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https://github.com/dppalomar/sparseIndexTracking

Design of Portfolio of Stocks to Track an Index
https://github.com/dppalomar/sparseIndexTracking

financial-markets index portfolio tracking

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Design of Portfolio of Stocks to Track an Index

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README 

        
---

output:

  md_document:

    variant: markdown_github

  html_document:

    variant: markdown_github

    keep_md: true

---



```{r, echo = FALSE}

library(knitr)

opts_chunk$set(

  collapse = TRUE,

  comment = "#>",

  fig.path = "man/figures/README-",

  fig.align = "center",

  fig.retina = 2,

  out.width = "75%",

  dpi = 96

)

knit_hooks$set(pngquant = hook_pngquant)

```



# sparseIndexTracking



[![CRAN_Status_Badge](https://www.r-pkg.org/badges/version/sparseIndexTracking)](https://CRAN.R-project.org/package=sparseIndexTracking)

[![CRAN Downloads](https://cranlogs.r-pkg.org/badges/sparseIndexTracking)](https://CRAN.R-project.org/package=sparseIndexTracking)

![CRAN Downloads Total](https://cranlogs.r-pkg.org/badges/grand-total/sparseIndexTracking?color=brightgreen)



Computation of sparse portfolios for financial index tracking, i.e., joint 

selection of a subset of the assets that compose the index and computation 

of their relative weights (capital allocation). The level of sparsity of the 

portfolios, i.e., the number of selected assets, is controlled through a 

regularization parameter. Different tracking measures are available, namely, 

the empirical tracking error (ETE), downside risk (DR), Huber empirical 

tracking error (HETE), and Huber downside risk (HDR). See vignette for a 

detailed documentation and comparison, with several illustrative examples.



The package is based on the paper:



K. Benidis, Y. Feng, and D. P. Palomar, "Sparse Portfolios for High-Dimensional 

Financial Index Tracking," _IEEE Trans. on Signal Processing_, vol. 66, no. 1, 

pp. 155-170, Jan. 2018. ()



The latest stable version of **sparseIndexTracking** is available at 

https://CRAN.R-project.org/package=sparseIndexTracking.



The latest development version of **sparseIndexTracking** is available at 

https://github.com/dppalomar/sparseIndexTracking.



## Installation

To install the latest stable version of **sparseIndexTracking** from CRAN, run the following commands in R:

```{r, eval = FALSE}

install.packages("sparseIndexTracking")

```



To install the development version of **sparseIndexTracking** from GitHub, run the following commands in R:

```{r, eval = FALSE}

install.packages("devtools")

devtools::install_github("dppalomar/sparseIndexTracking")

```



To get help:

```{r, eval = FALSE}

library(sparseIndexTracking)

help(package = "sparseIndexTracking")

package?sparseIndexTracking

?spIndexTrack

```



Please cite **sparseIndexTracking** in publications:

```{r, eval = FALSE}

citation("sparseIndexTracking")

```



## Documentation

For more detailed information, please check the vignette: 

[CRAN vignette](https://CRAN.R-project.org/package=sparseIndexTracking/vignettes/SparseIndexTracking.html) and

[GitHub vignette](https://raw.githack.com/dppalomar/sparseIndexTracking/master/vignettes/SparseIndexTracking.html).



## Usage of `spIndexTrack()`

We start by loading the package and real data of the index S&P 500 and its underlying assets:

```{r, message = FALSE}

library(sparseIndexTracking)

library(xts)

data(INDEX_2010)

```

The data `INDEX_2010` contains a list with two xts objects:



> 1. `X`: A $T\times N$ xts with the daily linear returns of the $N$ assets that were in the index during the year   2010 (total $T$ trading days)

  2. `SP500`: A $T\times 1$ xts with the daily linear returns of the index S\&P 500 during the same period.



Note that we use xts objects just for illustration purposes. The function `spIndexTracking()` can also be invoked passing simple data arrays or dataframes.



Based on the above quantities we create a training window, which we will use to create our portfolios, and a testing window, which will be used to assess the performance of the designed portfolios. For simplicity, here we consider the first six (trading) months of the dataset (~126 days) as the training window, and the subsequent six months as the testing window:

```{r}

X_train <- INDEX_2010$X[1:126]

X_test <- INDEX_2010$X[127:252]

r_train <- INDEX_2010$SP500[1:126]

r_test <- INDEX_2010$SP500[127:252]

```



Now, we use the four modes (four available tracking errors) of the `spIndexTracking()` algorithm to design our portfolios:

```{r, cache = TRUE}

# ETE

w_ete <- spIndexTrack(X_train, r_train, lambda = 1e-7, u = 0.5, measure = 'ete')

cat('Number of assets used:', sum(w_ete > 1e-6))



# DR

w_dr <- spIndexTrack(X_train, r_train, lambda = 2e-8, u = 0.5, measure = 'dr')

cat('Number of assets used:', sum(w_dr > 1e-6))



# HETE

w_hete <- spIndexTrack(X_train, r_train, lambda = 8e-8, u = 0.5, measure = 'hete', hub = 0.05)

cat('Number of assets used:', sum(w_hete > 1e-6))



# HDR

w_hdr <- spIndexTrack(X_train, r_train, lambda = 2e-8, u = 0.5, measure = 'hdr', hub = 0.05)

cat('Number of assets used:', sum(w_hdr > 1e-6))

```



Finally, we plot the actual value of the index in the testing window in comparison with the values of the designed portfolios:

```{r, pngquant = "--speed=1"}

plot(cbind("PortfolioETE" = cumprod(1 + X_test %*% w_ete), cumprod(1 + r_test)), 

     legend.loc = "topleft", main = "Cumulative P&L")

plot(cbind("PortfolioDR" = cumprod(1 + X_test %*% w_dr), cumprod(1 + r_test)),

     legend.loc = "topleft", main = "Cumulative P&L")

plot(cbind("PortfolioHETE" = cumprod(1 + X_test %*% w_hete), cumprod(1 + r_test)),

     legend.loc = "topleft", main = "Cumulative P&L")

plot(cbind("PortfolioHDR" = cumprod(1 + X_test %*% w_hdr), cumprod(1 + r_test)),

     legend.loc = "topleft", main = "Cumulative P&L")

```



## Links

Package: [CRAN](https://CRAN.R-project.org/package=sparseIndexTracking) and [GitHub](https://github.com/dppalomar/sparseIndexTracking).



README file: [CRAN-readme](https://CRAN.R-project.org/package=sparseIndexTracking/readme/README.html) and [GitHub-readme](https://github.com/dppalomar/sparseIndexTracking/blob/master/README.md).



Vignette: [CRAN-html-vignette](https://CRAN.R-project.org/package=sparseIndexTracking/vignettes/SparseIndexTracking.html),

[CRAN-pdf-vignette](https://CRAN.R-project.org/package=sparseIndexTracking/vignettes/SparseIndexTracking-pdf.pdf),

[GitHub-html-vignette](https://raw.githack.com/dppalomar/sparseIndexTracking/master/vignettes/SparseIndexTracking.html), and

[GitHub-pdf-vignette](https://docs.google.com/viewer?url=https://github.com/dppalomar/sparseIndexTracking/raw/master/vignettes/SparseIndexTracking-pdf.pdf).