# [R-SIG-Finance] [R-sig-finance] VaR again

Thu Apr 30 04:37:34 CEST 2009

```megh,

Like you, I agree with Brian as well about the normality issue.  I have the
following code to estimate fractional contributions to risk assuming normal
returns (for calculating var-cov matrix at least).   I tried to make it
general so you can slap it in with a minimal effort.  It should work for N
assets, just as long as you define vector of weights to reflect the number
of assets...

The calculations are based on a paper by Edward Qian: On the Financial
Interpretation of Risk Contribution: Risk Budgets Do Add Up, located at:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=684221

hope that helps out.

res

#----------------------------------------------------------------------------------------------
# Standard mean-variance portfolio estimates
# Use mean returns on closing prices for covariance matrix construction

# The following code assumes you have a vector of weights such as:
#         wts <- matrix(c(0.4,0.6),ncol=2,nrow=1,byrow=T)
# and a matrix of asset prices where the columns are the individual assets
such as:
#         assets <- cbind(open, high, low, close) = cbind(O,H,L,C)
# so for multiple assets:
#         assets <- cbind(O1,H1,L1,C1, O2,H2,L2,C2, ..., On,Hn,Ln,Cn)
# then transform assets to log assets by:
# ln.assets <- log(assets)

# assets.labels is a vector of length N of the asset names:
#         assets.labels <- c("SBUX", "SPX", "C", ..., "asset-N")
# annualization is the factor used to adjust the volatility to annual
volatility
# Rf is the risk-free rate
#

ind <- 1:length(assets.labels)
assets.rtn <- ln.assets[2:N,(4*ind)] - ln.assets[1:(N-1),(4*ind)]
cov.rtn <- cov(assets.rtn); colnames(cov.rtn) = assets.labels ;
rownames(cov.rtn) = assets.labels
cor.rtn <- cor(assets.rtn); colnames(cor.rtn) = assets.labels ;
rownames(cor.rtn) = assets.labels

vol.scen <- matrix(0.0,ncol=2,nrow=nrow(wts))
vol.scen[,1] <- sqrt(wts%*%cov.rtn%*%t(wts))
vol.scen[,2] <- vol.scen[,1]*sqrt(annualization)
vol.scen <- t(vol.scen)

# Expected Returns & Sharpe Ratio
E.rtn <- sum(wts*colMeans(assets.rtn))- Rf
Srp <- E.rtn/vol.scen[1,1]

cat("Standard Portfolio E(R) & Vol Given Scenario Weights:", "\n")
print(round(vol.scen*100,2))
cat("E(R):     ", round(E.rtn*100,4), "\n")
cat("Sharpe:   ", round(Srp*100,4), "\n")
cat("Weights:  ", "\n")
print(round(wts,3))
cat("Assest Exposure:  ",sum(wts), "\n")
cat("-----------------------------------------------------------------------------------------",
"\n")

#----------------------------------------------------------------------------------------------
# Proportional Contribution to Risk Estimate

partials <- matrix(0.0,ncol=1 ,nrow=length(wts))
for(i in 1:length(wts)){
partials[i,] <- sum(wts%*%cov.rtn[i,])
}
partials <- partials*(1/vol.scen[1,1])
frac.contrib <- t(wts)*partials*(1/vol.scen[1,1])
rownames(frac.contrib) = assets.labels ; colnames(frac.contrib) = ann.name

cat("Percentage Contribution To Total Risk:", "\n")
print(round(frac.contrib*100,2))
cat("-----------------------------------------------------------------------------------------",
"\n")
#----------------------------------------------------------------------------------------------

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