demo/ButterflyTrading.R

In R-Finance/Meucci: Collection of functionality ported from the MATLAB code of Attilio Meucci.

#' This script performs the butterfly-trading case study for the Entropy-Pooling approach by Attilio Meucci, 
#' as it appears in A. Meucci, "Fully Flexible Views: Theory and Practice", The Risk Magazine, October 2008, 
#' p 100-106
#'
#' Most recent version of article and MATLAB code available at
#' http://www.symmys.com/node/158
#'
#' @references 
#' A. Meucci, "Fully Flexible Views: Theory and Practice" \url{http://www.symmys.com/node/158}
#' See Meucci script for "ButterflyTrading/S_MAIN.m"
#' 
#' @author Xavier Valls \email{flamejat@@gmail.com} and Ram Ahluwalia \email{ram@@wingedfootcapital.com}

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# Load panel X of joint factors realizations and vector p of respective probabilities
# In real life, these are provided by the estimation process
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data("factorsDistribution" )

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# Load current prices, deltas and other analytics of the securities 
# In real life, these are provided by data provider
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data("butterfliesAnalytics")

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# Map factors scenarios into p&l scenarios at the investment horizon
# In real life with complex products, the pricing can be VERY costly 
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PnL = HorizonPricing( butterfliesAnalytics, factorsDistribution$X );

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# compute mean-risk efficient frontier based on prior market distribution
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Options = list()
Options$Quant    	 = 0.95  	# quantile level for CVaR
Options$NumPortf 	 = 30  		# number of portfolios in efficient frontier
Options$FrontierSpan = cbind( 0.1 , 0.8 ) # range of normalized exp.vals. spanned by efficient frontier
Options$DeltaNeutral = 1 		# 1 = portfolio is delta neutral, 0 = no constraint
Options$Budget 		 = 0 		# initial capital
Options$Limit 		 = 10000 	# limit to absolute value of each investment

optimalPortfolios = LongShortMeanCVaRFrontier( PnL , as.matrix(factorsDistribution$p ) , butterfliesAnalytics , Options )

#View( optimalPortfolios ) # Note that composition is measured in dollars. Here we are short GOOG_vol_91 and long GOOG_vol_182

PlotFrontier( optimalPortfolios$Exp , optimalPortfolios$CVaR , optimalPortfolios$Composition )

#PlotEfficientFrontier(Exp,CVaR,w)

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# process views (this is the core of the Entropy Pooling approach
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p_1 = ViewImpliedVol( factorsDistribution$X, factorsDistribution$p );

# View 1 (inequality view): bearish on on 2m-6pm implied volaility spread for Google
# Note that the mean-CVaR efficient frontier is long based on the reference model
# After processing the view, the G6m-G2m spread is now short in the mean-CVaR long-short efficient frontier

p_2 = ViewRealizedVol( factorsDistribution$X, factorsDistribution$p );

# view 2 (relative inequality view on median): bullish on realized volatility of MSFT (i.e. absolute log-change in the underlying). 
# This is the variable such that, if larger than a threshold, a long position in the butterfly turns into a profit (e.g. Rachev 2003)
# we issue a relative statement on the media comparing it with the third quintile implied by the reference market model

p_3 = ViewCurveSlope( factorsDistribution$X, factorsDistribution$p );

# view 3 (equality view - expectations and binding constraints): slope of the yield curve will increase by 5 bp
 
# assign confidence to the views and pool opinions
# sum of weights should be equal 1
# .35 is the weight on the reference model
# .2 is the confidence on View 1; .25 is the confidence on View 2; .2 is the confidence on View 3

c = cbind( 0.35 , 0.2 , 0.25 , 0.2 )
p_= cbind( factorsDistribution$p , p_1 , p_2 , p_3 ) %*% t(c) # compute the uncertainty weighted posterior probabilities


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# compute mean-risk efficient frontier based on posterior market distribution
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#[Exp_,SDev_,CVaR_,w_]
optimalPortfoliosPosterior = LongShortMeanCVaRFrontier( PnL , p_ , butterfliesAnalytics , Options )
#PlotEfficientFrontier(Exp_,CVaR_,w_)

View( optimalPortfoliosPosterior ) # Note that composition is measured in dollars. Now we are long GOOG_vol_91, and short Goog_vol_182

# plot efficient frontier ( Exp_ , CVaR_ , w_ )
PlotFrontier(optimalPortfoliosPosterior$Exp, optimalPortfoliosPosterior$SDev , optimalPortfoliosPosterior$Composition)

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# tests
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p_3b = ViewCurveSlope( factorsDistribution$X , factorsDistribution$p )
p_4  = ViewCurveSlopeTest( factorsDistribution$X , factorsDistribution$p )