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braverock
GitHub Repository: braverock/portfolioanalytics
 Path: blob/master/sandbox/rp_method_comparison.R
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library(PortfolioAnalytics)

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data(edhec)

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R <- edhec[, 1:4]

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# set up simple portfolio with leverage and box constraints 

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pspec <- portfolio.spec(assets=colnames(R))

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pspec <- add.constraint(portfolio=pspec, type="leverage", min_sum=0.99, max_sum=1.01)

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pspec <- add.constraint(portfolio=pspec, type="box", min=0, max=1)

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# generate random portfolios using the 3 methods

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rp1 <- random_portfolios(portfolio=pspec, permutations=5000, rp_method='sample')

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rp2 <- random_portfolios(portfolio=pspec, permutations=5000, rp_method='simplex') 

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rp3 <- random_portfolios(portfolio=pspec, permutations=5000, rp_method='grid')

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# show feasible portfolios in mean-StdDev space

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tmp1.mean <- apply(rp1, 1, function(x) mean(R %*% x))

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tmp1.StdDev <- apply(rp1, 1, function(x) StdDev(R=R, weights=x))

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tmp2.mean <- apply(rp2, 1, function(x) mean(R %*% x))

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tmp2.StdDev <- apply(rp2, 1, function(x) StdDev(R=R, weights=x))

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tmp3.mean <- apply(rp3, 1, function(x) mean(R %*% x))

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tmp3.StdDev <- apply(rp3, 1, function(x) StdDev(R=R, weights=x))

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# plot feasible portfolios 

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plot(x=tmp1.StdDev, y=tmp1.mean, col="gray", main="Random Portfolio Methods")

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points(x=tmp2.StdDev, y=tmp2.mean, col="red", pch=2)

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points(x=tmp3.StdDev, y=tmp3.mean, col="lightgreen", pch=5)

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legend("bottomright", legend=c("sample", "simplex", "grid"), col=c("gray", "red", "lightgreen"),

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       pch=c(1, 2, 5), bty="n")

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# sample has pretty even coverage of feasible space

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# simplex is concentrated around the assets

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# grid is 'pushed'/concentrated to the interior due to normalization

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# demonstrate how different values of fev influence the random portfolios of

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# the simplex method

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# This could be a really good example with Shiny for an interactive example

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fev <- 0:5

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par(mfrow=c(2, 3))

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for(i in 1:length(fev)){

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  rp <- random_portfolios(portfolio=pspec, permutations=2000, rp_method='simplex', fev=fev[i])

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  tmp.mean <- apply(rp, 1, function(x) mean(R %*% x))

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  tmp.StdDev <- apply(rp, 1, function(x) StdDev(R=R, weights=x))

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  plot(x=tmp.StdDev, y=tmp.mean, main=paste("FEV =", fev[i]),

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       ylab="mean", xlab="StdDev", col=rgb(0, 0, 100, 50, maxColorValue=255))

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}

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par(mfrow=c(1,1))

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# charts to compare simplex and sample random portfolio generation

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par(mfrow=c(1, 2))

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# simplex

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rp_simplex <- random_portfolios(portfolio=pspec, permutations=2000, rp_method='simplex', fev=0:5)

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tmp.mean <- apply(rp_simplex, 1, function(x) mean(R %*% x))

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tmp.StdDev <- apply(rp_simplex, 1, function(x) StdDev(R=R, weights=x))

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plot(x=tmp.StdDev, y=tmp.mean, main="rp_method=simplex fev=0:5",

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     ylab="mean", xlab="StdDev", col=rgb(0, 0, 100, 50, maxColorValue=255))

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#sample

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rp_sample <- random_portfolios(portfolio=pspec, permutations=2000, rp_method='sample')

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tmp.mean <- apply(rp_sample, 1, function(x) mean(R %*% x))

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tmp.StdDev <- apply(rp_sample, 1, function(x) StdDev(R=R, weights=x))

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plot(x=tmp.StdDev, y=tmp.mean, main="rp_method=sample",

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     ylab="mean", xlab="StdDev", col=rgb(0, 0, 100, 50, maxColorValue=255))

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par(mfrow=c(1,1))

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