library(PortfolioAnalytics)
# Examples of solving optimization problems to minimize expected shortfall (ES)
# The objective can also be specified as "CVaR" and "ETL".
data(edhec)
R <- edhec[, 1:10]
funds <- colnames(R)
# Construct initial portfolio
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")
# Add objective to minimize expected shortfall with a confidence level of
# 0.9.
init.portf <- add.objective(portfolio=init.portf, type="risk", name="ES",
arguments=list(p=0.9))
print(init.portf)
# Minimizing expected shortfall can be formulated as a linear programming
# problem and solved very quickly using optimize_method="ROI". The linear
# programming problem is formulated to minimize sample ES.
minES.lo.ROI <- optimize.portfolio(R=R, portfolio=init.portf,
optimize_method="ROI",
trace=TRUE)
print(minES.lo.ROI)
plot(minES.lo.ROI, risk.col="ES", return.col="mean",
main="Long Only Minimize Expected Shortfall")
# 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)
minES.box.ROI <- optimize.portfolio(R=R, portfolio=init.portf,
optimize_method="ROI",
trace=TRUE)
print(minES.box.ROI)
chart.Weights(minES.box.ROI, main="Minimize ES with Box Constraints")
# Although the minimum ES 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. These
# solvers have the added flexibility of using different methods to calculate
# ES (e.g. gaussian, modified, or historical). The default is to calculate
# modified ES.
# For random portfolios and DEoptim, the leverage constraints should be
# relaxed slightly.
init.portf$constraints[[1]]$min_sum=0.99
init.portf$constraints[[1]]$max_sum=1.01
# Add mean as an objective 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-ES space.
init.portf <- add.objective(portfolio=init.portf, type="return",
name="mean", 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)
minES.box1.RP <- optimize.portfolio(R=R, portfolio=port1,
optimize_method="random",
search_size=2000,
trace=TRUE)
print(minES.box1.RP)
plot(minES.box1.RP, risk.col="ES", return.col="mean")
# 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)
minES.box2.RP <- optimize.portfolio(R=R, portfolio=port2,
optimize_method="random",
search_size=2000,
trace=TRUE)
print(minES.box2.RP)
plot(minES.box2.RP, risk.col="ES", return.col="mean")
# Now solve the problem with DEoptim
minES.box.DE <- optimize.portfolio(R=R, portfolio=init.portf,
optimize_method="DEoptim",
search_size=2000,
trace=TRUE)
print(minES.box.DE)
plot(minES.box.DE, risk.col="ES", return.col="mean")
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.