Using the ROI solvers with PortfolioAnalytics

Using the ROI solvers with PortfolioAnalytics

Ross Bennett May 17, 2018

Abstract

The purpose of this vignette is to demonstrate a sample of the optimzation problems that can be solved in PortfolioAnalytics with the ROI solvers. See demo(demo_ROI) for a more complete set of examples.

Contents

1 Getting Started

2

1.1 Load Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Maximizing Mean Return

3

2.1 Portfolio Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Minimizing Portfolio Variance

10

3.1 Global Minimum Variance Portfolio . . . . . . . . . . . . . . . . . . . . . . 10

3.1.1 Portfolio Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.3 Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Constrained Minimum Variance Portfolio . . . . . . . . . . . . . . . . . . . 11

3.2.1 Portfolio Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2.3 Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1

4 Maximizing Quadratic Utility

12

4.1 Portfolio Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3 Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5 Minimizing Expected Tail Loss

14

1 Getting Started

1.1 Load Packages

Load the necessary packages.

> suppressMessages(library(PortfolioAnalytics)) > suppressMessages(library(foreach)) > suppressMessages(library(iterators)) > suppressMessages(library(ROI)) > suppressMessages(library(ROI.plugin.quadprog)) > suppressMessages(library(ROI.plugin.glpk))

1.2 Data

The edhec data set from the PerformanceAnalytics package will be used as example data.

> data(edhec) > # Use the first 4 columns in edhec for a returns object > returns colnames(returns) print(head(returns, 5))

CA CTAG

DS

EM

1997-01-31 0.0119 0.0393 0.0178 0.0791

1997-02-28 0.0123 0.0298 0.0122 0.0525

1997-03-31 0.0078 -0.0021 -0.0012 -0.0120

1997-04-30 0.0086 -0.0170 0.0030 0.0119

1997-05-31 0.0156 -0.0015 0.0233 0.0315

> # Get a character vector of the fund names > funds # Create portfolio object

> portf_maxret # Add constraints to the portfolio object

> portf_maxret portf_maxret # Add objective to the portfolio object

> portf_maxret print(portf_maxret)

************************************************** PortfolioAnalytics Portfolio Specification **************************************************

Call: portfolio.spec(assets = funds)

Number of assets: 4 Asset Names [1] "CA" "CTAG" "DS"

"EM"

Constraints

3

Enabled constraint types - full_investment - box

Objectives: Enabled objective names

- mean

> summary(portf_maxret)

$assets CA CTAG DS EM

0.25 0.25 0.25 0.25

$enabled_constraints $enabled_constraints[[1]] An object containing 6 nonlinear constraints.

$enabled_constraints[[2]] An object containing 5 nonlinear constraints.

$disabled_constraints list()

$enabled_objectives $enabled_objectives[[1]] $name [1] "mean"

$target NULL

$arguments list()

$enabled [1] TRUE

$multiplier [1] -1

4

$call add.objective(portfolio = portf_maxret, type = "return", name = "mean")

attr(,"class") [1] "return_objective" "objective"

$disabled_objectives list()

attr(,"class") [1] "summary.portfolio"

2.2 Optimization

The next step is to run the optimization. Note that optimize_method="ROI" is specified in the call to optimize.portfolio to select the solver used for the optimization.

> # Run the optimization

> opt_maxret print(opt_maxret)

*********************************** PortfolioAnalytics Optimization ***********************************

Call: optimize.portfolio(R = returns, portfolio = portf_maxret, optimize_method = "ROI",

trace = TRUE)

Optimal Weights: CA CTAG DS EM

0.02 0.05 0.43 0.50

Objective Measure:

5

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