Portfolio Construction and Optimization with R

Kyle Balkissoon

KKB Research and Development

2016-10-26

Introduction

At the end of this presentation you will know how to the following

Get Data
Process Data
Create Portfolio objectives
Optimize Portfolios
Analyse Portfolios
Case Study: Stance Equity

Get Data

Before we can do anything we need data, some good R libraries for getting data are:

library(Quandl) # see Quandl.com for more info
library(quantmod) #Has preconfigured api with yahoo info

##Quandl - Note requires assignment, type xts is xtensible time series
SPTSXComp=Quandl("YAHOO/INDEX_GSPTSE",type='xts')

##quantmod - assigns to object named GSPTSE - automatically in xts/zoo
 getSymbols("^GSPTSE")

A realistic case - US SP500 Sectors

symbol_list = c('XLF','XLE','XLU','XLK','XLB','XLP','XLY','XLI','XLV')

getSymbols(symbol_list, from = '1990-01-01')
getSymbols("SPY",from='1990-01-01')

Preprocess Data into Returns

library(PerformanceAnalytics)

securities_matrix = NULL
for( sym in symbol_list){
  securities_matrix = merge.xts(securities_matrix,
                     Return.calculate(Ad(get(paste(sym))),
                                                 method='discrete'))}
securities_matrix=securities_matrix[complete.cases(securities_matrix)]
SPYReturn=Return.calculate(Ad(SPY),method='discrete')

Introduction to PerformanceAnalytics

Library to compute many functions in return space
Used by hedge funds, proprietary trading firms, mutual funds, SMA's and banks
Robust tools for measuring portfolio and security performance with all the standard risk metrics.

Have a look at our data

chart.CumReturns(securities_matrix)

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Portfolio Objective creation

Coming up with an objective function is non-trivial, the issue is that any potential function needs to capture the risk-return preferences of the investor in a coherent manner. Key issues in objective formulation:

Parameter Estimation
Alignment of objectives of function with client
Directional Preference
Smoothness
Computational difficulty

Some common and not so common objectives

Minimum Variance
Max Sharpe Ratio
Minimize Expected Tail Loss
Max Return / Expected Tail Loss

PortfolioAnalytics - Tools for Creating and Optimizing Portfolios

Library to create and optimize portfolios
Initially built for hedge funds, trading firms and equity funds
Used heavily by practictioners for portfolio specification and optimization

An Example of PortfolioAnalytics - Minimum Variance

library(PortfolioAnalytics)
MinimumVariancePortfolio=portfolio.spec(
  assets=colnames(securities_matrix))

MinimumVariancePortfolio=add.objective(
  portfolio=MinimumVariancePortfolio,
  type='risk',
  name='StdDev')

An Example of PortfolioAnalytics - Setting up Constraints

MinimumVariancePortfolio=add.constraint(
  portfolio = MinimumVariancePortfolio,
  type="full_investment")

MinimumVariancePortfolio=add.constraint(
  portfolio = MinimumVariancePortfolio,
  type="long_only")

MinimumVariancePortfolio=add.constraint(
  portfolio = MinimumVariancePortfolio,
  type="box",
  min=0,max=0.3)

Optimization with PortfolioAnalytics

Easy to use with optimize.portfolio calls
Can work with many optimizers default is DEoptim

OptimizedPortfolioMinVariance=optimize.portfolio(
  R=securities_matrix,
  portfolio=MinimumVariancePortfolio,
  trace=TRUE)

Analysing our portfolio

chart.Weights(OptimizedPortfolioMinVariance)

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Mean Variance Optimization

MeanVariancePortfolio=add.objective(
  portfolio=MinimumVariancePortfolio,
  type='return',
  name='mean')

OptimizedPortfolioMeanVariance=optimize.portfolio(
  R=securities_matrix,
  portfolio=MeanVariancePortfolio,
  trace=TRUE)

Analysing our portfolio

chart.Weights(OptimizedPortfolioMeanVariance)

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Risk to Return Analysis

chart.RiskReward(OptimizedPortfolioMeanVariance,
                return.col = 'mean',
                risk.col = 'StdDev',
                main='Risk to Return Plot of various Portfolio Combinations')

Risk to Return Analysis - Plot

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Backtesting with PortfolioAnalytics

MinimumVarianceBT=optimize.portfolio.rebalancing(R=securities_matrix,
                                                 MinimumVariancePortfolio,
                                                 rebalance_on = 'years',
                                                 training_period = 252,
                                                 rolling_window = 252)

Backtesting with PortfolioAnalytics

MeanVarianceBT=optimize.portfolio.rebalancing(R=securities_matrix,
                                              MeanVariancePortfolio,
                                              rebalance_on = 'years',
                                              training_period = 252,
                                              rolling_window = 252)

Using PerformanceAnalytics to compute portfolio returns

MinVariancePortfReturns=Return.rebalancing(R=securities_matrix,
                                           weights=extractWeights(MinimumVarianceBT))
colnames(MinVariancePortfReturns)=c('MinVariance')
MeanVariancePortfReturns=Return.rebalancing(R=securities_matrix,
                                            weights=extractWeights(MeanVarianceBT))
colnames(MeanVariancePortfReturns)=c('MeanVariance')
EqualWeightPortfReturns=Return.rebalancing(R=securities_matrix)
colnames(EqualWeightPortfReturns)=c('EqualWeight')

Analysing our portfolios

PortfolioComparisonData=merge.xts(MinVariancePortfReturns,
                                  MeanVariancePortfReturns,
                                  EqualWeightPortfReturns,
                                  SPYReturn)['2000-01-01/2016-10-25']

chart.CumReturns(PortfolioComparisonData,
                main='Performance of Various Strategies',
                legend.loc='topleft')

Analysing our portfolios Plot

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Analysing our portfolios - Functions

table.AnnualizedReturns(PortfolioComparisonData)
maxDrawdown(PortfolioComparisonData)
table.CAPM(PortfolioComparisonData[,1:3],
           PortfolioComparisonData[,4])[c(2,6,9,10,11,12),]

Analysing our portfolios - Total Return, Vol, Sharpe

	MinVariance	MeanVariance	EqualWeight	SPY.Adjusted
Annualized Return	0.0564	0.0643	0.0575	0.0419
Annualized Std Dev	0.1627	0.1584	0.1915	0.1994
Annualized Sharpe (Rf=0%)	0.3467	0.4061	0.3002	0.2101

Analysing our portfolios - Max Drawdown

	MinVariance	MeanVariance	EqualWeight	SPY.Adjusted
Worst Drawdown	0.4945	0.4447	0.5264	0.5519

Analysing our portfolios - CAPM

	MinVariance to SPY.Adjusted	MeanVariance to SPY.Adjusted	EqualWeight to SPY.Adjusted
Beta	0.7503	0.7219	0.9177
Annualized Alpha	0.0225	0.0313	0.0183
Tracking Error	0.0810	0.0863	0.0586
Active Premium	0.0143	0.0222	0.0154
Information Ratio	0.1763	0.2575	0.2620
Treynor Ratio	0.0752	0.0891	0.0626

Case Study: Stance Equity

Portfolio built to incorporate any investor set of values
Investor can use values based screen to select any 250 stocks
ML model then intersects that list with top stocks from benchmark
Rebalanced quarterly to maximize diversification and minimize tail risk

Case Study: Stance Equity - Performance

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Case Study: Stance Equity - Analysis

	Composite	SP500TR.Adjusted
Cumulative Return	0.2748	0.2429
Annualized Return	0.0923	0.0823
Annualized Standard Deviation	0.0872	0.1095
Annualized Sharpe Ratio (Rf=0%)	1.0586	0.7516
Annualized Alpha	0.0415	0.0000
Beta	0.6056	1.0000
Worst Drawdown	0.0461	0.0836

Case Study: Stance Equity - Rolling Alpha

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Case Study: Stance Equity - Rolling Beta

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Case Study: Stance Equity - Rolling volatility

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Case Study: Stance Equity - Rolling Returns

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Case Study: Stance Equity - Rolling Sharpe Ratio

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The End

Thanks to all the authors, contributors, testers of the various R packages used
PortfolioAnalytics, PerformanceAnalytics,quantmod
Questions?