demo/demo_max_return.R

In PortfolioAnalytics: Portfolio Analysis, Including Numerical Methods for Optimization of Portfolios

#' ---
#' title: "Maximizing Return Demo"
#' author: Ross Bennett
#' date: "7/17/2014"
#' ---

#' This script demonstrates how to solve a constrained maximimum return
#' portfolio optimization problem.

#' Load the package and data
library(PortfolioAnalytics)
data(edhec)
R <- edhec[, 1:10]
funds <- colnames(R)

#' Construct initial portfolio with basic constraints
init.portf <- portfolio.spec(assets=funds)
init.portf <- add.constraint(portfolio=init.portf, type="full_investment")
init.portf <- add.constraint(portfolio=init.portf, type="long_only")
init.portf <- add.objective(portfolio=init.portf, type="return", name="mean")
init.portf

#' Maximizing return can be formulated as a linear programming problem and
#' solved very quickly using optimize_method="ROI". We are using long_only
#' constraints so it is expected that allocation is to the portfolio with the
#' highest mean return.
maxret.lo.ROI <- optimize.portfolio(R=R, portfolio=init.portf, 
                                    optimize_method="ROI", trace=TRUE)
maxret.lo.ROI

chart.Weights(maxret.lo.ROI, main="Long Only Maximize Return")

#' It is more practical to impose box constraints on the weights of assets.
#' Update the second constraint element with box constraints
init.portf <- add.constraint(portfolio=init.portf, type="box", 
                             min=0.05, max=0.3, indexnum=2)

maxret.box.ROI <- optimize.portfolio(R=R, portfolio=init.portf, 
                                     optimize_method="ROI", trace=TRUE)
maxret.box.ROI

chart.Weights(maxret.box.ROI, main="Box Maximize Return")

#' Although the maximum return objective can be solved quickly and accurately
#' with optimize_method="ROI", it is also possible to solve this optimization
#' problem using other solvers such as random portfolios or DEoptim.

#' For random portfolios, the leverage constraints should be relaxed slightly.
init.portf$constraints[[1]]$min_sum=0.99
init.portf$constraints[[1]]$max_sum=1.01

#' Add StdDev as an object with multiplier=0. The multiplier=0 argument means 
#' that it will not be used in the objective function, but will be calculated
#' for each portfolio so that we can plot the optimal portfolio in 
#' mean-StdDev space.
init.portf <- add.objective(portfolio=init.portf, type="risk", 
                            name="StdDev", multiplier=0)

#' First run the optimization with a wider bound on the box constraints that 
#' also allows shorting. Then use more restrictive box constraints. This is 
# 'useful to visualize impact of the constraints on the feasible space

#' Create a new portfolio called 'port1' by using init.portf and modify the
#' box constraints.
port1 <- add.constraint(portfolio=init.portf, type="box", 
                             min=-0.3, max=0.8, indexnum=2)

maxret.box1.RP <- optimize.portfolio(R=R, portfolio=port1, 
                                    optimize_method="random", 
                                    search_size=2000, 
                                    trace=TRUE)
maxret.box1.RP
plot(maxret.box1.RP, risk.col="StdDev")

#' Create a new portfolio called 'port2' by using init.portf and modify the 
#' box constraints.
port2 <- add.constraint(portfolio=init.portf, type="box", 
                             min=0.05, max=0.3, indexnum=2)

#' Run the optimization using random portfolios.
maxret.box2.RP <- optimize.portfolio(R=R, portfolio=port2, 
                                    optimize_method="random", 
                                    search_size=2000, 
                                    trace=TRUE)
maxret.box2.RP
plot(maxret.box2.RP, risk.col="StdDev")

# Now run the optimization with DEoptim.
maxret.box.DE <- optimize.portfolio(R=R, portfolio=init.portf, 
                                    optimize_method="DEoptim", 
                                    search_size=2000, 
                                    trace=TRUE)
maxret.box.DE
plot(maxret.box.DE, risk.col="StdDev", return.col="mean")