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braverock
GitHub Repository: braverock/portfolioanalytics
 Path: blob/master/demo/demo_max_quadratic_utility.R
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#' ---

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#' title: "Maximizing Quadratic Utility Demo"

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#' author: Ross Bennett

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#' date: "7/17/2014"

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#' ---

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#' This script demonstrates how to solve a constrained maximimum quadratic

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#' utility portfolio optimization problem.

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#' Load the package and data

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library(PortfolioAnalytics)

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data(edhec)

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R <- edhec[, 1:10]

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funds <- colnames(R)

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#' Construct initial portfolio with basic constraints

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init.portf <- portfolio.spec(assets=funds)

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init.portf <- add.constraint(portfolio=init.portf, type="full_investment")

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init.portf <- add.constraint(portfolio=init.portf, type="long_only")

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init.portf <- add.objective(portfolio=init.portf, type="return", name="mean")

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#' Here we can set the risk_aversion parameter to control how much risk

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#' is penalized.

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init.portf <- add.objective(portfolio=init.portf, type="risk", name="StdDev",

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                            risk_aversion=4)

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init.portf

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#' Maximizing quadratic utility can be formulated as a quardratic programming 

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#' problem and solved very quickly using optimize_method="ROI". Although "StdDev"

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#' was specified as an objective, the quadratic programming problem uses the 

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#' variance-covariance matrix in the objective function.

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maxQU.lo.ROI <- optimize.portfolio(R=R, portfolio=init.portf, 

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                                    optimize_method="ROI", trace=TRUE)

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maxQU.lo.ROI

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plot(maxQU.lo.ROI, risk.col="StdDev", 

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     main=expression("Long Only Max Quadratic Utility" ~ lambda ~"=0.25"))

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#' A risk aversion parameter that is very small, will effectively make the term

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#' that penalizes risk zero and approximates the maximum return. Note that the

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#' risk_aversion parameter must be non-zero.

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init.portf$objectives[[2]]$risk_aversion <- 1e-6

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maxQU.maxret.ROI <- optimize.portfolio(R=R, portfolio=init.portf, 

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                                       optimize_method="ROI", trace=TRUE)

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maxQU.maxret.ROI

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plot(maxQU.maxret.ROI, risk.col="StdDev", 

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     main=expression("Long Only Max Quadratic Utility" ~ lambda ~"= 1e-6"))

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#' A risk aversion parameter that is very large will heavily penalize the risk 

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#' term in the objective function and approximates the minimum variance portfolio.

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init.portf$objectives[[2]]$risk_aversion <- 1e6

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maxQU.minvol.ROI <- optimize.portfolio(R=R, portfolio=init.portf, 

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                                       optimize_method="ROI", trace=TRUE)

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maxQU.minvol.ROI

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plot(maxQU.minvol.ROI, risk.col="StdDev", 

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     main=expression("Long Only Max Quadratic Utility" ~ lambda ~"= 1e6"))

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