multi_layer_optimization.R

#' ---
#' title: "Multi Layer Optimization Demo"
#' author: Ross Bennett
#' date: "7/17/2014"
#' ---

#' Demonstrate multi layer portfolio optimization
#' The top level (i.e. layer) optimization problem is to minimize modified ES
#' with equal component contribution to modified ES of the two portfolios in 
#' the lower layer.
#' 
#' The sub portfolios consist of different assets and different objectives
#' relative to each other. The out of sample returns for each sub portfolio
#' are calculated based on their respective constraints, objectives, and
#' optimization parameters. The out of sample returns are then used as the
#' returns input for the top level optimization.

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

#' The first sub-portfolio, portf1, will contain assets 1:5 of edhec
#' with an objective to minimize standard deviation.
portf1 <- portfolio.spec(assets=funds[1:5])
portf1 <- add.constraint(portfolio=portf1, type="weight_sum", 
                         min_sum=0.99, max_sum=1.01)
portf1 <- add.constraint(portfolio=portf1, type="long_only")
portf1 <- add.objective(portfolio=portf1, type="risk", name="StdDev")

#' The second sub-portfolio, portf2, will contain assets 6:10 of edhec
#' with an objective to minimize expected shortfall.
portf2 <- portfolio.spec(assets=funds[6:10])
# portf2 <- portfolio.spec(assets=5)
portf2 <- add.constraint(portfolio=portf2, type="weight_sum", 
                         min_sum=0.99, max_sum=1.01)
portf2 <- add.constraint(portfolio=portf2, type="long_only")
portf2 <- add.objective(portfolio=portf2, type="risk", name="ES",
                            arguments=list(p=0.9))

#' portf1 and portf2 have the same constraints so they can used the same
#' set of random portfolios.
set.seed(123)
rp <- random_portfolios(portf2, 2000)


#' The 'top level' portfolio has objectives for equal contribution to risk
#' where modified ES is the risk measure.
portf <- portfolio.spec(assets=paste("proxy",1:2, sep="."))
portf <- add.constraint(portfolio=portf, type="weight_sum", 
                        min_sum=0.99, max_sum=1.01)
portf <- add.constraint(portfolio=portf, type="long_only")
portf <- add.objective(portfolio=portf, type="risk", name="ES",
                        arguments=list(p=0.9))
portf <- add.objective(portfolio=portf, type="risk_budget", name="ES",
                       arguments=list(p=0.9), min_concentration=TRUE)

#' Specify a mult-layer portfolio.
mult.portf <- mult.portfolio.spec(portf)

#' Add portf1 as a sub portfolio with optimization parameters specific to 
#' running optimize.portfolio.rebalancing with portf1.
mult.portf <- add.sub.portfolio(mult.portf, portf1, rp=rp, 
                                optimize_method="random",
                                rebalance_on="quarters", 
                                training_period=136)

#' Add portf2 as a sub portfolio with optimization parameters specific to 
#' running optimize.portfolio.rebalancing with portf2.
mult.portf <- add.sub.portfolio(mult.portf, portf2, rp=rp,
                                optimize_method="random",
                                rebalance_on="months", 
                                training_period=136, 
                                trailing_periods=48)

#' Generate random portfolios for the top layer optimization
set.seed(123)
rp.top <- random_portfolios(portf, 1000)

#' Run the multi layer optimization
opt.mult <- optimize.portfolio(R, mult.portf,
                               optimize_method="random", 
                               trace=TRUE, rp=rp.top)
opt.mult