFloat}"),i(": the cumulative wealth of investment during the investment period.")])],-1),U=s("p",null,[s("strong",null,"Keyword Arguments")],-1),G=s("ul",null,[s("li",null,[s("code",null,"dpy"),i(": the number of days in a year.")])],-1),Z=s("p",null,[s("strong",null,"Returns")],-1),W=s("code",null,"::AbstractFloat",-1),K={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.65ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.284ex",height:"1.625ex",role:"img",focusable:"false",viewBox:"0 -431 1009.7 718.2","aria-hidden":"true"},J=a('',1),X=[J],$=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"σ"),s("mi",null,"p")])])],-1),ss=s("p",null,[s("a",{href:"https://github.com/shayandavoodii/OnlinePortfolioSelection.jl/blob/627020d7225a0a3ecc416fd4340a8c6519fe675d/src/Tools/metrics.jl#L194-L207",target:"_blank",rel:"noreferrer"},"source")],-1),is={class:"jldocstring custom-block",open:""},as=s("a",{id:"OnlinePortfolioSelection.anticor-Union{Tuple{T}, Tuple{Matrix{T}, Int64}} where T<:Real",href:"#OnlinePortfolioSelection.anticor-Union{Tuple{T}, Tuple{Matrix{T}, Int64}} where T<:Real"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.anticor")],-1),ts=a(`
julia
anticor(adj_close::Matrix{T}, window::Int) where {T<:Real}

Run the Anticor algorithm on adj_close with window sizes window.

Beware!

adj_close should be a matrix of size n_assets × n_periods.

Arguments

  • adj_close::Matrix{T}: matrix of adjusted close prices

  • window::Int: size of the window

Returns

  • ::OPSAlgorithm(n_assets, b, alg): An OPSAlgorithm object.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> adj_close = [
        1. 2.
@@ -68,7 +68,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.5  0.5  0.5  0.5     1.0  1.0  1.0  0.0
 
 julia> sum(m_anticor.b, dims=1) .|> isapprox(1., atol=1e-8) |> all
-true

References

Can We Learn to Beat the Best Stock

source

`,12),ns={class:"jldocstring custom-block",open:""},ls=s("a",{id:"OnlinePortfolioSelection.apy-Union{Tuple{S}, Tuple{AbstractFloat, S}} where S<:Int64",href:"#OnlinePortfolioSelection.apy-Union{Tuple{S}, Tuple{AbstractFloat, S}} where S<:Int64"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.apy")],-1),hs=a('
julia
apy(Sn::AbstractFloat, n_periods::S; dpy::S=252) where S<:Int

Calculate the Annual Percentage Yield (APY) of investment. Also, see sn, mer, ann_std, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • Sn::AbstractFloat: the cumulative wealth of investment.

  • n_periods::S: the number investment periods.

  • dpy::S=252: the number of days in a year.

Returns

  • ::AbstractFloat: the APY of investment.

source

',7),es={class:"jldocstring custom-block",open:""},ks=s("a",{id:"OnlinePortfolioSelection.at-Tuple{AbstractMatrix, AbstractMatrix}",href:"#OnlinePortfolioSelection.at-Tuple{AbstractMatrix, AbstractMatrix}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.at")],-1),ps=a('
julia
at(rel_pr::AbstractMatrix, b::AbstractMatrix)

Calculate the average turnover of the portfolio. Also, see sn, mer, ir, ann_std, apy, ann_sharpe, mdd, and calmar.

Arguments

  • rel_pr::AbstractMatrix: The relative price of the stocks.

  • b::AbstractMatrix: The weights of the portfolio.

Returns

  • ::AbstractFloat: the average turnover of the portfolio.

source

',7),rs={class:"jldocstring custom-block",open:""},ds=s("a",{id:"OnlinePortfolioSelection.bcrp-Union{Tuple{AbstractMatrix{T}}, Tuple{T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.bcrp-Union{Tuple{AbstractMatrix{T}}, Tuple{T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.bcrp")],-1),os=a(`
julia
bcrp(rel_pr::AbstractMatrix{T}) where T<:AbstractFloat

Run Best Constant Rebalanced Portfolio (BCRP) algorithm.

Arguments

  • rel_pr::AbstractMatrix{T}: Relative price matrix.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
+true

References

Can We Learn to Beat the Best Stock

source

`,12),ns={class:"jldocstring custom-block",open:""},ls=s("a",{id:"OnlinePortfolioSelection.apy-Union{Tuple{S}, Tuple{AbstractFloat, S}} where S<:Int64",href:"#OnlinePortfolioSelection.apy-Union{Tuple{S}, Tuple{AbstractFloat, S}} where S<:Int64"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.apy")],-1),hs=a('
julia
apy(Sn::AbstractFloat, n_periods::S; dpy::S=252) where S<:Int

Calculate the Annual Percentage Yield (APY) of investment. Also, see sn, mer, ann_std, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • Sn::AbstractFloat: the cumulative wealth of investment.

  • n_periods::S: the number investment periods.

  • dpy::S=252: the number of days in a year.

Returns

  • ::AbstractFloat: the APY of investment.

source

',7),es={class:"jldocstring custom-block",open:""},ks=s("a",{id:"OnlinePortfolioSelection.at-Tuple{AbstractMatrix, AbstractMatrix}",href:"#OnlinePortfolioSelection.at-Tuple{AbstractMatrix, AbstractMatrix}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.at")],-1),ps=a('
julia
at(rel_pr::AbstractMatrix, b::AbstractMatrix)

Calculate the average turnover of the portfolio. Also, see sn, mer, ir, ann_std, apy, ann_sharpe, mdd, and calmar.

Arguments

  • rel_pr::AbstractMatrix: The relative price of the stocks.

  • b::AbstractMatrix: The weights of the portfolio.

Returns

  • ::AbstractFloat: the average turnover of the portfolio.

source

',7),rs={class:"jldocstring custom-block",open:""},ds=s("a",{id:"OnlinePortfolioSelection.bcrp-Union{Tuple{AbstractMatrix{T}}, Tuple{T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.bcrp-Union{Tuple{AbstractMatrix{T}}, Tuple{T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.bcrp")],-1),os=a(`
julia
bcrp(rel_pr::AbstractMatrix{T}) where T<:AbstractFloat

Run Best Constant Rebalanced Portfolio (BCRP) algorithm.

Arguments

  • rel_pr::AbstractMatrix{T}: Relative price matrix.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> rel_pr = rand(3, 8);
 
@@ -81,7 +81,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
 
 julia> sum(m_bcrp.b, dims=1) .|> isapprox(1.) |> all
-true

References

Universal Portfolios

source

`,12),gs={class:"jldocstring custom-block",open:""},Es=s("a",{id:"OnlinePortfolioSelection.bk-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, S, S, T}} where {T<:AbstractFloat, S<:Integer}",href:"#OnlinePortfolioSelection.bk-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, S, S, T}} where {T<:AbstractFloat, S<:Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.bk")],-1),cs=a(`
julia
bk(rel_price::AbstractMatrix{T}, K::S, L::S, c::T) where {T<:AbstractFloat, S<:Integer}

Run Bᴷ algorithm.

Arguments

  • rel_price::AbstractMatrix{T}: Relative prices of assets.

  • K::S: Number of experts.

  • L::S: Number of time windows.

  • c::T: The similarity threshold.

Beware!

rel_price should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
+true

References

Universal Portfolios

source

`,12),gs={class:"jldocstring custom-block",open:""},Es=s("a",{id:"OnlinePortfolioSelection.bk-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, S, S, T}} where {T<:AbstractFloat, S<:Integer}",href:"#OnlinePortfolioSelection.bk-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, S, S, T}} where {T<:AbstractFloat, S<:Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.bk")],-1),cs=a(`
julia
bk(rel_price::AbstractMatrix{T}, K::S, L::S, c::T) where {T<:AbstractFloat, S<:Integer}

Run Bᴷ algorithm.

Arguments

  • rel_price::AbstractMatrix{T}: Relative prices of assets.

  • K::S: Number of experts.

  • L::S: Number of time windows.

  • c::T: The similarity threshold.

Beware!

rel_price should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> daily_relative_prices = rand(3, 20);
 julia> nexperts = 10;
@@ -97,7 +97,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.333333  0.333333  0.322581  0.318677     0.333331  0.329797  0.322842  0.295789
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

Reference

NONPARAMETRIC KERNEL-BASED SEQUENTIAL INVESTMENT STRATEGIES

source

`,12),Fs={class:"jldocstring custom-block",open:""},ys=s("a",{id:"OnlinePortfolioSelection.bs-Union{Tuple{Matrix{T}}, Tuple{T}} where T<:Float64",href:"#OnlinePortfolioSelection.bs-Union{Tuple{Matrix{T}}, Tuple{T}} where T<:Float64"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.bs")],-1),Cs=a(`
julia
bs(adj_close::Matrix{T}; last_n::Int=0) where {T<:Float64}

Run the Best So Far algorithm on the given data.

Arguments

  • adj_close::Matrix{T}: A matrix of adjusted closing prices of assets.

Keyword Arguments

  • last_n::Int: The number of periods to look back for the performance of each asset. If last_n is 0, then the performance is calculated from the first period to the previous period.

Beware!

The adj_close matrix should be in the order of assets x periods.

Returns

  • ::OPSAlgorithm(n_assets, b, alg): An instance of OPSAlgorithm.

Example

julia
julia> using OnlinePortfolioSelection
+true

Reference

NONPARAMETRIC KERNEL-BASED SEQUENTIAL INVESTMENT STRATEGIES

source

`,12),Fs={class:"jldocstring custom-block",open:""},ys=s("a",{id:"OnlinePortfolioSelection.bs-Union{Tuple{Matrix{T}}, Tuple{T}} where T<:Float64",href:"#OnlinePortfolioSelection.bs-Union{Tuple{Matrix{T}}, Tuple{T}} where T<:Float64"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.bs")],-1),Cs=a(`
julia
bs(adj_close::Matrix{T}; last_n::Int=0) where {T<:Float64}

Run the Best So Far algorithm on the given data.

Arguments

  • adj_close::Matrix{T}: A matrix of adjusted closing prices of assets.

Keyword Arguments

  • last_n::Int: The number of periods to look back for the performance of each asset. If last_n is 0, then the performance is calculated from the first period to the previous period.

Beware!

The adj_close matrix should be in the order of assets x periods.

Returns

  • ::OPSAlgorithm(n_assets, b, alg): An instance of OPSAlgorithm.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> adj_close = rand(5, 10);
 
@@ -112,7 +112,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.2  0.0  0.0  0.0  0.0  0.0  0.0  1.0  0.0  0.0
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

References

KERNEL-BASED SEMI-LOG-OPTIMAL EMPIRICAL PORTFOLIO SELECTION STRATEGIES

source

`,14),us={class:"jldocstring custom-block",open:""},Ts=s("a",{id:"OnlinePortfolioSelection.caeg-Tuple{AbstractMatrix, AbstractVector}",href:"#OnlinePortfolioSelection.caeg-Tuple{AbstractMatrix, AbstractVector}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.caeg")],-1),As=a(`
julia
caeg(rel_pr::AbstractMatrix, ηs::AbstractVector)

Run CAEG algorithm.

Arguments

  • rel_pr::AbstractMatrix: Historical relative prices. The paper's authors used "the ratio of closing price to last closing price".

  • ηs::AbstractVector: Learning rates.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection, YFinance
+true

References

KERNEL-BASED SEMI-LOG-OPTIMAL EMPIRICAL PORTFOLIO SELECTION STRATEGIES

source

`,14),us={class:"jldocstring custom-block",open:""},Ts=s("a",{id:"OnlinePortfolioSelection.caeg-Tuple{AbstractMatrix, AbstractVector}",href:"#OnlinePortfolioSelection.caeg-Tuple{AbstractMatrix, AbstractVector}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.caeg")],-1),As=a(`
julia
caeg(rel_pr::AbstractMatrix, ηs::AbstractVector)

Run CAEG algorithm.

Arguments

  • rel_pr::AbstractMatrix: Historical relative prices. The paper's authors used "the ratio of closing price to last closing price".

  • ηs::AbstractVector: Learning rates.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "GOOG"];
 
@@ -136,7 +136,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 3×6 Matrix{Float64}:
  0.333333  0.333322  0.333286  0.333271  0.333287  0.333368
  0.333333  0.333295  0.333271  0.333171  0.333123  0.333076
- 0.333333  0.333383  0.333443  0.333558  0.33359   0.333557

References

Aggregating exponential gradient expert advice for online portfolio selection

source

`,12),ms={class:"jldocstring custom-block",open:""},Bs=s("a",{id:"OnlinePortfolioSelection.calmar-Union{Tuple{T}, Tuple{T, T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.calmar-Union{Tuple{T}, Tuple{T, T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.calmar")],-1),bs=a('
julia
calmar(APY::T, MDD::T) where T<:AbstractFloat

Calculate the Calmar Ratio of investment. Also, see sn, mer, ann_std, apy, ann_sharpe, mdd, and opsmetrics.

Arguments

  • APY::T: the APY of investment.

  • MDD::T: the MDD of investment.

Returns

  • ::AbstractFloat: the Calmar Ratio of investment.

source

',7),_s={class:"jldocstring custom-block",open:""},fs=s("a",{id:"OnlinePortfolioSelection.cluslog",href:"#OnlinePortfolioSelection.cluslog"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cluslog")],-1),Qs=a(`
julia
cluslog(
+ 0.333333  0.333383  0.333443  0.333558  0.33359   0.333557

References

Aggregating exponential gradient expert advice for online portfolio selection

source

`,12),ms={class:"jldocstring custom-block",open:""},Bs=s("a",{id:"OnlinePortfolioSelection.calmar-Union{Tuple{T}, Tuple{T, T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.calmar-Union{Tuple{T}, Tuple{T, T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.calmar")],-1),bs=a('
julia
calmar(APY::T, MDD::T) where T<:AbstractFloat

Calculate the Calmar Ratio of investment. Also, see sn, mer, ann_std, apy, ann_sharpe, mdd, and opsmetrics.

Arguments

  • APY::T: the APY of investment.

  • MDD::T: the MDD of investment.

Returns

  • ::AbstractFloat: the Calmar Ratio of investment.

source

',7),_s={class:"jldocstring custom-block",open:""},fs=s("a",{id:"OnlinePortfolioSelection.cluslog",href:"#OnlinePortfolioSelection.cluslog"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cluslog")],-1),Qs=a(`
julia
cluslog(
   rel_pr::AbstractMatrix{<:AbstractFloat},
   horizon::Int,
   TW::Int,
@@ -178,7 +178,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 2.02964e-6  2.02787e-6  2.02964e-6
 
 julia> sum(model.b , dims=1) .|> isapprox(1.) |> all
-true

See also KMNLOG, and KMDLOG.

Reference

An online portfolio selection algorithm using clustering approaches and considering transaction costs

source

`,19),Ds={class:"jldocstring custom-block",open:""},vs=s("a",{id:"OnlinePortfolioSelection.cornk-Union{Tuple{T}, Tuple{AbstractMatrix{<:AbstractFloat}, Vararg{T, 4}}} where T<:Integer",href:"#OnlinePortfolioSelection.cornk-Union{Tuple{T}, Tuple{AbstractMatrix{<:AbstractFloat}, Vararg{T, 4}}} where T<:Integer"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cornk")],-1),js=a(`
julia
cornk(
+true

See also KMNLOG, and KMDLOG.

Reference

An online portfolio selection algorithm using clustering approaches and considering transaction costs

source

`,19),Ds={class:"jldocstring custom-block",open:""},vs=s("a",{id:"OnlinePortfolioSelection.cornk-Union{Tuple{T}, Tuple{AbstractMatrix{<:AbstractFloat}, Vararg{T, 4}}} where T<:Integer",href:"#OnlinePortfolioSelection.cornk-Union{Tuple{T}, Tuple{AbstractMatrix{<:AbstractFloat}, Vararg{T, 4}}} where T<:Integer"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cornk")],-1),js=a(`
julia
cornk(
   x::AbstractMatrix{<:AbstractFloat},
   horizon::T,
   k::T,
@@ -196,7 +196,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 "CORN-K"
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

See cornu, and dricornk.

Reference

CORN: Correlation-driven nonparametric learning approach for portfolio selection

source

`,15),xs={class:"jldocstring custom-block",open:""},Ss=s("a",{id:"OnlinePortfolioSelection.cornu-Union{Tuple{M}, Tuple{T}, Tuple{AbstractMatrix{T}, M, M}} where {T<:AbstractFloat, M<:Integer}",href:"#OnlinePortfolioSelection.cornu-Union{Tuple{M}, Tuple{T}, Tuple{AbstractMatrix{T}, M, M}} where {T<:AbstractFloat, M<:Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cornu")],-1),ws=a(`
julia
cornu(
+true

See cornu, and dricornk.

Reference

CORN: Correlation-driven nonparametric learning approach for portfolio selection

source

`,15),xs={class:"jldocstring custom-block",open:""},Ss=s("a",{id:"OnlinePortfolioSelection.cornu-Union{Tuple{M}, Tuple{T}, Tuple{AbstractMatrix{T}, M, M}} where {T<:AbstractFloat, M<:Integer}",href:"#OnlinePortfolioSelection.cornu-Union{Tuple{M}, Tuple{T}, Tuple{AbstractMatrix{T}, M, M}} where {T<:AbstractFloat, M<:Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cornu")],-1),ws=a(`
julia
cornu(
   x::AbstractMatrix{T},
   horizon::M,
   w::M;
@@ -213,7 +213,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 "CORN-U"
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

See cornk, and dricornk.

Reference

CORN: Correlation-driven nonparametric learning approach for portfolio selection

source

`,15),Ps={class:"jldocstring custom-block",open:""},Os=s("a",{id:"OnlinePortfolioSelection.cwmr",href:"#OnlinePortfolioSelection.cwmr"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cwmr")],-1),Ms=a(`
julia
cwmr(
+true

See cornk, and dricornk.

Reference

CORN: Correlation-driven nonparametric learning approach for portfolio selection

source

`,15),Ps={class:"jldocstring custom-block",open:""},Os=s("a",{id:"OnlinePortfolioSelection.cwmr",href:"#OnlinePortfolioSelection.cwmr"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cwmr")],-1),Ms=a(`
julia
cwmr(
   rel_pr::AbstractMatrix,
   ϕ::AbstractFloat,
   ϵ::AbstractFloat,
@@ -269,7 +269,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 3×5 Matrix{Float64}:
  0.318927  0.768507  0.721524  0.753618  0.135071
  0.338759  0.111292  0.16003   0.133229  0.741106
- 0.342314  0.120201  0.118446  0.113154  0.123823

See Confidence Weighted Mean Reversion (CWMR) for more informaton and examples.

References

Confidence Weighted Mean Reversion Strategy for Online Portfolio Selection

source

`,34),qs={class:"jldocstring custom-block",open:""},Rs=s("a",{id:"OnlinePortfolioSelection.cwogd-Tuple{AbstractMatrix, AbstractFloat, Any}",href:"#OnlinePortfolioSelection.cwogd-Tuple{AbstractMatrix, AbstractFloat, Any}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cwogd")],-1),Is=a(`
julia
cwogd(
+ 0.342314  0.120201  0.118446  0.113154  0.123823

See Confidence Weighted Mean Reversion (CWMR) for more informaton and examples.

References

Confidence Weighted Mean Reversion Strategy for Online Portfolio Selection

source

`,34),qs={class:"jldocstring custom-block",open:""},Rs=s("a",{id:"OnlinePortfolioSelection.cwogd-Tuple{AbstractMatrix, AbstractFloat, Any}",href:"#OnlinePortfolioSelection.cwogd-Tuple{AbstractMatrix, AbstractFloat, Any}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.cwogd")],-1),Is=a(`
julia
cwogd(
   rel_pr::AbstractMatrix,
   γ::AbstractFloat,
   H;
@@ -320,7 +320,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.333333  0.347847  0.342083  0.358819  0.355655  0.352137
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

References

[1] Combining expert weights for online portfolio selection based on the gradient descent algorithm.

source

`,16),Vs={class:"jldocstring custom-block",open:""},Ls=s("a",{id:"OnlinePortfolioSelection.dmr",href:"#OnlinePortfolioSelection.dmr"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.dmr")],-1),Hs=a(`
julia
dmr(
+true

References

[1] Combining expert weights for online portfolio selection based on the gradient descent algorithm.

source

`,16),Vs={class:"jldocstring custom-block",open:""},Ls=s("a",{id:"OnlinePortfolioSelection.dmr",href:"#OnlinePortfolioSelection.dmr"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.dmr")],-1),Hs=a(`
julia
dmr(
   x::AbstractMatrix,
   horizon::Integer,
   α::Union{Nothing, AbstractVector{<:AbstractFloat}},
@@ -374,7 +374,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.0454545  0.00218155  0.0930112       0.0934464    0.00218155   0.00218155
  0.0454545  0.0914433   0.0915956       0.000654204  0.000654204  0.000654204
  0.0454545  0.0937513   0.00289981   …  0.00289981   0.0937545    0.00289981
- 0.0454545  0.00669052  0.00669052      0.00669052   0.00669052   0.00669052

Reference

Distributed mean reversion online portfolio strategy with stock network

source

`,11),zs={class:"jldocstring custom-block",open:""},Ns=s("a",{id:"OnlinePortfolioSelection.dricornk-Union{Tuple{M}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractVector{T}, Vararg{M, 4}}} where {T<:AbstractFloat, M<:Integer}",href:"#OnlinePortfolioSelection.dricornk-Union{Tuple{M}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractVector{T}, Vararg{M, 4}}} where {T<:AbstractFloat, M<:Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.dricornk")],-1),Us=a(`
julia
dricornk(
+ 0.0454545  0.00669052  0.00669052      0.00669052   0.00669052   0.00669052

Reference

Distributed mean reversion online portfolio strategy with stock network

source

`,11),zs={class:"jldocstring custom-block",open:""},Ns=s("a",{id:"OnlinePortfolioSelection.dricornk-Union{Tuple{M}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractVector{T}, Vararg{M, 4}}} where {T<:AbstractFloat, M<:Integer}",href:"#OnlinePortfolioSelection.dricornk-Union{Tuple{M}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractVector{T}, Vararg{M, 4}}} where {T<:AbstractFloat, M<:Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.dricornk")],-1),Us=a(`
julia
dricornk(
   x::AbstractMatrix{T},
   relpr_market::AbstractVector{T},
   horizon::M,
@@ -391,7 +391,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 julia> m_dricornk = dricornk(stocks_ret, market_ret, 5, 2, 4, 3);
 
 julia> sum(m_dricornk.b, dims=1) .|> isapprox(1.) |> all
-true

See cornk, and cornu.

Reference

DRICORN-K: A Dynamic RIsk CORrelation-driven Non-parametric Algorithm for Online Portfolio Selection

source

`,15),Gs={class:"jldocstring custom-block",open:""},Zs=s("a",{id:"OnlinePortfolioSelection.eg-Tuple{AbstractMatrix}",href:"#OnlinePortfolioSelection.eg-Tuple{AbstractMatrix}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.eg")],-1),Ws=a(`
julia
eg(rel_pr::AbstractMatrix; eta::AbstractFloat=0.05)

Run Exponential Gradient (EG) algorithm.

Arguments

  • rel_pr::AbstractMatrix: Historical relative prices.

Keyword Arguments

  • eta::AbstractFloat=0.05: Learning rate.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection
+true

See cornk, and cornu.

Reference

DRICORN-K: A Dynamic RIsk CORrelation-driven Non-parametric Algorithm for Online Portfolio Selection

source

`,15),Gs={class:"jldocstring custom-block",open:""},Zs=s("a",{id:"OnlinePortfolioSelection.eg-Tuple{AbstractMatrix}",href:"#OnlinePortfolioSelection.eg-Tuple{AbstractMatrix}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.eg")],-1),Ws=a(`
julia
eg(rel_pr::AbstractMatrix; eta::AbstractFloat=0.05)

Run Exponential Gradient (EG) algorithm.

Arguments

  • rel_pr::AbstractMatrix: Historical relative prices.

Keyword Arguments

  • eta::AbstractFloat=0.05: Learning rate.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection
 
 julia> typeof(rel_pr), size(rel_pr)
 (Matrix{Float64}, (3, 10))
@@ -405,7 +405,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.333333  0.32063   0.327267  0.331649  0.325843  0.31204   0.308873  0.294239  0.300652  0.304799
 
 julia> sum(m_eg.b, dims=1) .|> isapprox(1.0) |> all
-true

References

On-Line Portfolio Selection Using Multiplicative Updates

source

`,14),Ks={class:"jldocstring custom-block",open:""},Ys=s("a",{id:"OnlinePortfolioSelection.egm",href:"#OnlinePortfolioSelection.egm"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.egm")],-1),Js=a(`
julia
egm(rel_pr::AbstractMatrix, model::EGMFramework, η::AbstractFloat=0.05)

Run the Exponential Gradient with Momentum (EGM) algorithm. This framework contains three variants: EGE, EGR and EGA.

Arguments

  • rel_pr::AbstractMatrix: matrix of size n_assets by n_periods containing the relative prices.

  • model::EGMFramework: EGM framework. EGE, EGR or EGA can be used.

  • η::AbstractFloat=0.05: learning rate.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+true

References

On-Line Portfolio Selection Using Multiplicative Updates

source

`,14),Ks={class:"jldocstring custom-block",open:""},Ys=s("a",{id:"OnlinePortfolioSelection.egm",href:"#OnlinePortfolioSelection.egm"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.egm")],-1),Js=a(`
julia
egm(rel_pr::AbstractMatrix, model::EGMFramework, η::AbstractFloat=0.05)

Run the Exponential Gradient with Momentum (EGM) algorithm. This framework contains three variants: EGE, EGR and EGA.

Arguments

  • rel_pr::AbstractMatrix: matrix of size n_assets by n_periods containing the relative prices.

  • model::EGMFramework: EGM framework. EGE, EGR or EGA can be used.

  • η::AbstractFloat=0.05: learning rate.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "GOOG"];
 
@@ -450,7 +450,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 3×7 Matrix{Float64}:
  0.333333  0.349056  0.350429  0.350706  0.348071  0.345757  0.343929
  0.333333  0.326833  0.327223  0.326516  0.327857  0.326514  0.327842
- 0.333333  0.324111  0.322348  0.322779  0.324072  0.327729  0.328229

References

Exponential Gradient with Momentum for Online Portfolio Selection

source

`,11),Xs={class:"jldocstring custom-block",open:""},$s=s("a",{id:"OnlinePortfolioSelection.gwr",href:"#OnlinePortfolioSelection.gwr"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.gwr")],-1),si=a(`
julia
gwr(
+ 0.333333  0.324111  0.322348  0.322779  0.324072  0.327729  0.328229

References

Exponential Gradient with Momentum for Online Portfolio Selection

source

`,11),Xs={class:"jldocstring custom-block",open:""},$s=s("a",{id:"OnlinePortfolioSelection.gwr",href:"#OnlinePortfolioSelection.gwr"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.gwr")],-1),si=a(`
julia
gwr(
   prices::AbstractMatrix,
   horizon::Integer,
   τ::Real=2.8,
@@ -504,12 +504,12 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 3×3 Matrix{Float64}:
  0.333333  0.0  1.20769e-11
  0.333333  0.0  0.0
- 0.333333  1.0  1.0

Reference

Gaussian Weighting Reversion Strategy for Accurate On-line Portfolio Selection

source

`,22),ii={class:"jldocstring custom-block",open:""},ai=s("a",{id:"OnlinePortfolioSelection.ir-Union{Tuple{S}, Tuple{AbstractMatrix{S}, AbstractMatrix{S}, AbstractVector{S}}} where S<:AbstractFloat",href:"#OnlinePortfolioSelection.ir-Union{Tuple{S}, Tuple{AbstractMatrix{S}, AbstractMatrix{S}, AbstractVector{S}}} where S<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ir")],-1),ti=a(`
julia
ir(
+ 0.333333  1.0  1.0

Reference

Gaussian Weighting Reversion Strategy for Accurate On-line Portfolio Selection

source

`,22),ii={class:"jldocstring custom-block",open:""},ai=s("a",{id:"OnlinePortfolioSelection.ir-Union{Tuple{S}, Tuple{AbstractMatrix{S}, AbstractMatrix{S}, AbstractVector{S}}} where S<:AbstractFloat",href:"#OnlinePortfolioSelection.ir-Union{Tuple{S}, Tuple{AbstractMatrix{S}, AbstractMatrix{S}, AbstractVector{S}}} where S<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ir")],-1),ti=a(`
julia
ir(
   weights::AbstractMatrix{S},
   rel_pr::AbstractMatrix{S},
   rel_pr_market::AbstractVector{S};
   init_inv::S=1.
-) where S<:AbstractFloat

Calculate the Information Ratio (IR) of portfolio. Also, see sn, mer, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

The formula for calculating the Information Ratio (IR) of portfolio is as follows:

`,3),ni={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},li={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.03ex",height:"5.814ex",role:"img",focusable:"false",viewBox:"0 -1610 8411.1 2570","aria-hidden":"true"},hi=a('',1),ei=[hi],ki=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"I"),s("mi",null,"R"),s("mo",null,"="),s("mfrac",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("mover",null,[s("mi",null,"R"),s("mo",{stretchy:"false"},"¯")])])]),s("mi",null,"s")])]),s("mo",null,"−"),s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("mover",null,[s("mi",null,"R"),s("mo",{stretchy:"false"},"¯")])])]),s("mi",null,"m")])])]),s("mrow",{"data-mjx-texclass":"ORD"},[s("mi",null,"σ"),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"R"),s("mi",null,"s")])]),s("mo",null,"−"),s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"R"),s("mi",null,"m")])])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])])])],-1),pi={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ri={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.355ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.655ex",height:"1.901ex",role:"img",focusable:"false",viewBox:"0 -683 1173.6 840.1","aria-hidden":"true"},di=a('',1),oi=[di],gi=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"R"),s("mi",null,"s")])])],-1),Ei={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ci={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.31ex",height:"1.902ex",role:"img",focusable:"false",viewBox:"0 -683 1462.8 840.8","aria-hidden":"true"},Fi=a('',1),yi=[Fi],Ci=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"R"),s("mi",null,"m")])])],-1),ui={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Ti={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.355ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.655ex",height:"2.468ex",role:"img",focusable:"false",viewBox:"0 -934 1173.6 1091.1","aria-hidden":"true"},Ai=a('',1),mi=[Ai],Bi=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mover",null,[s("mi",null,"R"),s("mo",{stretchy:"false"},"¯")])]),s("mi",null,"s")])])],-1),bi={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},_i={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.31ex",height:"2.47ex",role:"img",focusable:"false",viewBox:"0 -934 1462.8 1091.8","aria-hidden":"true"},fi=a('',1),Qi=[fi],Di=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mover",null,[s("mi",null,"R"),s("mo",{stretchy:"false"},"¯")])]),s("mi",null,"m")])])],-1),vi={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ji={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.292ex",height:"1ex",role:"img",focusable:"false",viewBox:"0 -431 571 442","aria-hidden":"true"},xi=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D70E",d:"M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z",style:{"stroke-width":"3"}})])])],-1),Si=[xi],wi=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"σ")])],-1),Pi=a('

Arguments

  • weights::AbstractMatrix{S}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{S}: the relative price of the stocks.

  • rel_pr_market::AbstractVector{S}: the relative price of the market.

Keyword Arguments

  • init_inv::S=1: the initial investment.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used. The size of rel_pr_market will automatically be adjusted to the size of w.

Returns

  • ::AbstractFloat: the Information Ratio (IR) of portfolio for the investment period.

References

Adaptive online portfolio strategy based on exponential gradient updates

source

',11),Oi={class:"jldocstring custom-block",open:""},Mi=s("a",{id:"OnlinePortfolioSelection.ktpt",href:"#OnlinePortfolioSelection.ktpt"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ktpt")],-1),qi=a(`
julia
function ktpt(
+) where S<:AbstractFloat

Calculate the Information Ratio (IR) of portfolio. Also, see sn, mer, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

The formula for calculating the Information Ratio (IR) of portfolio is as follows:

`,3),ni={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},li={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.03ex",height:"5.814ex",role:"img",focusable:"false",viewBox:"0 -1610 8411.1 2570","aria-hidden":"true"},hi=a('',1),ei=[hi],ki=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"I"),s("mi",null,"R"),s("mo",null,"="),s("mfrac",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("mover",null,[s("mi",null,"R"),s("mo",{stretchy:"false"},"¯")])])]),s("mi",null,"s")])]),s("mo",null,"−"),s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("mover",null,[s("mi",null,"R"),s("mo",{stretchy:"false"},"¯")])])]),s("mi",null,"m")])])]),s("mrow",{"data-mjx-texclass":"ORD"},[s("mi",null,"σ"),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"R"),s("mi",null,"s")])]),s("mo",null,"−"),s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"R"),s("mi",null,"m")])])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])])])],-1),pi={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ri={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.355ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.655ex",height:"1.901ex",role:"img",focusable:"false",viewBox:"0 -683 1173.6 840.1","aria-hidden":"true"},di=a('',1),oi=[di],gi=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"R"),s("mi",null,"s")])])],-1),Ei={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ci={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.31ex",height:"1.902ex",role:"img",focusable:"false",viewBox:"0 -683 1462.8 840.8","aria-hidden":"true"},Fi=a('',1),yi=[Fi],Ci=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"R"),s("mi",null,"m")])])],-1),ui={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Ti={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.355ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.655ex",height:"2.468ex",role:"img",focusable:"false",viewBox:"0 -934 1173.6 1091.1","aria-hidden":"true"},Ai=a('',1),mi=[Ai],Bi=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mover",null,[s("mi",null,"R"),s("mo",{stretchy:"false"},"¯")])]),s("mi",null,"s")])])],-1),bi={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},_i={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.31ex",height:"2.47ex",role:"img",focusable:"false",viewBox:"0 -934 1462.8 1091.8","aria-hidden":"true"},fi=a('',1),Qi=[fi],Di=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mrow",{"data-mjx-texclass":"ORD"},[s("mover",null,[s("mi",null,"R"),s("mo",{stretchy:"false"},"¯")])]),s("mi",null,"m")])])],-1),vi={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ji={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.292ex",height:"1ex",role:"img",focusable:"false",viewBox:"0 -431 571 442","aria-hidden":"true"},xi=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D70E",d:"M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z",style:{"stroke-width":"3"}})])])],-1),Si=[xi],wi=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"σ")])],-1),Pi=a('

Arguments

  • weights::AbstractMatrix{S}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{S}: the relative price of the stocks.

  • rel_pr_market::AbstractVector{S}: the relative price of the market.

Keyword Arguments

  • init_inv::S=1: the initial investment.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used. The size of rel_pr_market will automatically be adjusted to the size of w.

Returns

  • ::AbstractFloat: the Information Ratio (IR) of portfolio for the investment period.

References

Adaptive online portfolio strategy based on exponential gradient updates

source

',11),Oi={class:"jldocstring custom-block",open:""},Mi=s("a",{id:"OnlinePortfolioSelection.ktpt",href:"#OnlinePortfolioSelection.ktpt"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ktpt")],-1),qi=a(`
julia
function ktpt(
   prices::AbstractMatrix,
   horizon::S,
   w::S,
@@ -536,7 +536,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.25  0.0  1.0  1.0  1.0
  0.25  0.0  0.0  0.0  0.0
  0.25  1.0  0.0  0.0  0.0
- 0.25  0.0  0.0  0.0  0.0

Reference

A kernel-based trend pattern tracking system for portfolio optimization

source

`,13),Ri={class:"jldocstring custom-block",open:""},Ii=s("a",{id:"OnlinePortfolioSelection.load-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, T, S, S, T}} where {T<:Float64, S<:Int64}",href:"#OnlinePortfolioSelection.load-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, T, S, S, T}} where {T<:Float64, S<:Int64}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.load")],-1),Vi=a(`
julia
load(adj_close::AbstractMatrix{T}, α::T, ω::S, horizon::S, η::T, ϵ::T=1.5) where {T<:Float64, S<:Int}

Run LOAD algorithm.

Arguments

  • adj_close::AbstractMatrix{T}: Adjusted close price data.

  • α::T: Decay factor. (0 < α < 1)

  • ω::S: Window size. (ω > 0)

  • horizon::S: Investment horizon. (n_periods > horizon > 0)

  • η::T: Threshold value. (η > 0)

  • ϵ::T=1.5: Expected return threshold value.

Beware!

adj_close should be a matrix of size n_assets × n_periods.

Returns

  • ::OPSAlgorithm: An object of type OPSAlgorithm containing the weights of each asset for each period.

Example

julia
# Get data
+ 0.25  0.0  0.0  0.0  0.0

Reference

A kernel-based trend pattern tracking system for portfolio optimization

source

`,13),Ri={class:"jldocstring custom-block",open:""},Ii=s("a",{id:"OnlinePortfolioSelection.load-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, T, S, S, T}} where {T<:Float64, S<:Int64}",href:"#OnlinePortfolioSelection.load-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, T, S, S, T}} where {T<:Float64, S<:Int64}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.load")],-1),Vi=a(`
julia
load(adj_close::AbstractMatrix{T}, α::T, ω::S, horizon::S, η::T, ϵ::T=1.5) where {T<:Float64, S<:Int}

Run LOAD algorithm.

Arguments

  • adj_close::AbstractMatrix{T}: Adjusted close price data.

  • α::T: Decay factor. (0 < α < 1)

  • ω::S: Window size. (ω > 0)

  • horizon::S: Investment horizon. (n_periods > horizon > 0)

  • η::T: Threshold value. (η > 0)

  • ϵ::T=1.5: Expected return threshold value.

Beware!

adj_close should be a matrix of size n_assets × n_periods.

Returns

  • ::OPSAlgorithm: An object of type OPSAlgorithm containing the weights of each asset for each period.

Example

julia
# Get data
 julia> using YFinance
 julia> startdt, enddt = "2022-04-01", "2023-04-27";
 julia> querry = [
@@ -558,7 +558,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.2  6.06128e-9  0.0        0.0       0.0
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

References

A local adaptive learning system for online portfolio selection

source

`,12),Li={class:"jldocstring custom-block",open:""},Hi=s("a",{id:"OnlinePortfolioSelection.maeg-Tuple{AbstractMatrix, Integer, AbstractVector}",href:"#OnlinePortfolioSelection.maeg-Tuple{AbstractMatrix, Integer, AbstractVector}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.maeg")],-1),zi=a(`
julia
maeg(x::AbstractMatrix, w::Integer, H::AbstractVector)

Run Moving-window-based Adaptive Exponential Gradient (MAEG) algorithm.

Arguments

  • x::AbstractMatrix: A matrix of price relatives of n_assets over n_periods.

  • w::Integer: The window size.

  • H::AbstractVector: A vector of learning rates.

Returns

Beware!

x should be a matrix of size n_assets × n_periods.

Example

julia
julia> using OnlinePortfolioSelection
+true

References

A local adaptive learning system for online portfolio selection

source

`,12),Li={class:"jldocstring custom-block",open:""},Hi=s("a",{id:"OnlinePortfolioSelection.maeg-Tuple{AbstractMatrix, Integer, AbstractVector}",href:"#OnlinePortfolioSelection.maeg-Tuple{AbstractMatrix, Integer, AbstractVector}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.maeg")],-1),zi=a(`
julia
maeg(x::AbstractMatrix, w::Integer, H::AbstractVector)

Run Moving-window-based Adaptive Exponential Gradient (MAEG) algorithm.

Arguments

  • x::AbstractMatrix: A matrix of price relatives of n_assets over n_periods.

  • w::Integer: The window size.

  • H::AbstractVector: A vector of learning rates.

Returns

Beware!

x should be a matrix of size n_assets × n_periods.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> rel_pr = rand(4, 10);
 
@@ -573,11 +573,11 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.25  0.250307  0.25129   0.251673  0.250823  0.267687  0.313794  0.319425  0.378182  0.427249
  0.25  0.249138  0.248921  0.249289  0.250482  0.23192   0.202576  0.179329  0.160005  0.168903
  0.25  0.250026  0.250656  0.24931   0.24995   0.226647  0.237694  0.237879  0.216076  0.192437
- 0.25  0.250528  0.249134  0.249728  0.248744  0.273746  0.245936  0.263367  0.245737  0.211411

References

Adaptive online portfolio strategy based on exponential gradient updates

source

`,12),Ni={class:"jldocstring custom-block",open:""},Ui=s("a",{id:"OnlinePortfolioSelection.mdd-Union{Tuple{AbstractVector{T}}, Tuple{T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.mdd-Union{Tuple{AbstractVector{T}}, Tuple{T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.mdd")],-1),Gi=a('
julia
mdd(Sn::AbstractVector{T}) where T<:AbstractFloat

Calculate the Maximum Drawdown (MDD) of investment. Also, see sn, mer, ann_std, apy, ann_sharpe, calmar, and opsmetrics.

Arguments

  • Sn::AbstractVector{T}: the cumulative wealth of investment during the investment period. see sn.

Returns

  • ::AbstractFloat: the MDD of investment.

source

',7),Zi={class:"jldocstring custom-block",open:""},Wi=s("a",{id:"OnlinePortfolioSelection.mer-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.mer-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.mer")],-1),Ki=a(`
julia
mer(
+ 0.25  0.250528  0.249134  0.249728  0.248744  0.273746  0.245936  0.263367  0.245737  0.211411

References

Adaptive online portfolio strategy based on exponential gradient updates

source

`,12),Ni={class:"jldocstring custom-block",open:""},Ui=s("a",{id:"OnlinePortfolioSelection.mdd-Union{Tuple{AbstractVector{T}}, Tuple{T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.mdd-Union{Tuple{AbstractVector{T}}, Tuple{T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.mdd")],-1),Gi=a('
julia
mdd(Sn::AbstractVector{T}) where T<:AbstractFloat

Calculate the Maximum Drawdown (MDD) of investment. Also, see sn, mer, ann_std, apy, ann_sharpe, calmar, and opsmetrics.

Arguments

  • Sn::AbstractVector{T}: the cumulative wealth of investment during the investment period. see sn.

Returns

  • ::AbstractFloat: the MDD of investment.

source

',7),Zi={class:"jldocstring custom-block",open:""},Wi=s("a",{id:"OnlinePortfolioSelection.mer-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.mer-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.mer")],-1),Ki=a(`
julia
mer(
   weights::AbstractMatrix{T},
   rel_pr::AbstractMatrix{T},
   𝘷::T=0.
-) where T<:AbstractFloat

Calculate the investments's Mean excess return (MER). Also, see sn, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

  • 𝘷::T=0.: the transaction cost rate.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

  • MER::AbstractFloat: the investments's Mean excess return (MER).

source

`,9),Yi={class:"jldocstring custom-block",open:""},Ji=s("a",{id:"OnlinePortfolioSelection.mrvol-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, S, S, S, T, T}} where {T<:AbstractFloat, S<:Integer}",href:"#OnlinePortfolioSelection.mrvol-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, S, S, S, T, T}} where {T<:AbstractFloat, S<:Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.mrvol")],-1),Xi=a(`
julia
mrvol(
+) where T<:AbstractFloat

Calculate the investments's Mean excess return (MER). Also, see sn, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

  • 𝘷::T=0.: the transaction cost rate.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

  • MER::AbstractFloat: the investments's Mean excess return (MER).

source

`,9),Yi={class:"jldocstring custom-block",open:""},Ji=s("a",{id:"OnlinePortfolioSelection.mrvol-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, S, S, S, T, T}} where {T<:AbstractFloat, S<:Integer}",href:"#OnlinePortfolioSelection.mrvol-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, S, S, S, T, T}} where {T<:AbstractFloat, S<:Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.mrvol")],-1),Xi=a(`
julia
mrvol(
   rel_pr::AbstractMatrix{T},
   rel_vol::AbstractMatrix{T},
   horizon::S,
@@ -618,7 +618,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 3×100 Matrix{Float64}:
  0.333333  0.0204062  0.0444759  …  0.38213   0.467793
  0.333333  0.359864   0.194139      0.213264  0.281519
- 0.333333  0.61973    0.761385      0.404606  0.250689

References

Online portfolio selection of integrating expert strategies based on mean reversion and trading volume.

source

`,12),$i={class:"jldocstring custom-block",open:""},sa=s("a",{id:"OnlinePortfolioSelection.oldem-Union{Tuple{T}, Tuple{S}, Tuple{AbstractMatrix, S, S, S, S, T, T, T}} where {S<:Integer, T<:AbstractFloat}",href:"#OnlinePortfolioSelection.oldem-Union{Tuple{T}, Tuple{S}, Tuple{AbstractMatrix, S, S, S, S, T, T, T}} where {S<:Integer, T<:AbstractFloat}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.oldem")],-1),ia=a(`
julia
oldem(
+ 0.333333  0.61973    0.761385      0.404606  0.250689

References

Online portfolio selection of integrating expert strategies based on mean reversion and trading volume.

source

`,12),$i={class:"jldocstring custom-block",open:""},sa=s("a",{id:"OnlinePortfolioSelection.oldem-Union{Tuple{T}, Tuple{S}, Tuple{AbstractMatrix, S, S, S, S, T, T, T}} where {S<:Integer, T<:AbstractFloat}",href:"#OnlinePortfolioSelection.oldem-Union{Tuple{T}, Tuple{S}, Tuple{AbstractMatrix, S, S, S, S, T, T, T}} where {S<:Integer, T<:AbstractFloat}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.oldem")],-1),ia=a(`
julia
oldem(
   rel_pr::AbstractMatrix,
   horizon::S,
   w::S,
@@ -661,7 +661,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.2  1.0         0.0         0.0
  0.2  0.0         0.0         1.99964e-8
  0.2  0.0         0.0         1.0
- 0.2  0.0         1.99964e-8  0.0

References

Online portfolio selection with predictive instantaneous risk assessment

source

`,8),da={class:"jldocstring custom-block",open:""},oa=s("a",{id:"OnlinePortfolioSelection.olmar-Tuple{AbstractMatrix, Int64, Int64, Int64}",href:"#OnlinePortfolioSelection.olmar-Tuple{AbstractMatrix, Int64, Int64, Int64}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.olmar")],-1),ga=a(`
julia
olmar(rel_pr::AbstractMatrix, horizon::Int, ω::Int, ϵ::Int)
+ 0.2  0.0         1.99964e-8  0.0

References

Online portfolio selection with predictive instantaneous risk assessment

source

`,8),da={class:"jldocstring custom-block",open:""},oa=s("a",{id:"OnlinePortfolioSelection.olmar-Tuple{AbstractMatrix, Int64, Int64, Int64}",href:"#OnlinePortfolioSelection.olmar-Tuple{AbstractMatrix, Int64, Int64, Int64}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.olmar")],-1),ga=a(`
julia
olmar(rel_pr::AbstractMatrix, horizon::Int, ω::Int, ϵ::Int)
 olmar(rel_pr::AbstractMatrix, horizon::Int, ω::AbstractVector{<:Int}, ϵ::Int)

Method 1

Run the Online Moving Average Reversion algorithm (OLMAR).

Arguments

  • rel_pr::AbstractMatrix: Matrix of relative prices.

  • horizon::Int: Investment horizon.

  • ω::Int: Window size.

  • ϵ::Int: Reversion threshold.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "AMZN", "GOOG", "META"];
@@ -713,7 +713,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.2  0.2  1.31177e-8  0.555158  0.0
  0.2  0.2  6.57906e-9  0.0       0.667358
  0.2  0.2  0.0         0.0       0.332642
- 0.2  0.2  0.666667    0.282545  0.0

References

On-Line Portfolio Selection with Moving Average Reversion

source

`,22),Ea={class:"jldocstring custom-block",open:""},ca=s("a",{id:"OnlinePortfolioSelection.ons",href:"#OnlinePortfolioSelection.ons"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ons")],-1),Fa=a(`
julia
ons(rel_pr::AbstractMatrix, β::Integer=1, 𝛿::AbstractFloat=1/8, η::AbstractFloat=0.)

Run Online Newton Step (ONS) algorithm.

Arguments

  • rel_pr::AbstractMatrix: relative prices.

  • β::Integer=1: Hyperparameter.

  • 𝛿::AbstractFloat=1/8: Heuristic tuning parameter.

  • η::AbstractFloat=0.: Learning rate.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+ 0.2  0.2  0.666667    0.282545  0.0

References

On-Line Portfolio Selection with Moving Average Reversion

source

`,22),Ea={class:"jldocstring custom-block",open:""},ca=s("a",{id:"OnlinePortfolioSelection.ons",href:"#OnlinePortfolioSelection.ons"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ons")],-1),Fa=a(`
julia
ons(rel_pr::AbstractMatrix, β::Integer=1, 𝛿::AbstractFloat=1/8, η::AbstractFloat=0.)

Run Online Newton Step (ONS) algorithm.

Arguments

  • rel_pr::AbstractMatrix: relative prices.

  • β::Integer=1: Hyperparameter.

  • 𝛿::AbstractFloat=1/8: Heuristic tuning parameter.

  • η::AbstractFloat=0.: Learning rate.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "GOOG"];
 
@@ -729,7 +729,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 3×6 Matrix{Float64}:
  0.333333  0.333327  0.333293  0.333295  0.333319  0.333375
  0.333333  0.333302  0.333221  0.333182  0.333205  0.333184
- 0.333333  0.333371  0.333486  0.333524  0.333475  0.333441

References

Algorithms for Portfolio Management based on the Newton Method

source

`,11),ya={class:"jldocstring custom-block",open:""},Ca=s("a",{id:"OnlinePortfolioSelection.opsmethods-Tuple{}",href:"#OnlinePortfolioSelection.opsmethods-Tuple{}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.opsmethods")],-1),ua=a(`
julia
opsmethods()

Print the available algorithms in the package.

Example

julia
julia> using OnlinePortfolioSelection
+ 0.333333  0.333371  0.333486  0.333524  0.333475  0.333441

References

Algorithms for Portfolio Management based on the Newton Method

source

`,11),ya={class:"jldocstring custom-block",open:""},Ca=s("a",{id:"OnlinePortfolioSelection.opsmethods-Tuple{}",href:"#OnlinePortfolioSelection.opsmethods-Tuple{}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.opsmethods")],-1),ua=a(`
julia
opsmethods()

Print the available algorithms in the package.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> opsmethods()
 
@@ -740,7 +740,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
         up: Universal Portfolio - Call \`up\`
         eg: Exponential Gradient - Call \`eg\`
      cornu: CORN-U - Call \`cornu\`
-          ⋮

source

`,5),Ta={class:"jldocstring custom-block",open:""},Aa=s("a",{id:"OnlinePortfolioSelection.opsmetrics-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, AbstractVector{T}}} where {T<:AbstractFloat, S<:Int64}",href:"#OnlinePortfolioSelection.opsmetrics-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, AbstractVector{T}}} where {T<:AbstractFloat, S<:Int64}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.opsmetrics")],-1),ma=a(`
julia
opsmetrics(
+          ⋮

source

`,5),Ta={class:"jldocstring custom-block",open:""},Aa=s("a",{id:"OnlinePortfolioSelection.opsmetrics-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, AbstractVector{T}}} where {T<:AbstractFloat, S<:Int64}",href:"#OnlinePortfolioSelection.opsmetrics-Union{Tuple{S}, Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}, AbstractVector{T}}} where {T<:AbstractFloat, S<:Int64}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.opsmetrics")],-1),ma=a(`
julia
opsmetrics(
   weights::AbstractMatrix{T},
   rel_pr::AbstractMatrix{T},
   rel_pr_market::AbstractVector{T};
@@ -749,7 +749,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
   dpy::S=252,
   v::T=0.
   dpy::S=252
-) where {T<:AbstractFloat, S<:Int}

Calculate the metrics of an OPS algorithm. Also, see sn, mer, ir, ann_std, apy, ann_sharpe, mdd, and calmar.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

  • rel_pr_market::AbstractVector{T}: the relative price of the market.

Keyword Arguments

  • init_inv::T=1: the initial investment.

  • Rf::T=0.02: the risk-free rate of return.

  • dpy::S=252: the number of days in a year.

  • v::T=0.: the transaction cost rate.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

source

`,11),Ba={class:"jldocstring custom-block",open:""},ba=s("a",{id:"OnlinePortfolioSelection.pamr-Tuple{AbstractMatrix, AbstractFloat, OnlinePortfolioSelection.PAMRModel}",href:"#OnlinePortfolioSelection.pamr-Tuple{AbstractMatrix, AbstractFloat, OnlinePortfolioSelection.PAMRModel}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.pamr")],-1),_a=a(`
julia
pamr(rel_pr::AbstractMatrix, ϵ::AbstractFloat, C::AbstractFloat, model::PAMRModel)

Run the PAMR algorithm on the matrix of relative prices rel_pr.

Arguments

  • rel_pr::AbstractMatrix: matrix of relative prices.

  • ϵ::AbstractFloat: Sensitivity parameter.

  • C::AbstractFloat: Aggressiveness parameter.

  • model::PAMRModel: PAMR model to use. All three variants, namely, PAMR(), PAMR1(), and PAMR2() are supported.

Beware!

rel_price should be a matrix of size n_assets × n_periods.

Output

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+) where {T<:AbstractFloat, S<:Int}

Calculate the metrics of an OPS algorithm. Also, see sn, mer, ir, ann_std, apy, ann_sharpe, mdd, and calmar.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

  • rel_pr_market::AbstractVector{T}: the relative price of the market.

Keyword Arguments

  • init_inv::T=1: the initial investment.

  • Rf::T=0.02: the risk-free rate of return.

  • dpy::S=252: the number of days in a year.

  • v::T=0.: the transaction cost rate.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

source

`,11),Ba={class:"jldocstring custom-block",open:""},ba=s("a",{id:"OnlinePortfolioSelection.pamr-Tuple{AbstractMatrix, AbstractFloat, OnlinePortfolioSelection.PAMRModel}",href:"#OnlinePortfolioSelection.pamr-Tuple{AbstractMatrix, AbstractFloat, OnlinePortfolioSelection.PAMRModel}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.pamr")],-1),_a=a(`
julia
pamr(rel_pr::AbstractMatrix, ϵ::AbstractFloat, C::AbstractFloat, model::PAMRModel)

Run the PAMR algorithm on the matrix of relative prices rel_pr.

Arguments

  • rel_pr::AbstractMatrix: matrix of relative prices.

  • ϵ::AbstractFloat: Sensitivity parameter.

  • C::AbstractFloat: Aggressiveness parameter.

  • model::PAMRModel: PAMR model to use. All three variants, namely, PAMR(), PAMR1(), and PAMR2() are supported.

Beware!

rel_price should be a matrix of size n_assets × n_periods.

Output

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "AMZN", "META", "GOOG"]
 
@@ -802,7 +802,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.2  0.197589  0.198123  0.199895     0.175224  0.179199  0.178376  0.178291
  0.2  0.193636  0.192928  0.183242     0.279176  0.27052   0.270138  0.271307
  0.2  0.194936  0.19525   0.197214     0.183626  0.185922  0.185215  0.188272
- 0.2  0.194746  0.192736  0.195701     0.242882  0.245346  0.247319  0.248279

References

PAMR: Passive aggressive mean reversion strategy for portfolio selection

source

`,14),fa={class:"jldocstring custom-block",open:""},Qa=s("a",{id:"OnlinePortfolioSelection.ppt",href:"#OnlinePortfolioSelection.ppt"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ppt")],-1),Da=a(`
julia
ppt(
+ 0.2  0.194746  0.192736  0.195701     0.242882  0.245346  0.247319  0.248279

References

PAMR: Passive aggressive mean reversion strategy for portfolio selection

source

`,14),fa={class:"jldocstring custom-block",open:""},Qa=s("a",{id:"OnlinePortfolioSelection.ppt",href:"#OnlinePortfolioSelection.ppt"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ppt")],-1),Da=a(`
julia
ppt(
   prices::AbstractMatrix,
   w::Int,
   ϵ::Int,
@@ -819,7 +819,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 julia> model = ppt(prices, 10, 100, 100);
 
 julia> sum(model, dims=1) .|> isapprox(1.) |> all
-true

References

A Peak Price Tracking-Based Learning System for Portfolio Selection

source

`,12),va={class:"jldocstring custom-block",open:""},ja=s("a",{id:"OnlinePortfolioSelection.rmr-Tuple{AbstractMatrix, Integer, Integer, Any, Any, Any}",href:"#OnlinePortfolioSelection.rmr-Tuple{AbstractMatrix, Integer, Integer, Any, Any, Any}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.rmr")],-1),xa=a(`
julia
rmr(p::AbstractMatrix, horizon::Integer, w::Integer, ϵ, m, τ)

Run Robust Median Reversion (RMR) algorithm.

Arguments

  • p::AbstractMatrix: Prices matrix.

  • horizon::Integer: Number of periods to run the algorithm.

  • w::Integer: Window size.

  • ϵ: Reversion threshold.

  • m: Maxmimum number of iterations.

  • τ: Toleration level.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+true

References

A Peak Price Tracking-Based Learning System for Portfolio Selection

source

`,12),va={class:"jldocstring custom-block",open:""},ja=s("a",{id:"OnlinePortfolioSelection.rmr-Tuple{AbstractMatrix, Integer, Integer, Any, Any, Any}",href:"#OnlinePortfolioSelection.rmr-Tuple{AbstractMatrix, Integer, Integer, Any, Any, Any}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.rmr")],-1),xa=a(`
julia
rmr(p::AbstractMatrix, horizon::Integer, w::Integer, ϵ, m, τ)

Run Robust Median Reversion (RMR) algorithm.

Arguments

  • p::AbstractMatrix: Prices matrix.

  • horizon::Integer: Number of periods to run the algorithm.

  • w::Integer: Window size.

  • ϵ: Reversion threshold.

  • m: Maxmimum number of iterations.

  • τ: Toleration level.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["GOOG", "AAPL", "MSFT", "AMZN"];
 
@@ -844,7 +844,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.25  1.0         1.0       1.0         1.0
  0.25  0.0         0.0       0.0         0.0
  0.25  0.0         0.0       0.0         0.0
- 0.25  1.14513e-8  9.979e-9  9.99353e-9  1.03254e-8

Reference

Robust Median Reversion Strategy for Online Portfolio Selection

source

`,11),Sa={class:"jldocstring custom-block",open:""},wa=s("a",{id:"OnlinePortfolioSelection.rprt-Union{Tuple{T}, Tuple{AbstractMatrix{T}, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer, T}, Tuple{AbstractMatrix{T}, Integer, Integer, T, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer, T, Integer, Union{Nothing, AbstractVector}}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.rprt-Union{Tuple{T}, Tuple{AbstractMatrix{T}, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer, T}, Tuple{AbstractMatrix{T}, Integer, Integer, T, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer, T, Integer, Union{Nothing, AbstractVector}}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.rprt")],-1),Pa=a(`
julia
function rprt(
+ 0.25  1.14513e-8  9.979e-9  9.99353e-9  1.03254e-8

Reference

Robust Median Reversion Strategy for Online Portfolio Selection

source

`,11),Sa={class:"jldocstring custom-block",open:""},wa=s("a",{id:"OnlinePortfolioSelection.rprt-Union{Tuple{T}, Tuple{AbstractMatrix{T}, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer, T}, Tuple{AbstractMatrix{T}, Integer, Integer, T, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer, T, Integer, Union{Nothing, AbstractVector}}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.rprt-Union{Tuple{T}, Tuple{AbstractMatrix{T}, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer, T}, Tuple{AbstractMatrix{T}, Integer, Integer, T, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer, T, Integer, Union{Nothing, AbstractVector}}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.rprt")],-1),Pa=a(`
julia
function rprt(
   rel_pr::AbstractMatrix{T},
   horizon::Integer,
   w::Integer=5,
@@ -869,7 +869,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.2  2.03615e-10
 
 julia> sum(m_rprt.b, dims=1) .|> isapprox(1.) |> all
-true

Reference

Reweighted Price Relative Tracking System for Automatic Portfolio Optimization

source

`,12),Oa={class:"jldocstring custom-block",open:""},Ma=s("a",{id:"OnlinePortfolioSelection.sn-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.sn-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.sn")],-1),qa=a('
julia
sn(weights::AbstractMatrix{T}, rel_pr::AbstractMatrix{T}; init_inv::T=1.) where T<:AbstractFloat

Calculate the cumulative wealth of the portfolio during a period of time. Also, see mer, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

The formula for calculating the cumulative wealth of the portfolio is as follows:

',3),Ra={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Ia={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.819ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.133ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1728.7 8014.9 2974.6","aria-hidden":"true"},Va=a('',1),La=[Va],Ha=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"S"),s("mi",null,"n")])]),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"S"),s("mn",null,"0")])]),s("munderover",null,[s("mo",{"data-mjx-texclass":"OP",movablelimits:"false"},"∏"),s("mrow",{"data-mjx-texclass":"ORD"},[s("mi",null,"t"),s("mo",null,"="),s("mn",null,"1")]),s("mi",null,"T")]),s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"⟨"),s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"b"),s("mi",null,"t")])]),s("mo",null,","),s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"x"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"⟩")])])])],-1),za={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Na={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.375ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.375ex",height:"1.97ex",role:"img",focusable:"false",viewBox:"0 -705 1049.6 870.6","aria-hidden":"true"},Ua=a('',1),Ga=[Ua],Za=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"S"),s("mn",null,"0")])])],-1),Wa={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Ka={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Ya=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),Ja=[Ya],Xa=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),$a={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},st={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.736ex",height:"1.927ex",role:"img",focusable:"false",viewBox:"0 -694 767.3 851.8","aria-hidden":"true"},it=a('',1),at=[it],tt=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"b"),s("mi",null,"t")])])],-1),nt={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},lt={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.817ex",height:"1.441ex",role:"img",focusable:"false",viewBox:"0 -626 361 637","aria-hidden":"true"},ht=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D461",d:"M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z",style:{"stroke-width":"3"}})])])],-1),et=[ht],kt=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"t")])],-1),pt={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},rt={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.059ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 910.3 599.8","aria-hidden":"true"},dt=a('',1),ot=[dt],gt=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"x"),s("mi",null,"t")])])],-1),Et={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ct={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.817ex",height:"1.441ex",role:"img",focusable:"false",viewBox:"0 -626 361 637","aria-hidden":"true"},Ft=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D461",d:"M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z",style:{"stroke-width":"3"}})])])],-1),yt=[Ft],Ct=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"t")])],-1),ut=a('

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

Keyword Arguments

  • init_inv::T=1: the initial investment.

Beware!

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

  • all_sn::Vector{T}: the cumulative wealth of investment during the investment period.

source

',9),Tt={class:"jldocstring custom-block",open:""},At=s("a",{id:"OnlinePortfolioSelection.spolc-Tuple{AbstractMatrix, AbstractFloat, Integer}",href:"#OnlinePortfolioSelection.spolc-Tuple{AbstractMatrix, AbstractFloat, Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.spolc")],-1),mt=a(`
julia
spolc(x::AbstractMatrix, 𝛾::AbstractFloat, w::Integer)

Run loss control strategy with a rank-one covariance estimate for short-term portfolio optimization (SPOLC).

Arguments

  • x::AbstractMatrix: Matrix of relative prices.

  • 𝛾::AbstractFloat: Mixing parameter that trades off between the increasing factor and the risk.

  • w::Integer: Window size.

Beware!

x should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+true

Reference

Reweighted Price Relative Tracking System for Automatic Portfolio Optimization

source

`,12),Oa={class:"jldocstring custom-block",open:""},Ma=s("a",{id:"OnlinePortfolioSelection.sn-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.sn-Union{Tuple{T}, Tuple{AbstractMatrix{T}, AbstractMatrix{T}}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.sn")],-1),qa=a('
julia
sn(weights::AbstractMatrix{T}, rel_pr::AbstractMatrix{T}; init_inv::T=1.) where T<:AbstractFloat

Calculate the cumulative wealth of the portfolio during a period of time. Also, see mer, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

The formula for calculating the cumulative wealth of the portfolio is as follows:

',3),Ra={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Ia={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.819ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.133ex",height:"6.73ex",role:"img",focusable:"false",viewBox:"0 -1728.7 8014.9 2974.6","aria-hidden":"true"},Va=a('',1),La=[Va],Ha=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"S"),s("mi",null,"n")])]),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"S"),s("mn",null,"0")])]),s("munderover",null,[s("mo",{"data-mjx-texclass":"OP",movablelimits:"false"},"∏"),s("mrow",{"data-mjx-texclass":"ORD"},[s("mi",null,"t"),s("mo",null,"="),s("mn",null,"1")]),s("mi",null,"T")]),s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"⟨"),s("mrow",{"data-mjx-texclass":"ORD"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"b"),s("mi",null,"t")])]),s("mo",null,","),s("mrow",{"data-mjx-texclass":"ORD"},[s("msub",null,[s("mi",null,"x"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"⟩")])])])],-1),za={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Na={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.375ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.375ex",height:"1.97ex",role:"img",focusable:"false",viewBox:"0 -705 1049.6 870.6","aria-hidden":"true"},Ua=a('',1),Ga=[Ua],Za=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"S"),s("mn",null,"0")])])],-1),Wa={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Ka={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Ya=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),Ja=[Ya],Xa=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),$a={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},st={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.736ex",height:"1.927ex",role:"img",focusable:"false",viewBox:"0 -694 767.3 851.8","aria-hidden":"true"},it=a('',1),at=[it],tt=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"b"),s("mi",null,"t")])])],-1),nt={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},lt={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.817ex",height:"1.441ex",role:"img",focusable:"false",viewBox:"0 -626 361 637","aria-hidden":"true"},ht=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D461",d:"M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z",style:{"stroke-width":"3"}})])])],-1),et=[ht],kt=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"t")])],-1),pt={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},rt={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.059ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 910.3 599.8","aria-hidden":"true"},dt=a('',1),ot=[dt],gt=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"x"),s("mi",null,"t")])])],-1),Et={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ct={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.817ex",height:"1.441ex",role:"img",focusable:"false",viewBox:"0 -626 361 637","aria-hidden":"true"},Ft=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D461",d:"M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z",style:{"stroke-width":"3"}})])])],-1),yt=[Ft],Ct=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"t")])],-1),ut=a('

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

Keyword Arguments

  • init_inv::T=1: the initial investment.

Beware!

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

  • all_sn::Vector{T}: the cumulative wealth of investment during the investment period.

source

',9),Tt={class:"jldocstring custom-block",open:""},At=s("a",{id:"OnlinePortfolioSelection.spolc-Tuple{AbstractMatrix, AbstractFloat, Integer}",href:"#OnlinePortfolioSelection.spolc-Tuple{AbstractMatrix, AbstractFloat, Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.spolc")],-1),mt=a(`
julia
spolc(x::AbstractMatrix, 𝛾::AbstractFloat, w::Integer)

Run loss control strategy with a rank-one covariance estimate for short-term portfolio optimization (SPOLC).

Arguments

  • x::AbstractMatrix: Matrix of relative prices.

  • 𝛾::AbstractFloat: Mixing parameter that trades off between the increasing factor and the risk.

  • w::Integer: Window size.

Beware!

x should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "AMZN", "GOOG", "MSFT"];
 
@@ -889,7 +889,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.25  0.260742  0.248247  0.243466     2.99939e-6  3.04485e-6  1.56805e-6
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

Reference

Loss Control with Rank-one Covariance Estimate for Short-term Portfolio Optimization

source

`,12),Bt={class:"jldocstring custom-block",open:""},bt=s("a",{id:"OnlinePortfolioSelection.sspo",href:"#OnlinePortfolioSelection.sspo"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.sspo")],-1),_t=a(`
julia
sspo(
+true

Reference

Loss Control with Rank-one Covariance Estimate for Short-term Portfolio Optimization

source

`,12),Bt={class:"jldocstring custom-block",open:""},bt=s("a",{id:"OnlinePortfolioSelection.sspo",href:"#OnlinePortfolioSelection.sspo"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.sspo")],-1),_t=a(`
julia
sspo(
   p::AbstractMatrix,
   horizon::Integer,
   w::Integer,
@@ -919,7 +919,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.25  9.92018e-9  1.0         1.0  1.0
  0.25  0.0         0.0         0.0  0.0
  0.25  0.0         0.0         0.0  0.0
- 0.25  1.0         9.94367e-9  0.0  0.0

Reference

Short-term Sparse Portfolio Optimization Based on Alternating Direction Method of Multipliers

source

`,11),ft={class:"jldocstring custom-block",open:""},Qt=s("a",{id:"OnlinePortfolioSelection.tco",href:"#OnlinePortfolioSelection.tco"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.tco")],-1),Dt=a(`
julia
tco(
+ 0.25  1.0         9.94367e-9  0.0  0.0

Reference

Short-term Sparse Portfolio Optimization Based on Alternating Direction Method of Multipliers

source

`,11),ft={class:"jldocstring custom-block",open:""},Qt=s("a",{id:"OnlinePortfolioSelection.tco",href:"#OnlinePortfolioSelection.tco"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.tco")],-1),Dt=a(`
julia
tco(
   x::AbstractMatrix,
   w::Integer,
   horizon::Integer,
@@ -955,7 +955,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.05  0.0809567  0.0850694  0.0871646  0.0865584
  0.05  0.0809567  0.0830907  0.0890398  0.0885799
  0.7   0.730957   0.756827   0.746137   0.748113
- 0.2   0.10713    0.0750128  0.0776584  0.0767483

Reference

Transaction cost optimization for online portfolio selection

source

`,14),vt={class:"jldocstring custom-block",open:""},jt=s("a",{id:"OnlinePortfolioSelection.tppt",href:"#OnlinePortfolioSelection.tppt"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.tppt")],-1),xt=a(`
julia
tppt(
+ 0.2   0.10713    0.0750128  0.0776584  0.0767483

Reference

Transaction cost optimization for online portfolio selection

source

`,14),vt={class:"jldocstring custom-block",open:""},jt=s("a",{id:"OnlinePortfolioSelection.tppt",href:"#OnlinePortfolioSelection.tppt"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.tppt")],-1),xt=a(`
julia
tppt(
   prices::AbstractMatrix,
   horizon::Integer,
   w::Integer,
@@ -977,7 +977,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 3×3 Matrix{Float64}:
  0.333333  1.52594e-6  7.35766e-7
  0.333333  5.30452e-6  3.90444e-6
- 0.333333  0.999993    0.999995

References

An online portfolio strategy based on trend promote price tracing ensemble learning algorithm

source

`,11),St={class:"jldocstring custom-block",open:""},wt=s("a",{id:"OnlinePortfolioSelection.ttest",href:"#OnlinePortfolioSelection.ttest"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ttest")],-1),Pt=a(`
julia
ttest(vec::AbstractVector{<:AbstractVector})
+ 0.333333  0.999993    0.999995

References

An online portfolio strategy based on trend promote price tracing ensemble learning algorithm

source

`,11),St={class:"jldocstring custom-block",open:""},wt=s("a",{id:"OnlinePortfolioSelection.ttest",href:"#OnlinePortfolioSelection.ttest"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.ttest")],-1),Pt=a(`
julia
ttest(vec::AbstractVector{<:AbstractVector})
 ttest(SB::AbstractVector, Sₜ::AbstractVector, SF::AbstractFloat)

Method 1

julia
ttest(vec::AbstractVector{<:AbstractVector})
`,3),Ot=s("code",null,"n",-1),Mt=s("code",null,"x̄",-1),qt={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Rt={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.489ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.352ex",height:"1.489ex",role:"img",focusable:"false",viewBox:"0 -442 1039.6 658","aria-hidden":"true"},It=a('',1),Vt=[It],Lt=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"μ"),s("mn",null,"0")])])],-1),Ht={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},zt={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.489ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.352ex",height:"1.489ex",role:"img",focusable:"false",viewBox:"0 -442 1039.6 658","aria-hidden":"true"},Nt=a('',1),Ut=[Nt],Gt=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("msub",null,[s("mi",null,"μ"),s("mn",null,"0")])])],-1),Zt=s("code",null,"vec",-1),Wt=a(`

Note

You have to install and import the HypothesisTests package to use this function.

Arguments

  • vec::AbstractVector{<:AbstractVector}: A vector of vectors. Each inner vector should be of the same size.

Returns

  • ::Matrix{<:AbstractFloat}: A matrix of p-values for each pair of algorithms.

Example

julia
julia> using OnlinePortfolioSelection, HypothesisTests
 
 julia> apys = [
@@ -990,12 +990,12 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
 3×3 Matrix{Float64}:
  0.0  1.0  0.702697
  0.0  0.0  0.843672
- 0.0  0.0  0.0

Method 2

julia
ttest(SB::AbstractVector, Sₜ::AbstractVector, SF::AbstractFloat)

Performs a t-student test to check whether the returns gained by a trading algorithm is due to a simple luck.

Note

You have to install and import the GLM package to use this function.

Arguments

  • SB::AbstractVector: Denotes the daily returns of the benchmark (market index)

  • Sₜ::AbstractVector: Portfolio daily returns

  • SF::AbstractFloat: Daily returns of the risk-free assets (Can be set to Treasury bill value or annual interest rate.)

  • ::StatsModels.TableRegressionModel: An object of type TableRegressionModel including the values of t-student test analysis.

source

`,14),Kt={class:"jldocstring custom-block",open:""},Yt=s("a",{id:"OnlinePortfolioSelection.uniform-Tuple{Int64, Int64}",href:"#OnlinePortfolioSelection.uniform-Tuple{Int64, Int64}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.uniform")],-1),Jt=a(`
julia
uniform(n_assets::Int, horizon::Int)

Construct uniform portfolios.

Arguments

  • n_assets::Int: The number of assets.

  • horizon::Int: The number of investment periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
+ 0.0  0.0  0.0

Method 2

julia
ttest(SB::AbstractVector, Sₜ::AbstractVector, SF::AbstractFloat)

Performs a t-student test to check whether the returns gained by a trading algorithm is due to a simple luck.

Note

You have to install and import the GLM package to use this function.

Arguments

  • SB::AbstractVector: Denotes the daily returns of the benchmark (market index)

  • Sₜ::AbstractVector: Portfolio daily returns

  • SF::AbstractFloat: Daily returns of the risk-free assets (Can be set to Treasury bill value or annual interest rate.)

  • ::StatsModels.TableRegressionModel: An object of type TableRegressionModel including the values of t-student test analysis.

source

`,14),Kt={class:"jldocstring custom-block",open:""},Yt=s("a",{id:"OnlinePortfolioSelection.uniform-Tuple{Int64, Int64}",href:"#OnlinePortfolioSelection.uniform-Tuple{Int64, Int64}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.uniform")],-1),Jt=a(`
julia
uniform(n_assets::Int, horizon::Int)

Construct uniform portfolios.

Arguments

  • n_assets::Int: The number of assets.

  • horizon::Int: The number of investment periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> model = uniform(3, 10)
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

source

`,9),Xt={class:"jldocstring custom-block",open:""},$t=s("a",{id:"OnlinePortfolioSelection.up-Union{Tuple{AbstractMatrix{T}}, Tuple{T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.up-Union{Tuple{AbstractMatrix{T}}, Tuple{T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.up")],-1),sn=a(`
julia
function up(
+true

source

`,9),Xt={class:"jldocstring custom-block",open:""},$t=s("a",{id:"OnlinePortfolioSelection.up-Union{Tuple{AbstractMatrix{T}}, Tuple{T}} where T<:AbstractFloat",href:"#OnlinePortfolioSelection.up-Union{Tuple{AbstractMatrix{T}}, Tuple{T}} where T<:AbstractFloat"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.up")],-1),sn=a(`
julia
function up(
   rel_pr::AbstractMatrix{T};
   eval_points::Integer=10^4
 ) where T<:AbstractFloat

Universal Portfolio (UP) algorithm.

Calculate the Universal Portfolio (UP) weights and budgets using the given historical prices and parameters.

Arguments

  • rel_pr::AbstractMatrix{T}: Historical relative prices.

Keyword Arguments

  • eval_points::Integer=10^4: Number of evaluation points.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection
@@ -1011,7 +1011,7 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.333333  0.439276  0.338551  0.364661  0.438512  0.429483  0.448695  0.388281  0.330729
 
 julia> sum(m_up.b, dims=1) .|> isapprox(1.) |> all
-true

References

Universal Portfolios

source

`,15),an={class:"jldocstring custom-block",open:""},tn=s("a",{id:"OnlinePortfolioSelection.waeg-Tuple{AbstractMatrix, AbstractFloat, AbstractFloat, Integer}",href:"#OnlinePortfolioSelection.waeg-Tuple{AbstractMatrix, AbstractFloat, AbstractFloat, Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.waeg")],-1),nn=a(`
julia
waeg(x::AbstractMatrix, ηₘᵢₙ::AbstractFloat, ηₘₐₓ::AbstractFloat, k::Integer)

Run Weak Aggregating Exponential Gradient (WAEG) algorithm.

Arguments

  • x::AbstractMatrix: matrix of relative prices.

  • ηₘᵢₙ::AbstractFloat: minimum learning rate.

  • ηₘₐₓ::AbstractFloat: maximum learning rate.

  • k::Integer: number of EG experts.

Returns

Beware!

x should be a matrix of size n_assets × n_periods.

Example

julia
julia> using OnlinePortfolioSelection
+true

References

Universal Portfolios

source

`,15),an={class:"jldocstring custom-block",open:""},tn=s("a",{id:"OnlinePortfolioSelection.waeg-Tuple{AbstractMatrix, AbstractFloat, AbstractFloat, Integer}",href:"#OnlinePortfolioSelection.waeg-Tuple{AbstractMatrix, AbstractFloat, AbstractFloat, Integer}"},[s("span",{class:"jlbinding"},"OnlinePortfolioSelection.waeg")],-1),nn=a(`
julia
waeg(x::AbstractMatrix, ηₘᵢₙ::AbstractFloat, ηₘₐₓ::AbstractFloat, k::Integer)

Run Weak Aggregating Exponential Gradient (WAEG) algorithm.

Arguments

  • x::AbstractMatrix: matrix of relative prices.

  • ηₘᵢₙ::AbstractFloat: minimum learning rate.

  • ηₘₐₓ::AbstractFloat: maximum learning rate.

  • k::Integer: number of EG experts.

Returns

Beware!

x should be a matrix of size n_assets × n_periods.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> rel_pr = rand(4, 8);
 
@@ -1025,4 +1025,4 @@ import{_ as e,c as l,m as s,a as i,J as n,a7 as a,E as k,o as h}from"./chunks/fr
  0.25  0.254368  0.25124   0.235057  0.23561   0.220668  0.219505  0.205937
 
 julia> sum(m.b, dims=1) .|> isapprox(1.) |> all
-true

References

Boosting Exponential Gradient Strategy for Online Portfolio Selection: An Aggregating Experts’ Advice Method

source

`,12);function ln(hn,en,kn,pn,rn,dn){const t=k("Badge");return h(),l("div",null,[r,s("details",d,[s("summary",null,[o,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),g]),s("details",E,[s("summary",null,[c,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),F,s("ul",null,[y,C,s("li",null,[s("p",null,[u,i(": the standard deviation of the portfolio "),s("mjx-container",T,[(h(),l("svg",A,B)),b]),i(".")])])]),_,f,Q]),s("details",D,[s("summary",null,[v,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),j,s("p",null,[i("Calculate the Annualized Standard Deviation ("),s("mjx-container",x,[(h(),l("svg",S,P)),O]),i(") of portfolio. Also, see "),M,i(", "),q,i(", "),R,i(", "),I,i(", "),V,i(", "),L,i(", and "),H,i(".")]),z,N,U,G,Z,s("ul",null,[s("li",null,[W,i(": the Annualized Standard Deviation ("),s("mjx-container",K,[(h(),l("svg",Y,X)),$]),i(") of portfolio.")])]),ss]),s("details",is,[s("summary",null,[as,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ts]),s("details",ns,[s("summary",null,[ls,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),hs]),s("details",es,[s("summary",null,[ks,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ps]),s("details",rs,[s("summary",null,[ds,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),os]),s("details",gs,[s("summary",null,[Es,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),cs]),s("details",Fs,[s("summary",null,[ys,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Cs]),s("details",us,[s("summary",null,[Ts,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),As]),s("details",ms,[s("summary",null,[Bs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),bs]),s("details",_s,[s("summary",null,[fs,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Qs]),s("details",Ds,[s("summary",null,[vs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),js]),s("details",xs,[s("summary",null,[Ss,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ws]),s("details",Ps,[s("summary",null,[Os,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Ms]),s("details",qs,[s("summary",null,[Rs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Is]),s("details",Vs,[s("summary",null,[Ls,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Hs]),s("details",zs,[s("summary",null,[Ns,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Us]),s("details",Gs,[s("summary",null,[Zs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Ws]),s("details",Ks,[s("summary",null,[Ys,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Js]),s("details",Xs,[s("summary",null,[$s,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),si]),s("details",ii,[s("summary",null,[ai,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ti,s("mjx-container",ni,[(h(),l("svg",li,ei)),ki]),s("p",null,[i("where "),s("mjx-container",pi,[(h(),l("svg",ri,oi)),gi]),i(" represents the portfolio's daily return, "),s("mjx-container",Ei,[(h(),l("svg",ci,yi)),Ci]),i(" represents the market's daily return, "),s("mjx-container",ui,[(h(),l("svg",Ti,mi)),Bi]),i(" represents the portfolio's average daily return, "),s("mjx-container",bi,[(h(),l("svg",_i,Qi)),Di]),i(" represents the market's average daily return, and "),s("mjx-container",vi,[(h(),l("svg",ji,Si)),wi]),i(" represents the standard deviation of the portfolio's daily excess return over the market. Note that in this package, the logarithmic return is used.")]),Pi]),s("details",Oi,[s("summary",null,[Mi,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),qi]),s("details",Ri,[s("summary",null,[Ii,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Vi]),s("details",Li,[s("summary",null,[Hi,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),zi]),s("details",Ni,[s("summary",null,[Ui,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Gi]),s("details",Zi,[s("summary",null,[Wi,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Ki]),s("details",Yi,[s("summary",null,[Ji,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Xi]),s("details",$i,[s("summary",null,[sa,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ia,s("ul",null,[s("li",null,[s("p",null,[aa,i(": A vector of length "),ta,i(" containing the initial portfolio weights. 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References

Boosting Exponential Gradient Strategy for Online Portfolio Selection: An Aggregating Experts’ Advice Method

source

`,12);function ln(hn,en,kn,pn,rn,dn){const t=k("Badge");return h(),l("div",null,[r,s("details",d,[s("summary",null,[o,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),g]),s("details",E,[s("summary",null,[c,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),F,s("ul",null,[y,C,s("li",null,[s("p",null,[u,i(": the standard deviation of the portfolio "),s("mjx-container",T,[(h(),l("svg",A,B)),b]),i(".")])])]),_,f,Q]),s("details",D,[s("summary",null,[v,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),j,s("p",null,[i("Calculate the Annualized Standard Deviation ("),s("mjx-container",x,[(h(),l("svg",S,P)),O]),i(") of portfolio. Also, see "),M,i(", "),q,i(", "),R,i(", "),I,i(", "),V,i(", "),L,i(", and "),H,i(".")]),z,N,U,G,Z,s("ul",null,[s("li",null,[W,i(": the Annualized Standard Deviation ("),s("mjx-container",K,[(h(),l("svg",Y,X)),$]),i(") of portfolio.")])]),ss]),s("details",is,[s("summary",null,[as,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ts]),s("details",ns,[s("summary",null,[ls,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),hs]),s("details",es,[s("summary",null,[ks,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ps]),s("details",rs,[s("summary",null,[ds,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),os]),s("details",gs,[s("summary",null,[Es,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),cs]),s("details",Fs,[s("summary",null,[ys,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Cs]),s("details",us,[s("summary",null,[Ts,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),As]),s("details",ms,[s("summary",null,[Bs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),bs]),s("details",_s,[s("summary",null,[fs,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Qs]),s("details",Ds,[s("summary",null,[vs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),js]),s("details",xs,[s("summary",null,[Ss,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ws]),s("details",Ps,[s("summary",null,[Os,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Ms]),s("details",qs,[s("summary",null,[Rs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Is]),s("details",Vs,[s("summary",null,[Ls,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Hs]),s("details",zs,[s("summary",null,[Ns,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Us]),s("details",Gs,[s("summary",null,[Zs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Ws]),s("details",Ks,[s("summary",null,[Ys,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Js]),s("details",Xs,[s("summary",null,[$s,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),si]),s("details",ii,[s("summary",null,[ai,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ti,s("mjx-container",ni,[(h(),l("svg",li,ei)),ki]),s("p",null,[i("where "),s("mjx-container",pi,[(h(),l("svg",ri,oi)),gi]),i(" represents the portfolio's daily return, "),s("mjx-container",Ei,[(h(),l("svg",ci,yi)),Ci]),i(" represents the market's daily return, "),s("mjx-container",ui,[(h(),l("svg",Ti,mi)),Bi]),i(" represents the portfolio's average daily return, "),s("mjx-container",bi,[(h(),l("svg",_i,Qi)),Di]),i(" represents the market's average daily return, and "),s("mjx-container",vi,[(h(),l("svg",ji,Si)),wi]),i(" represents the standard deviation of the portfolio's daily excess return over the market. 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Also, see "),M,i(", "),q,i(", "),R,i(", "),I,i(", "),V,i(", "),L,i(", and "),H,i(".")]),z,N,U,G,Z,s("ul",null,[s("li",null,[W,i(": the Annualized Standard Deviation ("),s("mjx-container",K,[(h(),l("svg",Y,X)),$]),i(") of portfolio.")])]),ss]),s("details",is,[s("summary",null,[as,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ts]),s("details",ns,[s("summary",null,[ls,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),hs]),s("details",es,[s("summary",null,[ks,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ps]),s("details",rs,[s("summary",null,[ds,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),os]),s("details",gs,[s("summary",null,[Es,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),cs]),s("details",Fs,[s("summary",null,[ys,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Cs]),s("details",us,[s("summary",null,[Ts,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),As]),s("details",ms,[s("summary",null,[Bs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),bs]),s("details",_s,[s("summary",null,[fs,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Qs]),s("details",Ds,[s("summary",null,[vs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),js]),s("details",xs,[s("summary",null,[Ss,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ws]),s("details",Ps,[s("summary",null,[Os,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Ms]),s("details",qs,[s("summary",null,[Rs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Is]),s("details",Vs,[s("summary",null,[Ls,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Hs]),s("details",zs,[s("summary",null,[Ns,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Us]),s("details",Gs,[s("summary",null,[Zs,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Ws]),s("details",Ks,[s("summary",null,[Ys,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Js]),s("details",Xs,[s("summary",null,[$s,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),si]),s("details",ii,[s("summary",null,[ai,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ti,s("mjx-container",ni,[(h(),l("svg",li,ei)),ki]),s("p",null,[i("where "),s("mjx-container",pi,[(h(),l("svg",ri,oi)),gi]),i(" represents the portfolio's daily return, "),s("mjx-container",Ei,[(h(),l("svg",ci,yi)),Ci]),i(" represents the market's daily return, "),s("mjx-container",ui,[(h(),l("svg",Ti,mi)),Bi]),i(" represents the portfolio's average daily return, "),s("mjx-container",bi,[(h(),l("svg",_i,Qi)),Di]),i(" represents the market's average daily return, and "),s("mjx-container",vi,[(h(),l("svg",ji,Si)),wi]),i(" represents the standard deviation of the portfolio's daily excess return over the market. Note that in this package, the logarithmic return is used.")]),Pi]),s("details",Oi,[s("summary",null,[Mi,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),qi]),s("details",Ri,[s("summary",null,[Ii,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Vi]),s("details",Li,[s("summary",null,[Hi,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),zi]),s("details",Ni,[s("summary",null,[Ui,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Gi]),s("details",Zi,[s("summary",null,[Wi,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Ki]),s("details",Yi,[s("summary",null,[Ji,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Xi]),s("details",$i,[s("summary",null,[sa,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ia,s("ul",null,[s("li",null,[s("p",null,[aa,i(": A vector of length "),ta,i(" containing the initial portfolio weights. Presumebly, the initial portfolio portfolio is the equally weighted portfolio. However, one can use any other portfolio weights that satisfy the following condition: "),s("mjx-container",na,[(h(),l("svg",la,ea)),ka]),i(".")])]),pa]),ra]),s("details",da,[s("summary",null,[oa,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ga]),s("details",Ea,[s("summary",null,[ca,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Fa]),s("details",ya,[s("summary",null,[Ca,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ua]),s("details",Ta,[s("summary",null,[Aa,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),ma]),s("details",Ba,[s("summary",null,[ba,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),_a]),s("details",fa,[s("summary",null,[Qa,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Da]),s("details",va,[s("summary",null,[ja,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),xa]),s("details",Sa,[s("summary",null,[wa,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Pa]),s("details",Oa,[s("summary",null,[Ma,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),qa,s("mjx-container",Ra,[(h(),l("svg",Ia,La)),Ha]),s("p",null,[i("where "),s("mjx-container",za,[(h(),l("svg",Na,Ga)),Za]),i(" is the initial budget, "),s("mjx-container",Wa,[(h(),l("svg",Ka,Ja)),Xa]),i(" is the investment horizon, "),s("mjx-container",$a,[(h(),l("svg",st,at)),tt]),i(" is the vector of weights of the period "),s("mjx-container",nt,[(h(),l("svg",lt,et)),kt]),i(", and "),s("mjx-container",pt,[(h(),l("svg",rt,ot)),gt]),i(" is the relative price of the "),s("mjx-container",Et,[(h(),l("svg",ct,yt)),Ct]),i("-th period.")]),ut]),s("details",Tt,[s("summary",null,[At,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),mt]),s("details",Bt,[s("summary",null,[bt,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),_t]),s("details",ft,[s("summary",null,[Qt,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Dt]),s("details",vt,[s("summary",null,[jt,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),xt]),s("details",St,[s("summary",null,[wt,i(),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),Pt,s("p",null,[i("Perform a one sample t-test of the null hypothesis that "),Ot,i(" values with mean "),Mt,i(" and sample standard deviation stddev come from a distribution with mean "),s("mjx-container",qt,[(h(),l("svg",Rt,Vt)),Lt]),i(" against the alternative hypothesis that the distribution does not have mean "),s("mjx-container",Ht,[(h(),l("svg",zt,Ut)),Gt]),i(". The t-test with 95% confidence level applies on each pair of vectors in the "),Zt,i(" vector. Each vector should contain the Annual Percentage Yield (APY) of a different algorithm on various datasets.")]),Wt]),s("details",Kt,[s("summary",null,[Yt,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),Jt]),s("details",Xt,[s("summary",null,[$t,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),sn]),s("details",an,[s("summary",null,[tn,i(),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),nn])])}const En=e(p,[["render",ln]]);export{gn as __pageData,En as default}; diff --git a/dev/assets/types.md.B3bPqqkV.js b/dev/assets/types.md.28jHlNVY.js similarity index 87% rename from dev/assets/types.md.B3bPqqkV.js rename to dev/assets/types.md.28jHlNVY.js index 8577f84..94cd7ad 100644 --- a/dev/assets/types.md.B3bPqqkV.js +++ b/dev/assets/types.md.28jHlNVY.js @@ -1,16 +1,16 @@ -import{_ as T,c as i,m as t,a as s,J as l,a7 as a,E as o,o as n}from"./chunks/framework.BasOtKVC.js";const D2=JSON.parse('{"title":"Types","description":"","frontmatter":{},"headers":[],"relativePath":"types.md","filePath":"types.md","lastUpdated":null}'),Q={name:"types.md"},d=t("h1",{id:"types",tabindex:"-1"},[s("Types "),t("a",{class:"header-anchor",href:"#types","aria-label":'Permalink to "Types"'},"​")],-1),m={class:"jldocstring custom-block",open:""},r=t("a",{id:"OnlinePortfolioSelection.EGA",href:"#OnlinePortfolioSelection.EGA"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.EGA")],-1),h=a(`
julia
EGA{T<:AbstractFloat}<:EGMFramework

EGA variant of the EGM algorithm.

Fields

  • gamma1::T: momentum parameter

  • gamma2::T: momentum parameter

Example

julia
julia> model = EGA(0.99, 0.)
-EGA{Float64}(0.99, 0.0)

source

`,7),p={class:"jldocstring custom-block",open:""},c=t("a",{id:"OnlinePortfolioSelection.EGE",href:"#OnlinePortfolioSelection.EGE"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.EGE")],-1),g=a(`
julia
EGE{T<:AbstractFloat}<:EGMFramework

EGE variant of the EGM algorithm.

Fields

  • gamma1::T: momentum parameter

Example

julia
julia> model = EGE(0.99)
-EGE{Float64}(0.99)

source

`,7),k={class:"jldocstring custom-block",open:""},H=t("a",{id:"OnlinePortfolioSelection.EGR",href:"#OnlinePortfolioSelection.EGR"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.EGR")],-1),u=a(`
julia
EGR{T<:AbstractFloat}<:EGMFramework

EGR variant of the EGM algorithm.

Fields

  • gamma2::T: momentum parameter

Example

julia
julia> model = EGR(0.)
-EGR{Float64}(0.0)

source

`,7),y={class:"jldocstring custom-block",open:""},x=t("a",{id:"OnlinePortfolioSelection.EMA",href:"#OnlinePortfolioSelection.EMA"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.EMA")],-1),_=a('
julia
EMA{T<:AbstractFloat}<:TrendRep

Exponential Moving Average trend representation. Formula:

',2),E={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"43.192ex",height:"8.884ex",role:"img",focusable:"false",viewBox:"0 -3046.6 19091.1 3926.6","aria-hidden":"true"},L=a('',1),b=[L],j=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",{mathvariant:"bold"},"x"),t("mo",{mathvariant:"bold",stretchy:"false"},"^")])])])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"E"),t("mo",null,","),t("mi",null,"t"),t("mo",null,"+"),t("mn",null,"1")])])]),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mi",null,"ϑ"),t("mo",{"data-mjx-texclass":"CLOSE"},")")]),t("mo",null,"="),t("mfrac",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("munderover",null,[t("mo",{"data-mjx-texclass":"OP",movablelimits:"false"},"∑"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k"),t("mo",null,"="),t("mn",null,"0")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mn",null,"1")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("msup",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1"),t("mo",null,"−"),t("mi",null,"ϑ")]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])]),t("mi",null,"k")])])]),t("mi",null,"ϑ"),t("mrow",{"data-mjx-texclass":"ORD"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"bold"},"p")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mi",null,"k")])])]),t("mo",null,"+"),t("mrow",{"data-mjx-texclass":"ORD"},[t("msup",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"1"),t("mo",null,"−"),t("mi",null,"ϑ")]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])]),t("mi",null,"t")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"bold"},"p")])]),t("mn",null,"0")])])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"bold"},"p")])]),t("mi",null,"t")])])])])])],-1),V=a(`

Fields

  • v::T: Smoothing factor.

Examples

julia
julia> using OnlinePortfolioSelection
+import{_ as T,c as i,m as a,a as s,J as l,a7 as t,E as o,o as n}from"./chunks/framework.BasOtKVC.js";const D2=JSON.parse('{"title":"Types","description":"","frontmatter":{},"headers":[],"relativePath":"types.md","filePath":"types.md","lastUpdated":null}'),Q={name:"types.md"},d=a("h1",{id:"types",tabindex:"-1"},[s("Types "),a("a",{class:"header-anchor",href:"#types","aria-label":'Permalink to "Types"'},"​")],-1),m={class:"jldocstring custom-block",open:""},r=a("a",{id:"OnlinePortfolioSelection.EGA",href:"#OnlinePortfolioSelection.EGA"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.EGA")],-1),h=t(`
julia
EGA{T<:AbstractFloat}<:EGMFramework
EGA variant of the EGM algorithm.
Fields
  • gamma1::T: momentum parameter
  • gamma2::T: momentum parameter
Example
julia
julia> model = EGA(0.99, 0.)
+EGA{Float64}(0.99, 0.0)
source
`,7),p={class:"jldocstring custom-block",open:""},c=a("a",{id:"OnlinePortfolioSelection.EGE",href:"#OnlinePortfolioSelection.EGE"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.EGE")],-1),g=t(`
julia
EGE{T<:AbstractFloat}<:EGMFramework
EGE variant of the EGM algorithm.
Fields
  • gamma1::T: momentum parameter
Example
julia
julia> model = EGE(0.99)
+EGE{Float64}(0.99)
source
`,7),k={class:"jldocstring custom-block",open:""},H=a("a",{id:"OnlinePortfolioSelection.EGR",href:"#OnlinePortfolioSelection.EGR"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.EGR")],-1),u=t(`
julia
EGR{T<:AbstractFloat}<:EGMFramework
EGR variant of the EGM algorithm.
Fields
  • gamma2::T: momentum parameter
Example
julia
julia> model = EGR(0.)
+EGR{Float64}(0.0)
source
`,7),y={class:"jldocstring custom-block",open:""},x=a("a",{id:"OnlinePortfolioSelection.EMA",href:"#OnlinePortfolioSelection.EMA"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.EMA")],-1),_=t('
julia
EMA{T<:AbstractFloat}<:TrendRep
Exponential Moving Average trend representation. Formula:
',2),E={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"43.192ex",height:"8.884ex",role:"img",focusable:"false",viewBox:"0 -3046.6 19091.1 3926.6","aria-hidden":"true"},L=t('',1),j=[L],V=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mi",{mathvariant:"bold"},"x"),a("mo",{mathvariant:"bold",stretchy:"false"},"^")])])])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"E"),a("mo",null,","),a("mi",null,"t"),a("mo",null,"+"),a("mn",null,"1")])])]),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"("),a("mi",null,"ϑ"),a("mo",{"data-mjx-texclass":"CLOSE"},")")]),a("mo",null,"="),a("mfrac",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("munderover",null,[a("mo",{"data-mjx-texclass":"OP",movablelimits:"false"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k"),a("mo",null,"="),a("mn",null,"0")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mn",null,"1")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"("),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1"),a("mo",null,"−"),a("mi",null,"ϑ")]),a("mo",{"data-mjx-texclass":"CLOSE"},")")])]),a("mi",null,"k")])])]),a("mi",null,"ϑ"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"bold"},"p")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mi",null,"k")])])]),a("mo",null,"+"),a("mrow",{"data-mjx-texclass":"ORD"},[a("msup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"("),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1"),a("mo",null,"−"),a("mi",null,"ϑ")]),a("mo",{"data-mjx-texclass":"CLOSE"},")")])]),a("mi",null,"t")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"bold"},"p")])]),a("mn",null,"0")])])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"bold"},"p")])]),a("mi",null,"t")])])])])])],-1),b=t(`
Fields
  • v::T: Smoothing factor.
Examples
julia
julia> using OnlinePortfolioSelection
 
 julia> ema = EMA(0.5)
-EMA{Float64}(0.5)
source
`,5),w={class:"jldocstring custom-block",open:""},A=t("a",{id:"OnlinePortfolioSelection.KMDLOG",href:"#OnlinePortfolioSelection.KMDLOG"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.KMDLOG")],-1),M=a('
julia
KMDLOG<:ClusLogVariant
KMDLOG is a concrete type used to represent the KMDLOG Model. Also, see KMNLOG.
source
',3),D={class:"jldocstring custom-block",open:""},O=t("a",{id:"OnlinePortfolioSelection.KMNLOG",href:"#OnlinePortfolioSelection.KMNLOG"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.KMNLOG")],-1),v=a('
julia
KMNLOG<:ClusLogVariant
KMNLOG is a concrete type used to represent the KMNLOG Model. Also, see KMDLOG.
source
',3),C={class:"jldocstring custom-block",open:""},R=t("a",{id:"OnlinePortfolioSelection.OPSAlgorithm",href:"#OnlinePortfolioSelection.OPSAlgorithm"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.OPSAlgorithm")],-1),P=a('
julia
OPSAlgorithm{T<:AbstractFloat}
An object that contains the result of running the algorithm.
Fields
  • n_asset::Int: Number of assets in the portfolio.
  • b::Matrix{T}: Weights of the created portfolios.
  • alg::String: Name of the algorithm.
source
',5),S={class:"jldocstring custom-block",open:""},F=t("a",{id:"OnlinePortfolioSelection.OPSMetrics",href:"#OnlinePortfolioSelection.OPSMetrics"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.OPSMetrics")],-1),Z=a('
julia
OPSMetrics{T<:AbstractFloat}
A struct to store the metrics of the OPS algorithm. This object is returned by the opsmetrics function.
Fields
  • Sn::Vector{T}: The cumulative wealth of investment during the investment period.
  • MER::T: The investments's Mean excess return (MER).
  • IR::T: The Information Ratio (IR) of portfolio for the investment period.
  • APY::T: The Annual Percentage Yield (APY) of investment.
  • Ann_Std::T: The Annualized Standard Deviation (σₚ) of investment.
  • Ann_Sharpe::T: The Annualized Sharpe Ratio (SR) of investment.
  • MDD::T: The Maximum Drawdown (MDD) of investment.
  • Calmar::T: The Calmar Ratio of investment.
  • AT::T: The Average Turnover (AT) of the investment.
source
',5),X={class:"jldocstring custom-block",open:""},B=t("a",{id:"OnlinePortfolioSelection.PAMR",href:"#OnlinePortfolioSelection.PAMR"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.PAMR")],-1),I=a('
julia
PAMR<: PAMRModel
Create a PAMR object. Also, see PAMR1, and PAMR2.
Example
julia
model = PAMR()
source
',5),N={class:"jldocstring custom-block",open:""},G=t("a",{id:"OnlinePortfolioSelection.PAMR1",href:"#OnlinePortfolioSelection.PAMR1"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.PAMR1")],-1),K=a('
julia
PAMR1{T<:AbstractFloat}<: PAMRModel
Create a PAMR1 object. Also, see PAMR, and PAMR2.
Keyword Arguments
  • C::AbstractFloat=1.: Aggressiveness parameter.
Example
julia
model = PAMR1(C=0.02)
source
',7),z={class:"jldocstring custom-block",open:""},J=t("a",{id:"OnlinePortfolioSelection.PAMR2",href:"#OnlinePortfolioSelection.PAMR2"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.PAMR2")],-1),$=a('
julia
PAMR2{T<:AbstractFloat}<: PAMRModel
Create a PAMR2 object. Also, see PAMR, and PAMR1.
Keyword Arguments
  • C::AbstractFloat=1.: Aggressiveness parameter.
Example
julia
model = PAMR2(C=0.02)
source
',7),Y={class:"jldocstring custom-block",open:""},U=t("a",{id:"OnlinePortfolioSelection.PP",href:"#OnlinePortfolioSelection.PP"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.PP")],-1),W=a('
julia
PP<:TrendRep
Pick Price trend representation. Formula:
',2),q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},t2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"42.61ex",height:"7.391ex",role:"img",focusable:"false",viewBox:"0 -2387 18833.5 3267","aria-hidden":"true"},a2=a('',1),s2=[a2],e2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",{mathvariant:"bold"},"x"),t("mo",{mathvariant:"bold",stretchy:"false"},"^")])])])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"M"),t("mo",null,","),t("mi",null,"t"),t("mo",null,"+"),t("mn",null,"1")])])]),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mi",null,"w"),t("mo",{"data-mjx-texclass":"CLOSE"},")")]),t("mo",null,"="),t("mfrac",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("munder",null,[t("mrow",{"data-mjx-texclass":"OP"},[t("mo",{"data-mjx-texclass":"OP"},"max")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",null,"0"),t("mo",null,"⩽"),t("mi",null,"k"),t("mo",null,"⩽"),t("mi",null,"w"),t("mo",null,"−"),t("mn",null,"1")])]),t("mo",{"data-mjx-texclass":"NONE"},"⁡"),t("msubsup",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"bold"},"p")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mi",null,"k")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",{stretchy:"false"},"("),t("mi",null,"i"),t("mo",{stretchy:"false"},")")])])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"bold"},"p")])]),t("mi",null,"t")])])])]),t("mo",null,","),t("mstyle",{scriptlevel:"0"},[t("mspace",{width:"1em"})]),t("mi",null,"i"),t("mo",null,"="),t("mn",null,"1"),t("mo",null,","),t("mn",null,"2"),t("mo",null,","),t("mo",null,"…"),t("mo",null,","),t("mi",null,"d")])],-1),l2=a(`
Examples
julia
julia> using OnlinePortfolioSelection
+EMA{Float64}(0.5)
source
`,5),w={class:"jldocstring custom-block",open:""},A=a("a",{id:"OnlinePortfolioSelection.KMDLOG",href:"#OnlinePortfolioSelection.KMDLOG"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.KMDLOG")],-1),M=t('
julia
KMDLOG<:ClusLogVariant
KMDLOG is a concrete type used to represent the KMDLOG Model. Also, see KMNLOG.
source
',3),D={class:"jldocstring custom-block",open:""},O=a("a",{id:"OnlinePortfolioSelection.KMNLOG",href:"#OnlinePortfolioSelection.KMNLOG"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.KMNLOG")],-1),v=t('
julia
KMNLOG<:ClusLogVariant
KMNLOG is a concrete type used to represent the KMNLOG Model. Also, see KMDLOG.
source
',3),C={class:"jldocstring custom-block",open:""},R=a("a",{id:"OnlinePortfolioSelection.OPSAlgorithm",href:"#OnlinePortfolioSelection.OPSAlgorithm"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.OPSAlgorithm")],-1),P=t('
julia
OPSAlgorithm{T<:AbstractFloat}
An object that contains the result of running the algorithm.
Fields
  • n_asset::Int: Number of assets in the portfolio.
  • b::Matrix{T}: Weights of the created portfolios.
  • alg::String: Name of the algorithm.
source
',5),S={class:"jldocstring custom-block",open:""},F=a("a",{id:"OnlinePortfolioSelection.OPSMetrics",href:"#OnlinePortfolioSelection.OPSMetrics"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.OPSMetrics")],-1),Z=t('
julia
OPSMetrics{T<:AbstractFloat}
A struct to store the metrics of the OPS algorithm. This object is returned by the opsmetrics function.
Fields
  • Sn::Vector{T}: The cumulative wealth of investment during the investment period.
  • MER::T: The investments's Mean excess return (MER).
  • IR::T: The Information Ratio (IR) of portfolio for the investment period.
  • APY::T: The Annual Percentage Yield (APY) of investment.
  • Ann_Std::T: The Annualized Standard Deviation (σₚ) of investment.
  • Ann_Sharpe::T: The Annualized Sharpe Ratio (SR) of investment.
  • MDD::T: The Maximum Drawdown (MDD) of investment.
  • Calmar::T: The Calmar Ratio of investment.
  • AT::T: The Average Turnover (AT) of the investment.
source
',5),X={class:"jldocstring custom-block",open:""},B=a("a",{id:"OnlinePortfolioSelection.PAMR",href:"#OnlinePortfolioSelection.PAMR"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.PAMR")],-1),I=t('
julia
PAMR<: PAMRModel
Create a PAMR object. Also, see PAMR1, and PAMR2.
Example
julia
model = PAMR()
source
',5),N={class:"jldocstring custom-block",open:""},G=a("a",{id:"OnlinePortfolioSelection.PAMR1",href:"#OnlinePortfolioSelection.PAMR1"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.PAMR1")],-1),K=t('
julia
PAMR1{T<:AbstractFloat}<: PAMRModel
Create a PAMR1 object. Also, see PAMR, and PAMR2.
Keyword Arguments
  • C::AbstractFloat=1.: Aggressiveness parameter.
Example
julia
model = PAMR1(C=0.02)
source
',7),z={class:"jldocstring custom-block",open:""},J=a("a",{id:"OnlinePortfolioSelection.PAMR2",href:"#OnlinePortfolioSelection.PAMR2"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.PAMR2")],-1),$=t('
julia
PAMR2{T<:AbstractFloat}<: PAMRModel
Create a PAMR2 object. Also, see PAMR, and PAMR1.
Keyword Arguments
  • C::AbstractFloat=1.: Aggressiveness parameter.
Example
julia
model = PAMR2(C=0.02)
source
',7),Y={class:"jldocstring custom-block",open:""},U=a("a",{id:"OnlinePortfolioSelection.PP",href:"#OnlinePortfolioSelection.PP"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.PP")],-1),W=t('
julia
PP<:TrendRep
Pick Price trend representation. Formula:
',2),q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},a2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"42.61ex",height:"7.391ex",role:"img",focusable:"false",viewBox:"0 -2387 18833.5 3267","aria-hidden":"true"},t2=t('',1),s2=[t2],e2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mi",{mathvariant:"bold"},"x"),a("mo",{mathvariant:"bold",stretchy:"false"},"^")])])])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"M"),a("mo",null,","),a("mi",null,"t"),a("mo",null,"+"),a("mn",null,"1")])])]),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"("),a("mi",null,"w"),a("mo",{"data-mjx-texclass":"CLOSE"},")")]),a("mo",null,"="),a("mfrac",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("munder",null,[a("mrow",{"data-mjx-texclass":"OP"},[a("mo",{"data-mjx-texclass":"OP"},"max")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"0"),a("mo",null,"⩽"),a("mi",null,"k"),a("mo",null,"⩽"),a("mi",null,"w"),a("mo",null,"−"),a("mn",null,"1")])]),a("mo",{"data-mjx-texclass":"NONE"},"⁡"),a("msubsup",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"bold"},"p")])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mi",null,"k")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mo",{stretchy:"false"},"("),a("mi",null,"i"),a("mo",{stretchy:"false"},")")])])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"bold"},"p")])]),a("mi",null,"t")])])])]),a("mo",null,","),a("mstyle",{scriptlevel:"0"},[a("mspace",{width:"1em"})]),a("mi",null,"i"),a("mo",null,"="),a("mn",null,"1"),a("mo",null,","),a("mn",null,"2"),a("mo",null,","),a("mo",null,"…"),a("mo",null,","),a("mi",null,"d")])],-1),l2=t(`
Examples
julia
julia> using OnlinePortfolioSelection
 
 julia> pp = PP()
-PP()
source
`,3),i2={class:"jldocstring custom-block",open:""},n2=t("a",{id:"OnlinePortfolioSelection.SMAP",href:"#OnlinePortfolioSelection.SMAP"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.SMAP")],-1),T2=a('
julia
SMAP<:TrendRep
Simple Moving Average trend representation using the close prices. Formula:
',2),o2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Q2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.863ex",height:"5.953ex",role:"img",focusable:"false",viewBox:"0 -1751.3 10547.3 2631.3","aria-hidden":"true"},d2=a('',1),m2=[d2],r2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mover",null,[t("mi",{mathvariant:"bold"},"x"),t("mo",{mathvariant:"bold",stretchy:"false"},"^")])])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"S"),t("mo",null,","),t("mi",null,"t"),t("mo",null,"+"),t("mn",null,"1")])]),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mi",null,"w"),t("mo",{"data-mjx-texclass":"CLOSE"},")")]),t("mo",null,"="),t("mfrac",null,[t("mrow",null,[t("munderover",null,[t("mo",{"data-mjx-texclass":"OP"},"∑"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k"),t("mo",null,"="),t("mn",null,"0")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"w"),t("mo",null,"−"),t("mn",null,"1")])]),t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"bold"},"p")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mi",null,"k")])])]),t("mrow",null,[t("mi",null,"w"),t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"bold"},"p")]),t("mi",null,"t")])])])])],-1),h2=a(`
Examples
julia
julia> using OnlinePortfolioSelection
+PP()
source
`,3),i2={class:"jldocstring custom-block",open:""},n2=a("a",{id:"OnlinePortfolioSelection.SMAP",href:"#OnlinePortfolioSelection.SMAP"},[a("span",{class:"jlbinding"},"OnlinePortfolioSelection.SMAP")],-1),T2=t('
julia
SMAP<:TrendRep
Simple Moving Average trend representation using the close prices. Formula:
',2),o2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Q2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.863ex",height:"5.953ex",role:"img",focusable:"false",viewBox:"0 -1751.3 10547.3 2631.3","aria-hidden":"true"},d2=t('',1),m2=[d2],r2=a("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mrow",{"data-mjx-texclass":"ORD"},[a("mover",null,[a("mi",{mathvariant:"bold"},"x"),a("mo",{mathvariant:"bold",stretchy:"false"},"^")])])]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"S"),a("mo",null,","),a("mi",null,"t"),a("mo",null,"+"),a("mn",null,"1")])]),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"("),a("mi",null,"w"),a("mo",{"data-mjx-texclass":"CLOSE"},")")]),a("mo",null,"="),a("mfrac",null,[a("mrow",null,[a("munderover",null,[a("mo",{"data-mjx-texclass":"OP"},"∑"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"k"),a("mo",null,"="),a("mn",null,"0")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"w"),a("mo",null,"−"),a("mn",null,"1")])]),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"bold"},"p")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",null,"t"),a("mo",null,"−"),a("mi",null,"k")])])]),a("mrow",null,[a("mi",null,"w"),a("msub",null,[a("mrow",{"data-mjx-texclass":"ORD"},[a("mi",{mathvariant:"bold"},"p")]),a("mi",null,"t")])])])])],-1),h2=t(`
Examples
julia
julia> using OnlinePortfolioSelection
 
 julia> sma = SMAP()
-SMA()
source
`,3),p2={class:"jldocstring custom-block",open:""},c2=t("a",{id:"OnlinePortfolioSelection.SMAR",href:"#OnlinePortfolioSelection.SMAR"},[t("span",{class:"jlbinding"},"OnlinePortfolioSelection.SMAR")],-1),g2=t("p",null,"SMAR<:TrendRep",-1),k2=t("p",null,[s("Simple Moving Average trend representation "),t("strong",null,"using the relative prices"),s(". Formula:")],-1),H2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.755ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.734ex",height:"5.766ex",role:"img",focusable:"false",viewBox:"0 -1331 11374.4 2548.6","aria-hidden":"true"},y2=a('',1),x2=[y2],_2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",{mathvariant:"bold"},"1")])]),t("mo",null,"+"),t("mfrac",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",{mathvariant:"bold"},"1")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"bold"},"x")])]),t("mi",null,"t")])])])]),t("mo",null,"+"),t("mo",null,"⋯"),t("mo",null,"+"),t("mfrac",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mn",{mathvariant:"bold"},"1")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("msubsup",null,[t("mo",null,"⊗"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"k"),t("mo",null,"="),t("mn",null,"0")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"w"),t("mo",null,"−"),t("mn",null,"2")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"bold"},"x")])]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"t"),t("mo",null,"−"),t("mi",null,"k")])])])])])])],-1),E2=a(`
Examples
julia
julia> using OnlinePortfolioSelection
+SMA()
source
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Examples
julia
julia> using OnlinePortfolioSelection
 
 julia> sma = SMAR()
-SMAR()
source
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+SMAR()

source

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You can analyse the algorithm's performance using several metrics that have been provided in this package. Check out the Performance evaluation section for more details.

References ​

Bibliography ​

  1. T. M. Cover. Universal Portfolios. Mathematical Finance 1, 1–29 (1991).

  2. L. GYÖRFI, A. URBÁN and I. VAJDA. KERNEL-BASED SEMI-LOG-OPTIMAL EMPIRICAL PORTFOLIO SELECTION STRATEGIES. International Journal of Theoretical and Applied Finance 10, 505–516 (2007).

  3. A. Agarwal, E. Hazan, S. Kale and R. E. Schapire. Algorithms for Portfolio Management Based on the Newton Method. In: Proceedings of the 23rd International Conference on Machine Learning, ICML '06 (Association for Computing Machinery, New York, NY, USA, 2006); pp. 9–16.

- + \ No newline at end of file diff --git a/dev/fetchdata.html b/dev/fetchdata.html index f90673d..9269d45 100644 --- a/dev/fetchdata.html +++ b/dev/fetchdata.html @@ -8,9 +8,9 @@ - + - + @@ -39,7 +39,7 @@ 1 │ 104.57 51.92 132.06 32.89 116.13 2 │ 102.25 51.82 131.6 33.1 115.02 3 │ 102.29 51.82 132.14 32.83 116.99

The provided data in several examples within this documentation has been obtained using the code mentioned above.

- + \ No newline at end of file diff --git a/dev/funcs.html b/dev/funcs.html index 4c8ac2b..f4173e2 100644 --- a/dev/funcs.html +++ b/dev/funcs.html @@ -8,11 +8,11 @@ - + - + - + @@ -58,7 +58,7 @@ 0.1 6.92278e-8 0.0 0.0 0.0 0.1 0.0 0.0 6.95036e-8 1.0 0.1 0.0 0.0 0.0 0.0 - 0.1 0.0 0.0 1.0 6.95537e-8

References

Radial Basis Functions With Adaptive Input and Composite Trend Representation for Portfolio Selection

source

OnlinePortfolioSelection.ann_sharpe Method
julia
ann_sharpe(APY::T, Rf::T, sigma_prtf::T) where T<:AbstractFloat

Calculate the Annualized Sharpe Ratio of investment. Also, see sn, mer, ann_std, apy, mdd, calmar, and opsmetrics.

Arguments

  • APY::T: the APY of investment.

  • Rf::T: the risk-free rate of return.

  • sigma_prtf::T: the standard deviation of the portfolio σp.

Returns

  • ::AbstractFloat: the Annualized Sharpe Ratio of investment.

source

OnlinePortfolioSelection.ann_std Method
julia
ann_std(cum_ret::AbstractVector{AbstractFloat}; dpy)

Calculate the Annualized Standard Deviation (σp) of portfolio. Also, see sn, mer, apy, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • cum_ret::AbstractVector{AbstractFloat}: the cumulative wealth of investment during the investment period.

Keyword Arguments

  • dpy: the number of days in a year.

Returns

  • ::AbstractFloat: the Annualized Standard Deviation (σp) of portfolio.

source

OnlinePortfolioSelection.anticor Method
julia
anticor(adj_close::Matrix{T}, window::Int) where {T<:Real}

Run the Anticor algorithm on adj_close with window sizes window.

Beware!

adj_close should be a matrix of size n_assets × n_periods.

Arguments

  • adj_close::Matrix{T}: matrix of adjusted close prices

  • window::Int: size of the window

Returns

  • ::OPSAlgorithm(n_assets, b, alg): An OPSAlgorithm object.

Example

julia
julia> using OnlinePortfolioSelection
+ 0.1  0.0         0.0         1.0         6.95537e-8

References

Radial Basis Functions With Adaptive Input and Composite Trend Representation for Portfolio Selection

source

OnlinePortfolioSelection.ann_sharpe Method
julia
ann_sharpe(APY::T, Rf::T, sigma_prtf::T) where T<:AbstractFloat

Calculate the Annualized Sharpe Ratio of investment. Also, see sn, mer, ann_std, apy, mdd, calmar, and opsmetrics.

Arguments

  • APY::T: the APY of investment.

  • Rf::T: the risk-free rate of return.

  • sigma_prtf::T: the standard deviation of the portfolio σp.

Returns

  • ::AbstractFloat: the Annualized Sharpe Ratio of investment.

source

OnlinePortfolioSelection.ann_std Method
julia
ann_std(cum_ret::AbstractVector{AbstractFloat}; dpy)

Calculate the Annualized Standard Deviation (σp) of portfolio. Also, see sn, mer, apy, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • cum_ret::AbstractVector{AbstractFloat}: the cumulative wealth of investment during the investment period.

Keyword Arguments

  • dpy: the number of days in a year.

Returns

  • ::AbstractFloat: the Annualized Standard Deviation (σp) of portfolio.

source

OnlinePortfolioSelection.anticor Method
julia
anticor(adj_close::Matrix{T}, window::Int) where {T<:Real}

Run the Anticor algorithm on adj_close with window sizes window.

Beware!

adj_close should be a matrix of size n_assets × n_periods.

Arguments

  • adj_close::Matrix{T}: matrix of adjusted close prices

  • window::Int: size of the window

Returns

  • ::OPSAlgorithm(n_assets, b, alg): An OPSAlgorithm object.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> adj_close = [
        1. 2.
@@ -87,7 +87,7 @@
  0.5  0.5  0.5  0.5     1.0  1.0  1.0  0.0
 
 julia> sum(m_anticor.b, dims=1) .|> isapprox(1., atol=1e-8) |> all
-true

References

Can We Learn to Beat the Best Stock

source

OnlinePortfolioSelection.apy Method
julia
apy(Sn::AbstractFloat, n_periods::S; dpy::S=252) where S<:Int

Calculate the Annual Percentage Yield (APY) of investment. Also, see sn, mer, ann_std, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • Sn::AbstractFloat: the cumulative wealth of investment.

  • n_periods::S: the number investment periods.

  • dpy::S=252: the number of days in a year.

Returns

  • ::AbstractFloat: the APY of investment.

source

OnlinePortfolioSelection.at Method
julia
at(rel_pr::AbstractMatrix, b::AbstractMatrix)

Calculate the average turnover of the portfolio. Also, see sn, mer, ir, ann_std, apy, ann_sharpe, mdd, and calmar.

Arguments

  • rel_pr::AbstractMatrix: The relative price of the stocks.

  • b::AbstractMatrix: The weights of the portfolio.

Returns

  • ::AbstractFloat: the average turnover of the portfolio.

source

OnlinePortfolioSelection.bcrp Method
julia
bcrp(rel_pr::AbstractMatrix{T}) where T<:AbstractFloat

Run Best Constant Rebalanced Portfolio (BCRP) algorithm.

Arguments

  • rel_pr::AbstractMatrix{T}: Relative price matrix.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
+true

References

Can We Learn to Beat the Best Stock

source

OnlinePortfolioSelection.apy Method
julia
apy(Sn::AbstractFloat, n_periods::S; dpy::S=252) where S<:Int

Calculate the Annual Percentage Yield (APY) of investment. Also, see sn, mer, ann_std, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • Sn::AbstractFloat: the cumulative wealth of investment.

  • n_periods::S: the number investment periods.

  • dpy::S=252: the number of days in a year.

Returns

  • ::AbstractFloat: the APY of investment.

source

OnlinePortfolioSelection.at Method
julia
at(rel_pr::AbstractMatrix, b::AbstractMatrix)

Calculate the average turnover of the portfolio. Also, see sn, mer, ir, ann_std, apy, ann_sharpe, mdd, and calmar.

Arguments

  • rel_pr::AbstractMatrix: The relative price of the stocks.

  • b::AbstractMatrix: The weights of the portfolio.

Returns

  • ::AbstractFloat: the average turnover of the portfolio.

source

OnlinePortfolioSelection.bcrp Method
julia
bcrp(rel_pr::AbstractMatrix{T}) where T<:AbstractFloat

Run Best Constant Rebalanced Portfolio (BCRP) algorithm.

Arguments

  • rel_pr::AbstractMatrix{T}: Relative price matrix.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> rel_pr = rand(3, 8);
 
@@ -100,7 +100,7 @@
  0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
 
 julia> sum(m_bcrp.b, dims=1) .|> isapprox(1.) |> all
-true

References

Universal Portfolios

source

OnlinePortfolioSelection.bk Method
julia
bk(rel_price::AbstractMatrix{T}, K::S, L::S, c::T) where {T<:AbstractFloat, S<:Integer}

Run Bᴷ algorithm.

Arguments

  • rel_price::AbstractMatrix{T}: Relative prices of assets.

  • K::S: Number of experts.

  • L::S: Number of time windows.

  • c::T: The similarity threshold.

Beware!

rel_price should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
+true

References

Universal Portfolios

source

OnlinePortfolioSelection.bk Method
julia
bk(rel_price::AbstractMatrix{T}, K::S, L::S, c::T) where {T<:AbstractFloat, S<:Integer}

Run Bᴷ algorithm.

Arguments

  • rel_price::AbstractMatrix{T}: Relative prices of assets.

  • K::S: Number of experts.

  • L::S: Number of time windows.

  • c::T: The similarity threshold.

Beware!

rel_price should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> daily_relative_prices = rand(3, 20);
 julia> nexperts = 10;
@@ -116,7 +116,7 @@
  0.333333  0.333333  0.322581  0.318677     0.333331  0.329797  0.322842  0.295789
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

Reference

NONPARAMETRIC KERNEL-BASED SEQUENTIAL INVESTMENT STRATEGIES

source

OnlinePortfolioSelection.bs Method
julia
bs(adj_close::Matrix{T}; last_n::Int=0) where {T<:Float64}

Run the Best So Far algorithm on the given data.

Arguments

  • adj_close::Matrix{T}: A matrix of adjusted closing prices of assets.

Keyword Arguments

  • last_n::Int: The number of periods to look back for the performance of each asset. If last_n is 0, then the performance is calculated from the first period to the previous period.

Beware!

The adj_close matrix should be in the order of assets x periods.

Returns

  • ::OPSAlgorithm(n_assets, b, alg): An instance of OPSAlgorithm.

Example

julia
julia> using OnlinePortfolioSelection
+true

Reference

NONPARAMETRIC KERNEL-BASED SEQUENTIAL INVESTMENT STRATEGIES

source

OnlinePortfolioSelection.bs Method
julia
bs(adj_close::Matrix{T}; last_n::Int=0) where {T<:Float64}

Run the Best So Far algorithm on the given data.

Arguments

  • adj_close::Matrix{T}: A matrix of adjusted closing prices of assets.

Keyword Arguments

  • last_n::Int: The number of periods to look back for the performance of each asset. If last_n is 0, then the performance is calculated from the first period to the previous period.

Beware!

The adj_close matrix should be in the order of assets x periods.

Returns

  • ::OPSAlgorithm(n_assets, b, alg): An instance of OPSAlgorithm.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> adj_close = rand(5, 10);
 
@@ -131,7 +131,7 @@
  0.2  0.0  0.0  0.0  0.0  0.0  0.0  1.0  0.0  0.0
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

References

KERNEL-BASED SEMI-LOG-OPTIMAL EMPIRICAL PORTFOLIO SELECTION STRATEGIES

source

OnlinePortfolioSelection.caeg Method
julia
caeg(rel_pr::AbstractMatrix, ηs::AbstractVector)

Run CAEG algorithm.

Arguments

  • rel_pr::AbstractMatrix: Historical relative prices. The paper's authors used "the ratio of closing price to last closing price".

  • ηs::AbstractVector: Learning rates.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection, YFinance
+true

References

KERNEL-BASED SEMI-LOG-OPTIMAL EMPIRICAL PORTFOLIO SELECTION STRATEGIES

source

OnlinePortfolioSelection.caeg Method
julia
caeg(rel_pr::AbstractMatrix, ηs::AbstractVector)

Run CAEG algorithm.

Arguments

  • rel_pr::AbstractMatrix: Historical relative prices. The paper's authors used "the ratio of closing price to last closing price".

  • ηs::AbstractVector: Learning rates.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "GOOG"];
 
@@ -155,7 +155,7 @@
 3×6 Matrix{Float64}:
  0.333333  0.333322  0.333286  0.333271  0.333287  0.333368
  0.333333  0.333295  0.333271  0.333171  0.333123  0.333076
- 0.333333  0.333383  0.333443  0.333558  0.33359   0.333557

References

Aggregating exponential gradient expert advice for online portfolio selection

source

OnlinePortfolioSelection.calmar Method
julia
calmar(APY::T, MDD::T) where T<:AbstractFloat

Calculate the Calmar Ratio of investment. Also, see sn, mer, ann_std, apy, ann_sharpe, mdd, and opsmetrics.

Arguments

  • APY::T: the APY of investment.

  • MDD::T: the MDD of investment.

Returns

  • ::AbstractFloat: the Calmar Ratio of investment.

source

OnlinePortfolioSelection.cluslog Function
julia
cluslog(
+ 0.333333  0.333383  0.333443  0.333558  0.33359   0.333557

References

Aggregating exponential gradient expert advice for online portfolio selection

source

OnlinePortfolioSelection.calmar Method
julia
calmar(APY::T, MDD::T) where T<:AbstractFloat

Calculate the Calmar Ratio of investment. Also, see sn, mer, ann_std, apy, ann_sharpe, mdd, and opsmetrics.

Arguments

  • APY::T: the APY of investment.

  • MDD::T: the MDD of investment.

Returns

  • ::AbstractFloat: the Calmar Ratio of investment.

source

OnlinePortfolioSelection.cluslog Function
julia
cluslog(
   rel_pr::AbstractMatrix{<:AbstractFloat},
   horizon::Int,
   TW::Int,
@@ -197,7 +197,7 @@
 2.02964e-6  2.02787e-6  2.02964e-6
 
 julia> sum(model.b , dims=1) .|> isapprox(1.) |> all
-true

See also KMNLOG, and KMDLOG.

Reference

An online portfolio selection algorithm using clustering approaches and considering transaction costs

source

OnlinePortfolioSelection.cornk Method
julia
cornk(
+true

See also KMNLOG, and KMDLOG.

Reference

An online portfolio selection algorithm using clustering approaches and considering transaction costs

source

OnlinePortfolioSelection.cornk Method
julia
cornk(
   x::AbstractMatrix{<:AbstractFloat},
   horizon::T,
   k::T,
@@ -215,7 +215,7 @@
 "CORN-K"
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

See cornu, and dricornk.

Reference

CORN: Correlation-driven nonparametric learning approach for portfolio selection

source

OnlinePortfolioSelection.cornu Method
julia
cornu(
+true

See cornu, and dricornk.

Reference

CORN: Correlation-driven nonparametric learning approach for portfolio selection

source

OnlinePortfolioSelection.cornu Method
julia
cornu(
   x::AbstractMatrix{T},
   horizon::M,
   w::M;
@@ -232,7 +232,7 @@
 "CORN-U"
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

See cornk, and dricornk.

Reference

CORN: Correlation-driven nonparametric learning approach for portfolio selection

source

OnlinePortfolioSelection.cwmr Function
julia
cwmr(
+true

See cornk, and dricornk.

Reference

CORN: Correlation-driven nonparametric learning approach for portfolio selection

source

OnlinePortfolioSelection.cwmr Function
julia
cwmr(
   rel_pr::AbstractMatrix,
   ϕ::AbstractFloat,
   ϵ::AbstractFloat,
@@ -288,7 +288,7 @@
 3×5 Matrix{Float64}:
  0.318927  0.768507  0.721524  0.753618  0.135071
  0.338759  0.111292  0.16003   0.133229  0.741106
- 0.342314  0.120201  0.118446  0.113154  0.123823

See Confidence Weighted Mean Reversion (CWMR) for more informaton and examples.

References

Confidence Weighted Mean Reversion Strategy for Online Portfolio Selection

source

OnlinePortfolioSelection.cwogd Method
julia
cwogd(
+ 0.342314  0.120201  0.118446  0.113154  0.123823

See Confidence Weighted Mean Reversion (CWMR) for more informaton and examples.

References

Confidence Weighted Mean Reversion Strategy for Online Portfolio Selection

source

OnlinePortfolioSelection.cwogd Method
julia
cwogd(
   rel_pr::AbstractMatrix,
   γ::AbstractFloat,
   H;
@@ -339,7 +339,7 @@
  0.333333  0.347847  0.342083  0.358819  0.355655  0.352137
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

References

[1] Combining expert weights for online portfolio selection based on the gradient descent algorithm.

source

OnlinePortfolioSelection.dmr Function
julia
dmr(
+true

References

[1] Combining expert weights for online portfolio selection based on the gradient descent algorithm.

source

OnlinePortfolioSelection.dmr Function
julia
dmr(
   x::AbstractMatrix,
   horizon::Integer,
   α::Union{Nothing, AbstractVector{<:AbstractFloat}},
@@ -393,7 +393,7 @@
  0.0454545  0.00218155  0.0930112       0.0934464    0.00218155   0.00218155
  0.0454545  0.0914433   0.0915956       0.000654204  0.000654204  0.000654204
  0.0454545  0.0937513   0.00289981   …  0.00289981   0.0937545    0.00289981
- 0.0454545  0.00669052  0.00669052      0.00669052   0.00669052   0.00669052

Reference

Distributed mean reversion online portfolio strategy with stock network

source

OnlinePortfolioSelection.dricornk Method
julia
dricornk(
+ 0.0454545  0.00669052  0.00669052      0.00669052   0.00669052   0.00669052

Reference

Distributed mean reversion online portfolio strategy with stock network

source

OnlinePortfolioSelection.dricornk Method
julia
dricornk(
   x::AbstractMatrix{T},
   relpr_market::AbstractVector{T},
   horizon::M,
@@ -410,7 +410,7 @@
 julia> m_dricornk = dricornk(stocks_ret, market_ret, 5, 2, 4, 3);
 
 julia> sum(m_dricornk.b, dims=1) .|> isapprox(1.) |> all
-true

See cornk, and cornu.

Reference

DRICORN-K: A Dynamic RIsk CORrelation-driven Non-parametric Algorithm for Online Portfolio Selection

source

OnlinePortfolioSelection.eg Method
julia
eg(rel_pr::AbstractMatrix; eta::AbstractFloat=0.05)

Run Exponential Gradient (EG) algorithm.

Arguments

  • rel_pr::AbstractMatrix: Historical relative prices.

Keyword Arguments

  • eta::AbstractFloat=0.05: Learning rate.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection
+true

See cornk, and cornu.

Reference

DRICORN-K: A Dynamic RIsk CORrelation-driven Non-parametric Algorithm for Online Portfolio Selection

source

OnlinePortfolioSelection.eg Method
julia
eg(rel_pr::AbstractMatrix; eta::AbstractFloat=0.05)

Run Exponential Gradient (EG) algorithm.

Arguments

  • rel_pr::AbstractMatrix: Historical relative prices.

Keyword Arguments

  • eta::AbstractFloat=0.05: Learning rate.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection
 
 julia> typeof(rel_pr), size(rel_pr)
 (Matrix{Float64}, (3, 10))
@@ -424,7 +424,7 @@
  0.333333  0.32063   0.327267  0.331649  0.325843  0.31204   0.308873  0.294239  0.300652  0.304799
 
 julia> sum(m_eg.b, dims=1) .|> isapprox(1.0) |> all
-true

References

On-Line Portfolio Selection Using Multiplicative Updates

source

OnlinePortfolioSelection.egm Function
julia
egm(rel_pr::AbstractMatrix, model::EGMFramework, η::AbstractFloat=0.05)

Run the Exponential Gradient with Momentum (EGM) algorithm. This framework contains three variants: EGE, EGR and EGA.

Arguments

  • rel_pr::AbstractMatrix: matrix of size n_assets by n_periods containing the relative prices.

  • model::EGMFramework: EGM framework. EGE, EGR or EGA can be used.

  • η::AbstractFloat=0.05: learning rate.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+true

References

On-Line Portfolio Selection Using Multiplicative Updates

source

OnlinePortfolioSelection.egm Function
julia
egm(rel_pr::AbstractMatrix, model::EGMFramework, η::AbstractFloat=0.05)

Run the Exponential Gradient with Momentum (EGM) algorithm. This framework contains three variants: EGE, EGR and EGA.

Arguments

  • rel_pr::AbstractMatrix: matrix of size n_assets by n_periods containing the relative prices.

  • model::EGMFramework: EGM framework. EGE, EGR or EGA can be used.

  • η::AbstractFloat=0.05: learning rate.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "GOOG"];
 
@@ -469,7 +469,7 @@
 3×7 Matrix{Float64}:
  0.333333  0.349056  0.350429  0.350706  0.348071  0.345757  0.343929
  0.333333  0.326833  0.327223  0.326516  0.327857  0.326514  0.327842
- 0.333333  0.324111  0.322348  0.322779  0.324072  0.327729  0.328229

References

Exponential Gradient with Momentum for Online Portfolio Selection

source

OnlinePortfolioSelection.gwr Function
julia
gwr(
+ 0.333333  0.324111  0.322348  0.322779  0.324072  0.327729  0.328229

References

Exponential Gradient with Momentum for Online Portfolio Selection

source

OnlinePortfolioSelection.gwr Function
julia
gwr(
   prices::AbstractMatrix,
   horizon::Integer,
   τ::Real=2.8,
@@ -523,12 +523,12 @@
 3×3 Matrix{Float64}:
  0.333333  0.0  1.20769e-11
  0.333333  0.0  0.0
- 0.333333  1.0  1.0

Reference

Gaussian Weighting Reversion Strategy for Accurate On-line Portfolio Selection

source

OnlinePortfolioSelection.ir Method
julia
ir(
+ 0.333333  1.0  1.0

Reference

Gaussian Weighting Reversion Strategy for Accurate On-line Portfolio Selection

source

OnlinePortfolioSelection.ir Method
julia
ir(
   weights::AbstractMatrix{S},
   rel_pr::AbstractMatrix{S},
   rel_pr_market::AbstractVector{S};
   init_inv::S=1.
-) where S<:AbstractFloat

Calculate the Information Ratio (IR) of portfolio. Also, see sn, mer, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

The formula for calculating the Information Ratio (IR) of portfolio is as follows:

IR=R¯s−R¯mσ(Rs−Rm)

where Rs represents the portfolio's daily return, Rm represents the market's daily return, R¯s represents the portfolio's average daily return, R¯m represents the market's average daily return, and σ represents the standard deviation of the portfolio's daily excess return over the market. Note that in this package, the logarithmic return is used.

Arguments

  • weights::AbstractMatrix{S}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{S}: the relative price of the stocks.

  • rel_pr_market::AbstractVector{S}: the relative price of the market.

Keyword Arguments

  • init_inv::S=1: the initial investment.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used. The size of rel_pr_market will automatically be adjusted to the size of w.

Returns

  • ::AbstractFloat: the Information Ratio (IR) of portfolio for the investment period.

References

Adaptive online portfolio strategy based on exponential gradient updates

source

OnlinePortfolioSelection.ktpt Function
julia
function ktpt(
+) where S<:AbstractFloat

Calculate the Information Ratio (IR) of portfolio. Also, see sn, mer, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

The formula for calculating the Information Ratio (IR) of portfolio is as follows:

IR=R¯s−R¯mσ(Rs−Rm)

where Rs represents the portfolio's daily return, Rm represents the market's daily return, R¯s represents the portfolio's average daily return, R¯m represents the market's average daily return, and σ represents the standard deviation of the portfolio's daily excess return over the market. Note that in this package, the logarithmic return is used.

Arguments

  • weights::AbstractMatrix{S}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{S}: the relative price of the stocks.

  • rel_pr_market::AbstractVector{S}: the relative price of the market.

Keyword Arguments

  • init_inv::S=1: the initial investment.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used. The size of rel_pr_market will automatically be adjusted to the size of w.

Returns

  • ::AbstractFloat: the Information Ratio (IR) of portfolio for the investment period.

References

Adaptive online portfolio strategy based on exponential gradient updates

source

OnlinePortfolioSelection.ktpt Function
julia
function ktpt(
   prices::AbstractMatrix,
   horizon::S,
   w::S,
@@ -555,7 +555,7 @@
  0.25  0.0  1.0  1.0  1.0
  0.25  0.0  0.0  0.0  0.0
  0.25  1.0  0.0  0.0  0.0
- 0.25  0.0  0.0  0.0  0.0

Reference

A kernel-based trend pattern tracking system for portfolio optimization

source

OnlinePortfolioSelection.load Method
julia
load(adj_close::AbstractMatrix{T}, α::T, ω::S, horizon::S, η::T, ϵ::T=1.5) where {T<:Float64, S<:Int}

Run LOAD algorithm.

Arguments

  • adj_close::AbstractMatrix{T}: Adjusted close price data.

  • α::T: Decay factor. (0 < α < 1)

  • ω::S: Window size. (ω > 0)

  • horizon::S: Investment horizon. (n_periods > horizon > 0)

  • η::T: Threshold value. (η > 0)

  • ϵ::T=1.5: Expected return threshold value.

Beware!

adj_close should be a matrix of size n_assets × n_periods.

Returns

  • ::OPSAlgorithm: An object of type OPSAlgorithm containing the weights of each asset for each period.

Example

julia
# Get data
+ 0.25  0.0  0.0  0.0  0.0

Reference

A kernel-based trend pattern tracking system for portfolio optimization

source

OnlinePortfolioSelection.load Method
julia
load(adj_close::AbstractMatrix{T}, α::T, ω::S, horizon::S, η::T, ϵ::T=1.5) where {T<:Float64, S<:Int}

Run LOAD algorithm.

Arguments

  • adj_close::AbstractMatrix{T}: Adjusted close price data.

  • α::T: Decay factor. (0 < α < 1)

  • ω::S: Window size. (ω > 0)

  • horizon::S: Investment horizon. (n_periods > horizon > 0)

  • η::T: Threshold value. (η > 0)

  • ϵ::T=1.5: Expected return threshold value.

Beware!

adj_close should be a matrix of size n_assets × n_periods.

Returns

  • ::OPSAlgorithm: An object of type OPSAlgorithm containing the weights of each asset for each period.

Example

julia
# Get data
 julia> using YFinance
 julia> startdt, enddt = "2022-04-01", "2023-04-27";
 julia> querry = [
@@ -577,7 +577,7 @@
  0.2  6.06128e-9  0.0        0.0       0.0
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

References

A local adaptive learning system for online portfolio selection

source

OnlinePortfolioSelection.maeg Method
julia
maeg(x::AbstractMatrix, w::Integer, H::AbstractVector)

Run Moving-window-based Adaptive Exponential Gradient (MAEG) algorithm.

Arguments

  • x::AbstractMatrix: A matrix of price relatives of n_assets over n_periods.

  • w::Integer: The window size.

  • H::AbstractVector: A vector of learning rates.

Returns

Beware!

x should be a matrix of size n_assets × n_periods.

Example

julia
julia> using OnlinePortfolioSelection
+true

References

A local adaptive learning system for online portfolio selection

source

OnlinePortfolioSelection.maeg Method
julia
maeg(x::AbstractMatrix, w::Integer, H::AbstractVector)

Run Moving-window-based Adaptive Exponential Gradient (MAEG) algorithm.

Arguments

  • x::AbstractMatrix: A matrix of price relatives of n_assets over n_periods.

  • w::Integer: The window size.

  • H::AbstractVector: A vector of learning rates.

Returns

Beware!

x should be a matrix of size n_assets × n_periods.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> rel_pr = rand(4, 10);
 
@@ -592,11 +592,11 @@
  0.25  0.250307  0.25129   0.251673  0.250823  0.267687  0.313794  0.319425  0.378182  0.427249
  0.25  0.249138  0.248921  0.249289  0.250482  0.23192   0.202576  0.179329  0.160005  0.168903
  0.25  0.250026  0.250656  0.24931   0.24995   0.226647  0.237694  0.237879  0.216076  0.192437
- 0.25  0.250528  0.249134  0.249728  0.248744  0.273746  0.245936  0.263367  0.245737  0.211411

References

Adaptive online portfolio strategy based on exponential gradient updates

source

OnlinePortfolioSelection.mdd Method
julia
mdd(Sn::AbstractVector{T}) where T<:AbstractFloat

Calculate the Maximum Drawdown (MDD) of investment. Also, see sn, mer, ann_std, apy, ann_sharpe, calmar, and opsmetrics.

Arguments

  • Sn::AbstractVector{T}: the cumulative wealth of investment during the investment period. see sn.

Returns

  • ::AbstractFloat: the MDD of investment.

source

OnlinePortfolioSelection.mer Method
julia
mer(
+ 0.25  0.250528  0.249134  0.249728  0.248744  0.273746  0.245936  0.263367  0.245737  0.211411

References

Adaptive online portfolio strategy based on exponential gradient updates

source

OnlinePortfolioSelection.mdd Method
julia
mdd(Sn::AbstractVector{T}) where T<:AbstractFloat

Calculate the Maximum Drawdown (MDD) of investment. Also, see sn, mer, ann_std, apy, ann_sharpe, calmar, and opsmetrics.

Arguments

  • Sn::AbstractVector{T}: the cumulative wealth of investment during the investment period. see sn.

Returns

  • ::AbstractFloat: the MDD of investment.

source

OnlinePortfolioSelection.mer Method
julia
mer(
   weights::AbstractMatrix{T},
   rel_pr::AbstractMatrix{T},
   𝘷::T=0.
-) where T<:AbstractFloat

Calculate the investments's Mean excess return (MER). Also, see sn, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

  • 𝘷::T=0.: the transaction cost rate.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

  • MER::AbstractFloat: the investments's Mean excess return (MER).

source

OnlinePortfolioSelection.mrvol Method
julia
mrvol(
+) where T<:AbstractFloat

Calculate the investments's Mean excess return (MER). Also, see sn, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

  • 𝘷::T=0.: the transaction cost rate.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

  • MER::AbstractFloat: the investments's Mean excess return (MER).

source

OnlinePortfolioSelection.mrvol Method
julia
mrvol(
   rel_pr::AbstractMatrix{T},
   rel_vol::AbstractMatrix{T},
   horizon::S,
@@ -637,7 +637,7 @@
 3×100 Matrix{Float64}:
  0.333333  0.0204062  0.0444759  …  0.38213   0.467793
  0.333333  0.359864   0.194139      0.213264  0.281519
- 0.333333  0.61973    0.761385      0.404606  0.250689

References

Online portfolio selection of integrating expert strategies based on mean reversion and trading volume.

source

OnlinePortfolioSelection.oldem Method
julia
oldem(
+ 0.333333  0.61973    0.761385      0.404606  0.250689

References

Online portfolio selection of integrating expert strategies based on mean reversion and trading volume.

source

OnlinePortfolioSelection.oldem Method
julia
oldem(
   rel_pr::AbstractMatrix,
   horizon::S,
   w::S,
@@ -680,7 +680,7 @@
  0.2  1.0         0.0         0.0
  0.2  0.0         0.0         1.99964e-8
  0.2  0.0         0.0         1.0
- 0.2  0.0         1.99964e-8  0.0

References

Online portfolio selection with predictive instantaneous risk assessment

source

OnlinePortfolioSelection.olmar Method
julia
olmar(rel_pr::AbstractMatrix, horizon::Int, ω::Int, ϵ::Int)
+ 0.2  0.0         1.99964e-8  0.0

References

Online portfolio selection with predictive instantaneous risk assessment

source

OnlinePortfolioSelection.olmar Method
julia
olmar(rel_pr::AbstractMatrix, horizon::Int, ω::Int, ϵ::Int)
 olmar(rel_pr::AbstractMatrix, horizon::Int, ω::AbstractVector{<:Int}, ϵ::Int)

Method 1

Run the Online Moving Average Reversion algorithm (OLMAR).

Arguments

  • rel_pr::AbstractMatrix: Matrix of relative prices.

  • horizon::Int: Investment horizon.

  • ω::Int: Window size.

  • ϵ::Int: Reversion threshold.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "AMZN", "GOOG", "META"];
@@ -732,7 +732,7 @@
  0.2  0.2  1.31177e-8  0.555158  0.0
  0.2  0.2  6.57906e-9  0.0       0.667358
  0.2  0.2  0.0         0.0       0.332642
- 0.2  0.2  0.666667    0.282545  0.0

References

On-Line Portfolio Selection with Moving Average Reversion

source

OnlinePortfolioSelection.ons Function
julia
ons(rel_pr::AbstractMatrix, β::Integer=1, 𝛿::AbstractFloat=1/8, η::AbstractFloat=0.)

Run Online Newton Step (ONS) algorithm.

Arguments

  • rel_pr::AbstractMatrix: relative prices.

  • β::Integer=1: Hyperparameter.

  • 𝛿::AbstractFloat=1/8: Heuristic tuning parameter.

  • η::AbstractFloat=0.: Learning rate.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+ 0.2  0.2  0.666667    0.282545  0.0

References

On-Line Portfolio Selection with Moving Average Reversion

source

OnlinePortfolioSelection.ons Function
julia
ons(rel_pr::AbstractMatrix, β::Integer=1, 𝛿::AbstractFloat=1/8, η::AbstractFloat=0.)

Run Online Newton Step (ONS) algorithm.

Arguments

  • rel_pr::AbstractMatrix: relative prices.

  • β::Integer=1: Hyperparameter.

  • 𝛿::AbstractFloat=1/8: Heuristic tuning parameter.

  • η::AbstractFloat=0.: Learning rate.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "GOOG"];
 
@@ -748,7 +748,7 @@
 3×6 Matrix{Float64}:
  0.333333  0.333327  0.333293  0.333295  0.333319  0.333375
  0.333333  0.333302  0.333221  0.333182  0.333205  0.333184
- 0.333333  0.333371  0.333486  0.333524  0.333475  0.333441

References

Algorithms for Portfolio Management based on the Newton Method

source

OnlinePortfolioSelection.opsmethods Method
julia
opsmethods()

Print the available algorithms in the package.

Example

julia
julia> using OnlinePortfolioSelection
+ 0.333333  0.333371  0.333486  0.333524  0.333475  0.333441

References

Algorithms for Portfolio Management based on the Newton Method

source

OnlinePortfolioSelection.opsmethods Method
julia
opsmethods()

Print the available algorithms in the package.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> opsmethods()
 
@@ -759,7 +759,7 @@
         up: Universal Portfolio - Call `up`
         eg: Exponential Gradient - Call `eg`
      cornu: CORN-U - Call `cornu`
-          ⋮

source

OnlinePortfolioSelection.opsmetrics Method
julia
opsmetrics(
+          ⋮

source

OnlinePortfolioSelection.opsmetrics Method
julia
opsmetrics(
   weights::AbstractMatrix{T},
   rel_pr::AbstractMatrix{T},
   rel_pr_market::AbstractVector{T};
@@ -768,7 +768,7 @@
   dpy::S=252,
   v::T=0.
   dpy::S=252
-) where {T<:AbstractFloat, S<:Int}

Calculate the metrics of an OPS algorithm. Also, see sn, mer, ir, ann_std, apy, ann_sharpe, mdd, and calmar.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

  • rel_pr_market::AbstractVector{T}: the relative price of the market.

Keyword Arguments

  • init_inv::T=1: the initial investment.

  • Rf::T=0.02: the risk-free rate of return.

  • dpy::S=252: the number of days in a year.

  • v::T=0.: the transaction cost rate.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

source

OnlinePortfolioSelection.pamr Method
julia
pamr(rel_pr::AbstractMatrix, ϵ::AbstractFloat, C::AbstractFloat, model::PAMRModel)

Run the PAMR algorithm on the matrix of relative prices rel_pr.

Arguments

  • rel_pr::AbstractMatrix: matrix of relative prices.

  • ϵ::AbstractFloat: Sensitivity parameter.

  • C::AbstractFloat: Aggressiveness parameter.

  • model::PAMRModel: PAMR model to use. All three variants, namely, PAMR(), PAMR1(), and PAMR2() are supported.

Beware!

rel_price should be a matrix of size n_assets × n_periods.

Output

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+) where {T<:AbstractFloat, S<:Int}

Calculate the metrics of an OPS algorithm. Also, see sn, mer, ir, ann_std, apy, ann_sharpe, mdd, and calmar.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

  • rel_pr_market::AbstractVector{T}: the relative price of the market.

Keyword Arguments

  • init_inv::T=1: the initial investment.

  • Rf::T=0.02: the risk-free rate of return.

  • dpy::S=252: the number of days in a year.

  • v::T=0.: the transaction cost rate.

Warning

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

source

OnlinePortfolioSelection.pamr Method
julia
pamr(rel_pr::AbstractMatrix, ϵ::AbstractFloat, C::AbstractFloat, model::PAMRModel)

Run the PAMR algorithm on the matrix of relative prices rel_pr.

Arguments

  • rel_pr::AbstractMatrix: matrix of relative prices.

  • ϵ::AbstractFloat: Sensitivity parameter.

  • C::AbstractFloat: Aggressiveness parameter.

  • model::PAMRModel: PAMR model to use. All three variants, namely, PAMR(), PAMR1(), and PAMR2() are supported.

Beware!

rel_price should be a matrix of size n_assets × n_periods.

Output

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "MSFT", "AMZN", "META", "GOOG"]
 
@@ -821,7 +821,7 @@
  0.2  0.197589  0.198123  0.199895     0.175224  0.179199  0.178376  0.178291
  0.2  0.193636  0.192928  0.183242     0.279176  0.27052   0.270138  0.271307
  0.2  0.194936  0.19525   0.197214     0.183626  0.185922  0.185215  0.188272
- 0.2  0.194746  0.192736  0.195701     0.242882  0.245346  0.247319  0.248279

References

PAMR: Passive aggressive mean reversion strategy for portfolio selection

source

OnlinePortfolioSelection.ppt Function
julia
ppt(
+ 0.2  0.194746  0.192736  0.195701     0.242882  0.245346  0.247319  0.248279

References

PAMR: Passive aggressive mean reversion strategy for portfolio selection

source

OnlinePortfolioSelection.ppt Function
julia
ppt(
   prices::AbstractMatrix,
   w::Int,
   ϵ::Int,
@@ -838,7 +838,7 @@
 julia> model = ppt(prices, 10, 100, 100);
 
 julia> sum(model, dims=1) .|> isapprox(1.) |> all
-true

References

A Peak Price Tracking-Based Learning System for Portfolio Selection

source

OnlinePortfolioSelection.rmr Method
julia
rmr(p::AbstractMatrix, horizon::Integer, w::Integer, ϵ, m, τ)

Run Robust Median Reversion (RMR) algorithm.

Arguments

  • p::AbstractMatrix: Prices matrix.

  • horizon::Integer: Number of periods to run the algorithm.

  • w::Integer: Window size.

  • ϵ: Reversion threshold.

  • m: Maxmimum number of iterations.

  • τ: Toleration level.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+true

References

A Peak Price Tracking-Based Learning System for Portfolio Selection

source

OnlinePortfolioSelection.rmr Method
julia
rmr(p::AbstractMatrix, horizon::Integer, w::Integer, ϵ, m, τ)

Run Robust Median Reversion (RMR) algorithm.

Arguments

  • p::AbstractMatrix: Prices matrix.

  • horizon::Integer: Number of periods to run the algorithm.

  • w::Integer: Window size.

  • ϵ: Reversion threshold.

  • m: Maxmimum number of iterations.

  • τ: Toleration level.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["GOOG", "AAPL", "MSFT", "AMZN"];
 
@@ -863,7 +863,7 @@
  0.25  1.0         1.0       1.0         1.0
  0.25  0.0         0.0       0.0         0.0
  0.25  0.0         0.0       0.0         0.0
- 0.25  1.14513e-8  9.979e-9  9.99353e-9  1.03254e-8

Reference

Robust Median Reversion Strategy for Online Portfolio Selection

source

OnlinePortfolioSelection.rprt Method
julia
function rprt(
+ 0.25  1.14513e-8  9.979e-9  9.99353e-9  1.03254e-8

Reference

Robust Median Reversion Strategy for Online Portfolio Selection

source

OnlinePortfolioSelection.rprt Method
julia
function rprt(
   rel_pr::AbstractMatrix{T},
   horizon::Integer,
   w::Integer=5,
@@ -888,7 +888,7 @@
  0.2  2.03615e-10
 
 julia> sum(m_rprt.b, dims=1) .|> isapprox(1.) |> all
-true

Reference

Reweighted Price Relative Tracking System for Automatic Portfolio Optimization

source

OnlinePortfolioSelection.sn Method
julia
sn(weights::AbstractMatrix{T}, rel_pr::AbstractMatrix{T}; init_inv::T=1.) where T<:AbstractFloat

Calculate the cumulative wealth of the portfolio during a period of time. Also, see mer, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

The formula for calculating the cumulative wealth of the portfolio is as follows:

Sn=S0∏t=1T⟨bt,xt⟩

where S0 is the initial budget, n is the investment horizon, bt is the vector of weights of the period t, and xt is the relative price of the t-th period.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

Keyword Arguments

  • init_inv::T=1: the initial investment.

Beware!

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

  • all_sn::Vector{T}: the cumulative wealth of investment during the investment period.

source

OnlinePortfolioSelection.spolc Method
julia
spolc(x::AbstractMatrix, 𝛾::AbstractFloat, w::Integer)

Run loss control strategy with a rank-one covariance estimate for short-term portfolio optimization (SPOLC).

Arguments

  • x::AbstractMatrix: Matrix of relative prices.

  • 𝛾::AbstractFloat: Mixing parameter that trades off between the increasing factor and the risk.

  • w::Integer: Window size.

Beware!

x should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
+true

Reference

Reweighted Price Relative Tracking System for Automatic Portfolio Optimization

source

OnlinePortfolioSelection.sn Method
julia
sn(weights::AbstractMatrix{T}, rel_pr::AbstractMatrix{T}; init_inv::T=1.) where T<:AbstractFloat

Calculate the cumulative wealth of the portfolio during a period of time. Also, see mer, ann_std, apy, ann_sharpe, mdd, calmar, and opsmetrics.

The formula for calculating the cumulative wealth of the portfolio is as follows:

Sn=S0∏t=1T⟨bt,xt⟩

where S0 is the initial budget, n is the investment horizon, bt is the vector of weights of the period t, and xt is the relative price of the t-th period.

Arguments

  • weights::AbstractMatrix{T}: the weights of the portfolio.

  • rel_pr::AbstractMatrix{T}: the relative price of the stocks.

Keyword Arguments

  • init_inv::T=1: the initial investment.

Beware!

The size of weights and rel_pr must be (n_stocks, n_periods).

Note

If size(rel_pr, 2) is greater than size(weights, 2), then the last size(weights, 2) columns of rel_pr will be used.

Returns

  • all_sn::Vector{T}: the cumulative wealth of investment during the investment period.

source

OnlinePortfolioSelection.spolc Method
julia
spolc(x::AbstractMatrix, 𝛾::AbstractFloat, w::Integer)

Run loss control strategy with a rank-one covariance estimate for short-term portfolio optimization (SPOLC).

Arguments

  • x::AbstractMatrix: Matrix of relative prices.

  • 𝛾::AbstractFloat: Mixing parameter that trades off between the increasing factor and the risk.

  • w::Integer: Window size.

Beware!

x should be a matrix of size n_assets × n_periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection, YFinance
 
 julia> tickers = ["AAPL", "AMZN", "GOOG", "MSFT"];
 
@@ -908,7 +908,7 @@
  0.25  0.260742  0.248247  0.243466     2.99939e-6  3.04485e-6  1.56805e-6
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

Reference

Loss Control with Rank-one Covariance Estimate for Short-term Portfolio Optimization

source

OnlinePortfolioSelection.sspo Function
julia
sspo(
+true

Reference

Loss Control with Rank-one Covariance Estimate for Short-term Portfolio Optimization

source

OnlinePortfolioSelection.sspo Function
julia
sspo(
   p::AbstractMatrix,
   horizon::Integer,
   w::Integer,
@@ -938,7 +938,7 @@
  0.25  9.92018e-9  1.0         1.0  1.0
  0.25  0.0         0.0         0.0  0.0
  0.25  0.0         0.0         0.0  0.0
- 0.25  1.0         9.94367e-9  0.0  0.0

Reference

Short-term Sparse Portfolio Optimization Based on Alternating Direction Method of Multipliers

source

OnlinePortfolioSelection.tco Function
julia
tco(
+ 0.25  1.0         9.94367e-9  0.0  0.0

Reference

Short-term Sparse Portfolio Optimization Based on Alternating Direction Method of Multipliers

source

OnlinePortfolioSelection.tco Function
julia
tco(
   x::AbstractMatrix,
   w::Integer,
   horizon::Integer,
@@ -974,7 +974,7 @@
  0.05  0.0809567  0.0850694  0.0871646  0.0865584
  0.05  0.0809567  0.0830907  0.0890398  0.0885799
  0.7   0.730957   0.756827   0.746137   0.748113
- 0.2   0.10713    0.0750128  0.0776584  0.0767483

Reference

Transaction cost optimization for online portfolio selection

source

OnlinePortfolioSelection.tppt Function
julia
tppt(
+ 0.2   0.10713    0.0750128  0.0776584  0.0767483

Reference

Transaction cost optimization for online portfolio selection

source

OnlinePortfolioSelection.tppt Function
julia
tppt(
   prices::AbstractMatrix,
   horizon::Integer,
   w::Integer,
@@ -996,7 +996,7 @@
 3×3 Matrix{Float64}:
  0.333333  1.52594e-6  7.35766e-7
  0.333333  5.30452e-6  3.90444e-6
- 0.333333  0.999993    0.999995

References

An online portfolio strategy based on trend promote price tracing ensemble learning algorithm

source

OnlinePortfolioSelection.ttest Function
julia
ttest(vec::AbstractVector{<:AbstractVector})
+ 0.333333  0.999993    0.999995

References

An online portfolio strategy based on trend promote price tracing ensemble learning algorithm

source

OnlinePortfolioSelection.ttest Function
julia
ttest(vec::AbstractVector{<:AbstractVector})
 ttest(SB::AbstractVector, Sₜ::AbstractVector, SF::AbstractFloat)

Method 1

julia
ttest(vec::AbstractVector{<:AbstractVector})

Perform a one sample t-test of the null hypothesis that n values with mean x̄ and sample standard deviation stddev come from a distribution with mean μ0 against the alternative hypothesis that the distribution does not have mean μ0. The t-test with 95% confidence level applies on each pair of vectors in the vec vector. Each vector should contain the Annual Percentage Yield (APY) of a different algorithm on various datasets.

Note

You have to install and import the HypothesisTests package to use this function.

Arguments

  • vec::AbstractVector{<:AbstractVector}: A vector of vectors. Each inner vector should be of the same size.

Returns

  • ::Matrix{<:AbstractFloat}: A matrix of p-values for each pair of algorithms.

Example

julia
julia> using OnlinePortfolioSelection, HypothesisTests
 
 julia> apys = [
@@ -1009,12 +1009,12 @@
 3×3 Matrix{Float64}:
  0.0  1.0  0.702697
  0.0  0.0  0.843672
- 0.0  0.0  0.0

Method 2

julia
ttest(SB::AbstractVector, Sₜ::AbstractVector, SF::AbstractFloat)

Performs a t-student test to check whether the returns gained by a trading algorithm is due to a simple luck.

Note

You have to install and import the GLM package to use this function.

Arguments

  • SB::AbstractVector: Denotes the daily returns of the benchmark (market index)

  • Sₜ::AbstractVector: Portfolio daily returns

  • SF::AbstractFloat: Daily returns of the risk-free assets (Can be set to Treasury bill value or annual interest rate.)

  • ::StatsModels.TableRegressionModel: An object of type TableRegressionModel including the values of t-student test analysis.

source

OnlinePortfolioSelection.uniform Method
julia
uniform(n_assets::Int, horizon::Int)

Construct uniform portfolios.

Arguments

  • n_assets::Int: The number of assets.

  • horizon::Int: The number of investment periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
+ 0.0  0.0  0.0

Method 2

julia
ttest(SB::AbstractVector, Sₜ::AbstractVector, SF::AbstractFloat)

Performs a t-student test to check whether the returns gained by a trading algorithm is due to a simple luck.

Note

You have to install and import the GLM package to use this function.

Arguments

  • SB::AbstractVector: Denotes the daily returns of the benchmark (market index)

  • Sₜ::AbstractVector: Portfolio daily returns

  • SF::AbstractFloat: Daily returns of the risk-free assets (Can be set to Treasury bill value or annual interest rate.)

  • ::StatsModels.TableRegressionModel: An object of type TableRegressionModel including the values of t-student test analysis.

source

OnlinePortfolioSelection.uniform Method
julia
uniform(n_assets::Int, horizon::Int)

Construct uniform portfolios.

Arguments

  • n_assets::Int: The number of assets.

  • horizon::Int: The number of investment periods.

Returns

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> model = uniform(3, 10)
 
 julia> sum(model.b, dims=1) .|> isapprox(1.) |> all
-true

source

OnlinePortfolioSelection.up Method
julia
function up(
+true

source

OnlinePortfolioSelection.up Method
julia
function up(
   rel_pr::AbstractMatrix{T};
   eval_points::Integer=10^4
 ) where T<:AbstractFloat

Universal Portfolio (UP) algorithm.

Calculate the Universal Portfolio (UP) weights and budgets using the given historical prices and parameters.

Arguments

  • rel_pr::AbstractMatrix{T}: Historical relative prices.

Keyword Arguments

  • eval_points::Integer=10^4: Number of evaluation points.

Beware!

rel_pr should be a matrix of size n_assets × n_periods.

Returns

Examples

julia
julia> using OnlinePortfolioSelection
@@ -1030,7 +1030,7 @@
  0.333333  0.439276  0.338551  0.364661  0.438512  0.429483  0.448695  0.388281  0.330729
 
 julia> sum(m_up.b, dims=1) .|> isapprox(1.) |> all
-true

References

Universal Portfolios

source

OnlinePortfolioSelection.waeg Method
julia
waeg(x::AbstractMatrix, ηₘᵢₙ::AbstractFloat, ηₘₐₓ::AbstractFloat, k::Integer)

Run Weak Aggregating Exponential Gradient (WAEG) algorithm.

Arguments

  • x::AbstractMatrix: matrix of relative prices.

  • ηₘᵢₙ::AbstractFloat: minimum learning rate.

  • ηₘₐₓ::AbstractFloat: maximum learning rate.

  • k::Integer: number of EG experts.

Returns

Beware!

x should be a matrix of size n_assets × n_periods.

Example

julia
julia> using OnlinePortfolioSelection
+true

References

Universal Portfolios

source

OnlinePortfolioSelection.waeg Method
julia
waeg(x::AbstractMatrix, ηₘᵢₙ::AbstractFloat, ηₘₐₓ::AbstractFloat, k::Integer)

Run Weak Aggregating Exponential Gradient (WAEG) algorithm.

Arguments

  • x::AbstractMatrix: matrix of relative prices.

  • ηₘᵢₙ::AbstractFloat: minimum learning rate.

  • ηₘₐₓ::AbstractFloat: maximum learning rate.

  • k::Integer: number of EG experts.

Returns

Beware!

x should be a matrix of size n_assets × n_periods.

Example

julia
julia> using OnlinePortfolioSelection
 
 julia> rel_pr = rand(4, 8);
 
@@ -1044,8 +1044,8 @@
  0.25  0.254368  0.25124   0.235057  0.23561   0.220668  0.219505  0.205937
 
 julia> sum(m.b, dims=1) .|> isapprox(1.) |> all
-true

References

Boosting Exponential Gradient Strategy for Online Portfolio Selection: An Aggregating Experts’ Advice Method

source

- +true

References

Boosting Exponential Gradient Strategy for Online Portfolio Selection: An Aggregating Experts’ Advice Method

source

+ \ No newline at end of file diff --git a/dev/hashmap.json b/dev/hashmap.json index 2ce9575..9fc6771 100644 --- a/dev/hashmap.json +++ b/dev/hashmap.json @@ -1 +1 @@ -{"combined.md":"BHEZsh8z","fl.md":"Duapix2k","fw.md":"BUAnLcBA","ml.md":"Btt0q-LA","pm.md":"BhngT5Q3","benchmark.md":"C2J6R3eR","fetchdata.md":"CJJ2qcfF","funcs.md":"Cq4wBRKn","index.md":"ueZVIQJj","performance_eval.md":"B6yrH4bi","python.md":"BTuohqcp","refs.md":"M4OdoUAT","types.md":"B3bPqqkV"} +{"combined.md":"BHEZsh8z","fl.md":"Duapix2k","fw.md":"BUAnLcBA","ml.md":"Btt0q-LA","pm.md":"BhngT5Q3","benchmark.md":"C2J6R3eR","fetchdata.md":"CJJ2qcfF","funcs.md":"OMbgMkND","index.md":"ueZVIQJj","performance_eval.md":"B6yrH4bi","python.md":"BTuohqcp","refs.md":"M4OdoUAT","types.md":"28jHlNVY"} diff --git a/dev/index.html b/dev/index.html index 51ed486..75eb937 100644 --- a/dev/index.html +++ b/dev/index.html @@ -8,9 +8,9 @@ - + - + @@ -73,7 +73,7 @@ 1 │ CORN-U 0.0514619 0.0963865 -0.126009 -0.505762 0.288691 -1.25383 0.100499 0.847198 2 │ CORN-K 0.054396 0.198546 0.826495 2.48378 0.324705 17.688 0.0467263 0.87319 3 │ DRICORN-K 0.0507907 0.0829576 -0.2487 -1.21085 0.22191 -2.54629 0.0976717 0.0053658

The comparison analysis, via comp_algs, highlights that CORN-K outperforms the other algorithms in terms of annualized percentage yield (APY), annualized Sharpe ratio, Calmar ratio, and maximum drawdown (MDD). However, it's essential to note that the annualized standard deviation of CORN-K surpasses that of the other algorithms within this dataset. These individual metrics can be computed separately by using corresponding functions such as sn, mer, ir. For further insights and details, please refer to the Performance evaluation.

References ​

Bibliography ​

  1. B. Li and S. C. Hoi. Online Portfolio Selection: A Survey (2013).
- + \ No newline at end of file diff --git a/dev/performance_eval.html b/dev/performance_eval.html index 8f728c4..184dc5f 100644 --- a/dev/performance_eval.html +++ b/dev/performance_eval.html @@ -8,9 +8,9 @@ - + - + @@ -151,7 +151,7 @@ (Intercept) -0.0224706 0.0117695 -1.91 0.0743 -0.0474209 0.00247968 x -0.0860158 0.724261 -0.12 0.9069 -1.62138 1.44935 ────────────────────────────────────────────────────────────────────────────

By analysing the table above, we can conclude that the returns gained by the algorithm are likely to be obtained by chance.

References ​

Bibliography ​

  1. Y. Li, X. Zheng, C. Chen, J. Wang and S. Xu. Exponential Gradient with Momentum for Online Portfolio Selection. Expert Systems with Applications 187, 115889 (2022).

  2. M. Khedmati and P. Azin. An online portfolio selection algorithm using clustering approaches and considering transaction costs. Expert Systems with Applications 159, 113546 (2020).

  3. W. Xi, Z. Li, X. Song and H. Ning. Online portfolio selection with predictive instantaneous risk assessment. Pattern Recognition 144, 109872 (2023).

  4. D. Huang, S. Yu, B. Li, S. C. Hoi and S. Zhou. Combination Forecasting Reversion Strategy for Online Portfolio Selection. ACM Trans. Intell. Syst. Technol. 9 (2018).

- + \ No newline at end of file diff --git a/dev/python.html b/dev/python.html index 3d3ea7f..c3f3dc8 100644 --- a/dev/python.html +++ b/dev/python.html @@ -8,9 +8,9 @@ - + - + @@ -170,7 +170,7 @@ array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]) - + \ No newline at end of file diff --git a/dev/refs.html b/dev/refs.html index f4d25ea..7c6ebae 100644 --- a/dev/refs.html +++ b/dev/refs.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
OnlinePortfolioSelection.jl

Appearance

References ​

Bibliography ​

  1. B. Li and S. C. Hoi. Online Portfolio Selection: A Survey (2013).

  2. T. M. Cover. Universal Portfolios. Mathematical Finance 1, 1–29 (1991).

  3. L. GYÖRFI, A. URBÁN and I. VAJDA. KERNEL-BASED SEMI-LOG-OPTIMAL EMPIRICAL PORTFOLIO SELECTION STRATEGIES. International Journal of Theoretical and Applied Finance 10, 505–516 (2007).

  4. A. Agarwal, E. Hazan, S. Kale and R. E. Schapire. Algorithms for Portfolio Management Based on the Newton Method. In: Proceedings of the 23rd International Conference on Machine Learning, ICML '06 (Association for Computing Machinery, New York, NY, USA, 2006); pp. 9–16.

  5. A. Borodin, R. El-Yaniv and V. Gogan. Can we learn to beat the best stock. Advances in Neural Information Processing Systems 16 (2003).

  6. Z.-R. Lai, P.-Y. Yang, L. Fang and X. Wu. Reweighted Price Relative Tracking System for Automatic Portfolio Optimization. IEEE Transactions on Systems, Man, and Cybernetics: Systems 50, 4349–4361 (2020).

  7. B. Li and S. C. Hoi. On-Line Portfolio Selection with Moving Average Reversion (2012), arXiv:1206.4626 [cs.CE].

  8. B. Li, S. C. Hoi, D. Sahoo and Z.-Y. Liu. Moving average reversion strategy for on-line portfolio selection. Artificial Intelligence 222, 104–123 (2015).

  9. B. Li, P. Zhao, S. C. Hoi and V. Gopalkrishnan. PAMR: Passive aggressive mean reversion strategy for portfolio selection. Machine Learning 87, 221–258 (2012).

  10. B. Li, S. C. Hoi, P. Zhao and V. Gopalkrishnan. Confidence Weighted Mean Reversion Strategy for Online Portfolio Selection. ACM Trans. Knowl. Discov. Data 7 (2013).

  11. X. Cai and Z. Ye. Gaussian Weighting Reversion Strategy for Accurate Online Portfolio Selection. IEEE Transactions on Signal Processing 67, 5558–5570 (2019).

  12. Y. Zhong, W. Xu, H. Li and W. Zhong. Distributed mean reversion online portfolio strategy with stock network. European Journal of Operational Research (2023).

  13. D. Huang, J. Zhou, B. Li, S. C. Hoi and S. Zhou. Robust Median Reversion Strategy for Online Portfolio Selection. IEEE Transactions on Knowledge and Data Engineering 28, 2480–2493 (2016).

  14. Z.-R. Lai, L. Tan, X. Wu and L. Fang. Loss control with rank-one covariance estimate for short-term portfolio optimization. J. Mach. Learn. Res. 21 (2020).

  15. L. Bin, W. Jialei, H. Dingjiang and S. C. Hoi. Transaction cost optimization for online portfolio selection. Quantitative Finance 18, 1411–1424 (2018).

  16. D. P. Helmbold, R. E. Schapire, Y. Singer and M. K. Warmuth. On-Line Portfolio Selection Using Multiplicative Updates. Mathematical Finance 8, 325–347 (1998).

  17. Z.-R. Lai, D.-Q. Dai, C.-X. Ren and K.-K. Huang. A Peak Price Tracking-Based Learning System for Portfolio Selection. IEEE Transactions on Neural Networks and Learning Systems 29, 2823–2832 (2018).

  18. Z.-R. Lai, D.-Q. Dai, C.-X. Ren and K.-K. Huang. Radial Basis Functions With Adaptive Input and Composite Trend Representation for Portfolio Selection. IEEE Transactions on Neural Networks and Learning Systems 29, 6214–6226 (2018).

  19. Y. Li, X. Zheng, C. Chen, J. Wang and S. Xu. Exponential Gradient with Momentum for Online Portfolio Selection. Expert Systems with Applications 187, 115889 (2022).

  20. Z.-R. Lai, P.-Y. Yang, L. Fang and X. Wu. Short-term Sparse Portfolio Optimization Based on Alternating Direction Method of Multipliers. Journal of Machine Learning Research 19, 1–28 (2018).

  21. B. Li, S. C. Hoi and V. Gopalkrishnan. CORN: Correlation-Driven Nonparametric Learning Approach for Portfolio Selection. ACM Trans. Intell. Syst. Technol. 2 (2011).

  22. S. Sooklal, T. L. van Zyl and A. Paskaramoorthy. DRICORN-K: A Dynamic RIsk CORrelation-driven Non-parametric Algorithm for Online Portfolio Selection. In: Artificial Intelligence Research, edited by A. Gerber (Springer International Publishing, Cham, 2020); pp. 183–196.

  23. L. Györfi, G. Lugosi and F. Udina. NONPARAMETRIC KERNEL-BASED SEQUENTIAL INVESTMENT STRATEGIES. Mathematical Finance 16, 337–357 (2006).

  24. M. Khedmati and P. Azin. An online portfolio selection algorithm using clustering approaches and considering transaction costs. Expert Systems with Applications 159, 113546 (2020).

  25. W. Xi, Z. Li, X. Song and H. Ning. Online portfolio selection with predictive instantaneous risk assessment. Pattern Recognition 144, 109872 (2023).

  26. Z.-R. Lai, P.-Y. Yang, X. Wu and L. Fang. A kernel-based trend pattern tracking system for portfolio optimization. Data Mining and Knowledge Discovery 32, 1708–1734 (2018).

  27. Y. Zhang, H. Lin, X. Yang and W. Long. Combining expert weights for online portfolio selection based on the gradient descent algorithm. Knowledge-Based Systems 234, 107533 (2021).

  28. J. H. Xingyu Yang and Y. Zhang. Aggregating exponential gradient expert advice for online portfolio selection. Journal of the Operational Research Society 73, 587–597 (2020).

  29. X. Yang, J. He, H. Lin and Y. Zhang. Boosting Exponential Gradient Strategy for Online Portfolio Selection: An Aggregating Experts' Advice Method. Computational Economics 55, 231–251 (2020).

  30. Y. Zhang, H. Lin, L. Zheng and X. Yang. Adaptive online portfolio strategy based on exponential gradient updates. Journal of Combinatorial Optimization 43, 672–696 (2022).

  31. H. Guan and Z. An. A local adaptive learning system for online portfolio selection. Knowledge-Based Systems 186, 104958 (2019).

  32. H. Lin, Y. Zhang and X. Yang. Online portfolio selection of integrating expert strategies based on mean reversion and trading volume. Expert Systems with Applications 238, 121472 (2024).

  33. H.-L. Dai, C.-X. Liang, H.-M. Dai, C.-Y. Huang and R. M. Adnan. An online portfolio strategy based on trend promote price tracing ensemble learning algorithm. Knowledge-Based Systems 239, 107957 (2022).

  34. D. Huang, S. Yu, B. Li, S. C. Hoi and S. Zhou. Combination Forecasting Reversion Strategy for Online Portfolio Selection. ACM Trans. Intell. Syst. Technol. 9 (2018).

- + \ No newline at end of file diff --git a/dev/types.html b/dev/types.html index 118037a..07f4b0a 100644 --- a/dev/types.html +++ b/dev/types.html @@ -8,32 +8,32 @@ - + - + - +
OnlinePortfolioSelection.jl

Appearance

Types ​

OnlinePortfolioSelection.EGA Type
julia
EGA{T<:AbstractFloat}<:EGMFramework

EGA variant of the EGM algorithm.

Fields

  • gamma1::T: momentum parameter

  • gamma2::T: momentum parameter

Example

julia
julia> model = EGA(0.99, 0.)
-EGA{Float64}(0.99, 0.0)

source

OnlinePortfolioSelection.EGE Type
julia
EGE{T<:AbstractFloat}<:EGMFramework

EGE variant of the EGM algorithm.

Fields

  • gamma1::T: momentum parameter

Example

julia
julia> model = EGE(0.99)
-EGE{Float64}(0.99)

source

OnlinePortfolioSelection.EGR Type
julia
EGR{T<:AbstractFloat}<:EGMFramework

EGR variant of the EGM algorithm.

Fields

  • gamma2::T: momentum parameter

Example

julia
julia> model = EGR(0.)
-EGR{Float64}(0.0)

source

OnlinePortfolioSelection.EMA Type
julia
EMA{T<:AbstractFloat}<:TrendRep

Exponential Moving Average trend representation. Formula:

x^E,t+1(ϑ)=∑k=0t−1(1−ϑ)kϑpt−k+(1−ϑ)tp0pt

Fields

  • v::T: Smoothing factor.

Examples

julia
julia> using OnlinePortfolioSelection
+EGA{Float64}(0.99, 0.0)

source

OnlinePortfolioSelection.EGE Type
julia
EGE{T<:AbstractFloat}<:EGMFramework

EGE variant of the EGM algorithm.

Fields

  • gamma1::T: momentum parameter

Example

julia
julia> model = EGE(0.99)
+EGE{Float64}(0.99)

source

OnlinePortfolioSelection.EGR Type
julia
EGR{T<:AbstractFloat}<:EGMFramework

EGR variant of the EGM algorithm.

Fields

  • gamma2::T: momentum parameter

Example

julia
julia> model = EGR(0.)
+EGR{Float64}(0.0)

source

OnlinePortfolioSelection.EMA Type
julia
EMA{T<:AbstractFloat}<:TrendRep

Exponential Moving Average trend representation. Formula:

x^E,t+1(ϑ)=∑k=0t−1(1−ϑ)kϑpt−k+(1−ϑ)tp0pt

Fields

  • v::T: Smoothing factor.

Examples

julia
julia> using OnlinePortfolioSelection
 
 julia> ema = EMA(0.5)
-EMA{Float64}(0.5)

source

OnlinePortfolioSelection.KMDLOG Type
julia
KMDLOG<:ClusLogVariant

KMDLOG is a concrete type used to represent the KMDLOG Model. Also, see KMNLOG.

source

OnlinePortfolioSelection.KMNLOG Type
julia
KMNLOG<:ClusLogVariant

KMNLOG is a concrete type used to represent the KMNLOG Model. Also, see KMDLOG.

source

OnlinePortfolioSelection.OPSAlgorithm Type
julia
OPSAlgorithm{T<:AbstractFloat}

An object that contains the result of running the algorithm.

Fields

  • n_asset::Int: Number of assets in the portfolio.

  • b::Matrix{T}: Weights of the created portfolios.

  • alg::String: Name of the algorithm.

source

OnlinePortfolioSelection.OPSMetrics Type
julia
OPSMetrics{T<:AbstractFloat}

A struct to store the metrics of the OPS algorithm. This object is returned by the opsmetrics function.

Fields

  • Sn::Vector{T}: The cumulative wealth of investment during the investment period.

  • MER::T: The investments's Mean excess return (MER).

  • IR::T: The Information Ratio (IR) of portfolio for the investment period.

  • APY::T: The Annual Percentage Yield (APY) of investment.

  • Ann_Std::T: The Annualized Standard Deviation (σₚ) of investment.

  • Ann_Sharpe::T: The Annualized Sharpe Ratio (SR) of investment.

  • MDD::T: The Maximum Drawdown (MDD) of investment.

  • Calmar::T: The Calmar Ratio of investment.

  • AT::T: The Average Turnover (AT) of the investment.

source

OnlinePortfolioSelection.PAMR Type
julia
PAMR<: PAMRModel

Create a PAMR object. Also, see PAMR1, and PAMR2.

Example

julia
model = PAMR()

source

OnlinePortfolioSelection.PAMR1 Type
julia
PAMR1{T<:AbstractFloat}<: PAMRModel

Create a PAMR1 object. Also, see PAMR, and PAMR2.

Keyword Arguments

  • C::AbstractFloat=1.: Aggressiveness parameter.

Example

julia
model = PAMR1(C=0.02)

source

OnlinePortfolioSelection.PAMR2 Type
julia
PAMR2{T<:AbstractFloat}<: PAMRModel

Create a PAMR2 object. Also, see PAMR, and PAMR1.

Keyword Arguments

  • C::AbstractFloat=1.: Aggressiveness parameter.

Example

julia
model = PAMR2(C=0.02)

source

OnlinePortfolioSelection.PP Type
julia
PP<:TrendRep

Pick Price trend representation. Formula:

x^M,t+1(w)=max0⩽k⩽w−1⁡pt−k(i)pt,i=1,2,…,d

Examples

julia
julia> using OnlinePortfolioSelection
+EMA{Float64}(0.5)

source

OnlinePortfolioSelection.KMDLOG Type
julia
KMDLOG<:ClusLogVariant

KMDLOG is a concrete type used to represent the KMDLOG Model. Also, see KMNLOG.

source

OnlinePortfolioSelection.KMNLOG Type
julia
KMNLOG<:ClusLogVariant

KMNLOG is a concrete type used to represent the KMNLOG Model. Also, see KMDLOG.

source

OnlinePortfolioSelection.OPSAlgorithm Type
julia
OPSAlgorithm{T<:AbstractFloat}

An object that contains the result of running the algorithm.

Fields

  • n_asset::Int: Number of assets in the portfolio.

  • b::Matrix{T}: Weights of the created portfolios.

  • alg::String: Name of the algorithm.

source

OnlinePortfolioSelection.OPSMetrics Type
julia
OPSMetrics{T<:AbstractFloat}

A struct to store the metrics of the OPS algorithm. This object is returned by the opsmetrics function.

Fields

  • Sn::Vector{T}: The cumulative wealth of investment during the investment period.

  • MER::T: The investments's Mean excess return (MER).

  • IR::T: The Information Ratio (IR) of portfolio for the investment period.

  • APY::T: The Annual Percentage Yield (APY) of investment.

  • Ann_Std::T: The Annualized Standard Deviation (σₚ) of investment.

  • Ann_Sharpe::T: The Annualized Sharpe Ratio (SR) of investment.

  • MDD::T: The Maximum Drawdown (MDD) of investment.

  • Calmar::T: The Calmar Ratio of investment.

  • AT::T: The Average Turnover (AT) of the investment.

source

OnlinePortfolioSelection.PAMR Type
julia
PAMR<: PAMRModel

Create a PAMR object. Also, see PAMR1, and PAMR2.

Example

julia
model = PAMR()

source

OnlinePortfolioSelection.PAMR1 Type
julia
PAMR1{T<:AbstractFloat}<: PAMRModel

Create a PAMR1 object. Also, see PAMR, and PAMR2.

Keyword Arguments

  • C::AbstractFloat=1.: Aggressiveness parameter.

Example

julia
model = PAMR1(C=0.02)

source

OnlinePortfolioSelection.PAMR2 Type
julia
PAMR2{T<:AbstractFloat}<: PAMRModel

Create a PAMR2 object. Also, see PAMR, and PAMR1.

Keyword Arguments

  • C::AbstractFloat=1.: Aggressiveness parameter.

Example

julia
model = PAMR2(C=0.02)

source

OnlinePortfolioSelection.PP Type
julia
PP<:TrendRep

Pick Price trend representation. Formula:

x^M,t+1(w)=max0⩽k⩽w−1⁡pt−k(i)pt,i=1,2,…,d

Examples

julia
julia> using OnlinePortfolioSelection
 
 julia> pp = PP()
-PP()

source

OnlinePortfolioSelection.SMAP Type
julia
SMAP<:TrendRep

Simple Moving Average trend representation using the close prices. Formula:

x^S,t+1(w)=∑k=0w−1pt−kwpt

Examples

julia
julia> using OnlinePortfolioSelection
+PP()

source

OnlinePortfolioSelection.SMAP Type
julia
SMAP<:TrendRep

Simple Moving Average trend representation using the close prices. Formula:

x^S,t+1(w)=∑k=0w−1pt−kwpt

Examples

julia
julia> using OnlinePortfolioSelection
 
 julia> sma = SMAP()
-SMA()

source

OnlinePortfolioSelection.SMAR Type

SMAR<:TrendRep

Simple Moving Average trend representation using the relative prices. Formula:

1+1xt+⋯+1⊗k=0w−2xt−k

Examples

julia
julia> using OnlinePortfolioSelection
+SMA()

source

OnlinePortfolioSelection.SMAR Type

SMAR<:TrendRep

Simple Moving Average trend representation using the relative prices. Formula:

1+1xt+⋯+1⊗k=0w−2xt−k

Examples

julia
julia> using OnlinePortfolioSelection
 
 julia> sma = SMAR()
-SMAR()

source

- +SMAR()

source

+ \ No newline at end of file