Dynamic Optimal Shrinkage Portfolio.

DOSPorfolio

The goal of DOSPorfolio is to provide a simple interface for computing portfolio weights according to the dynamic weighting scheme from (Bodnar, Parolya, and Thorsén 2021).

Installation

The development version can be installed from GitHub with:

# install.packages("devtools")
devtools::install_github("Statistics-In-Portfolio-Theory/DOSportfolio")

Example

This is a very simple example which shows you how use the package:

library(DOSPortfolio)
n <- 25*2
p <- 15
# Simulate data
data <- sqrt(5/3) * matrix(rt(n*p, df=5), ncol=p, nrow=n)
# specify the allocation points. The DOSPortfolio class will validate what is 
# "ok" allocation periods.
reallocation_points <- c(25, 42)
(portfolios <- DOSPortfolio(data, reallocation_points))
#> $weights
#>            [,1]       [,2]        [,3]      [,4]       [,5]       [,6]
#> [1,] 0.08697641 0.07240871 0.018210965 0.0800573 0.06954698 0.07120553
#> [2,] 0.09185841 0.07378896 0.006563325 0.0832761 0.07023934 0.07229657
#>            [,7]         [,8]       [,9]      [,10]      [,11]      [,12]
#> [1,] 0.05088562  0.006348246 0.06908115 0.08272137 0.08722852 0.06232573
#> [2,] 0.04709222 -0.008150919 0.06966153 0.08658055 0.09217112 0.06128227
#>           [,13]      [,14]      [,15]
#> [1,] 0.08156509 0.08208267 0.07935573
#> [2,] 0.08514633 0.08578832 0.08240588
#> 
#> $shrinkage_type
#> [1] "non-overlapping"
#> 
#> attr(,"class")
#> [1] "DOSPortfolio"

The variable portfolios is a “DOSPortfolio” class whose documentation can be viewed by ?DOSPortfolio. The constructor DOSPortfolio() looks for violations against the assumptions made in the reference. Here is an example when things does not work

reallocation_points <- c(37, 42)
# observe that there is little data between the first and second allcoation 
# point. Its actually to little since p > n_2, e.g. 15 > 42 - 37. 

# This will cause an error
DOSPortfolio(data, reallocation_points)
#> Error: Non-overlapping estimator can not handle concentration ratios above one.
#>             Consider excluding one (or more) break point(s) or provide more data.

However, by using the the argument shrinkage_type="overlapping" we can make it work!

DOSPortfolio(data, reallocation_points, shrinkage_type = "overlapping")
#> $weights
#>            [,1]       [,2]        [,3]       [,4]       [,5]       [,6]
#> [1,] 0.08409633 0.07159444 0.025082350 0.07815841 0.06913853 0.07056188
#> [2,] 0.09300762 0.07411387 0.003821481 0.08403381 0.07040232 0.07255340
#>            [,7]        [,8]       [,9]      [,10]      [,11]      [,12]
#> [1,] 0.05312349  0.01490185 0.06873876 0.08044469 0.08431269 0.06294131
#> [2,] 0.04619926 -0.01156401 0.06979815 0.08748900 0.09333460 0.06103664
#>           [,13]      [,14]      [,15]
#> [1,] 0.07945238 0.07989656 0.07755632
#> [2,] 0.08598935 0.08666063 0.08312389
#> 
#> $shrinkage_type
#> [1] "overlapping"
#> 
#> attr(,"class")
#> [1] "DOSPortfolio"

If you want to learn to more why this is then you can have a look at the “introduction” vignette or read the paper!

Possible further scope:

• Create summary function so that one can construct summaries of the portfolios as done in (Bodnar, Parolya, and Thorsén 2021).
• Include test on finite fourth moment, summary function to generate table from the article?
• Setup so that the portfolio estimators can work with the tsibble package?
• Extend theory to mean-variance portfolio and Shrinkage estimators.

References