Portfolio Optimization using Single Index Model in R

Portfolio Optimization using Single Index Model in R

# Load Libraries:
library(fEcofin)
library(fPortfolio)

# Load Data:
data(berndtInvest)
berndt <- as.timeSeries(berndtInvest)
names(data)
data <- berndt[, -c(10, 17)]
factors <- berndt[, 10]
attr(data, "factors") <- factors

# Sharpe's Single Index Factor Model:
sharpeFactorEstimator <- 
function(x, spec=NULL, ...)
{
    # Sharpe Single Index Model:
    data <- getDataPart(x)
    factors <- attr(x, "factors")
    nScenarios <- nrow(data)
    X.mat <- cbind(rep(1, times=nScenarios), factors)
    G.hat <- solve(qr(X.mat), data)
    beta.hat <- G.hat[2, ]
    eps.hat <- data - X.mat %*% G.hat
    diagD.hat <- diag(crossprod(eps.hat) / (nScenarios-2))
    mu <- G.hat[1, ] + G.hat[2, ] * colMeans(factors)  
    Sigma <- var(factors)[[1]] * (beta.hat %o% beta.hat) + diag(diagD.hat)
    
    # Return Value:
    list(mu = mu, Sigma = Sigma)
}

# Solve Long Only Markowitz Model:
markowitz <- portfolioFrontier(data)

# Solve Long Only Sharpe Single Index Model:
spec <- portfolioSpec()
setEstimator(spec) <- "sharpeFactorEstimator"
sharpe <- portfolioFrontier(data, spec)

# Plot:
tailoredFrontierPlot(markowitz)
points(frontierPoints(sharpe), col = "steelblue")

FUNCTION:                     DESCRIPTION:
sharpeFactorEstimator()       Sharpe's single index model
macroFactorEstimator()        General macroeconomic factor model
industryFactorEstimator()     Barra industry factor model
statisticalFactorEstimator()  Statistical factor model
pcaFactorEstimator()          PCA statistical factor model
asympcaFactorEstimator()      Asymptotic PCA statistical factor model

 Source: (https://www.rmetrics.org/blog/FactorModeling)
References:
Würtz, Chalabi, Chen, Ellis, Portfolio Optimization with R/Rmetrics, Rmetrics and Finance Online Publishing, Zurich 2009
Zivot and Wang, Modeling Financial Time Series with S-PLUS. Springer Publishing New York, 2nd edition 2006
Any Questions?
Do not hesitate to contact us or come to the Meielisalp 2010 Workshop to meet the authors.