# testport.r illustrate portfolio functions in portfolio.r and portfolio_noshorts.r # updates: # August 15, 2012 # updated to cover portfolio functions that impose no short sale constraints # August 11, 2011 # updated to work with R 2.13.1 options(digits=4, width=70) source("http://faculty.washington.edu/ezivot/econ424/portfolio_noshorts.r") # Functions: # 1. efficient.portfolio compute minimum variance portfolio # subject to target return # 2. globalMin.portfolio compute global minimum variance portfolio # 3. tangency.portfolio compute tangency portfolio # 4. efficient.frontier compute Markowitz bullet # 5. getPortfolio create portfolio object # # # Examples from Introduction to Financial Econometrics # asset.names = c("MSFT", "NORD", "SBUX") er = c(0.0427, 0.0015, 0.0285) names(er) = asset.names covmat = matrix(c(0.0100, 0.0018, 0.0011, 0.0018, 0.0109, 0.0026, 0.0011, 0.0026, 0.0199), nrow=3, ncol=3) r.free = 0.005 dimnames(covmat) = list(asset.names, asset.names) er covmat r.free # # compute equally weighted portfolio ew = rep(1,3)/3 equalWeight.portfolio = getPortfolio(er=er,cov.mat=covmat,weights=ew) class(equalWeight.portfolio) names(equalWeight.portfolio) equalWeight.portfolio summary(equalWeight.portfolio) plot(equalWeight.portfolio, col="blue") # # compute global minimum variance portfolio gmin.port = globalMin.portfolio(er, covmat) attributes(gmin.port) print(gmin.port) summary(gmin.port, risk.free=r.free) plot(gmin.port, col="blue") # # compute global minimum variance portfolio with no short sales gmin.port.ns = globalMin.portfolio(er, covmat, shorts=FALSE) attributes(gmin.port.ns) print(gmin.port.ns) summary(gmin.port.ns, risk.free=r.free) plot(gmin.port.ns, col="blue") # # compute efficient portfolio subject to target return target.return = er["MSFT"] e.port.msft = efficient.portfolio(er, covmat, target.return) e.port.msft summary(e.port.msft, risk.free=r.free) plot(e.port.msft, col="blue") # # compute efficient portfolio subject to target return with no short sales target.return = er["MSFT"] e.port.msft.ns = efficient.portfolio(er, covmat, target.return, shorts=FALSE) e.port.msft.ns summary(e.port.msft.ns, risk.free=r.free) plot(e.port.msft.ns, col="blue") # # compute tangency portfolio tan.port <- tangency.portfolio(er, covmat, r.free) tan.port summary(tan.port, risk.free=r.free) plot(tan.port, col="blue") # # compute tangency portfolio with no short sales tan.port.ns <- tangency.portfolio(er, covmat, r.free, shorts=FALSE) tan.port.ns summary(tan.port.ns, risk.free=r.free) plot(tan.port.ns, col="blue") # # compute portfolio frontier ef <- efficient.frontier(er, covmat, alpha.min=-2, alpha.max=1.5, nport=20) attributes(ef) ef plot(ef) plot(ef, plot.assets=TRUE, col="blue", pch=16) points(gmin.port\$sd, gmin.port\$er, col="green", pch=16, cex=2) points(tan.port\$sd, tan.port\$er, col="red", pch=16, cex=2) text(gmin.port\$sd, gmin.port\$er, labels="GLOBAL MIN", pos=2) text(tan.port\$sd, tan.port\$er, labels="TANGENCY", pos=2) sr.tan = (tan.port\$er - r.free)/tan.port\$sd abline(a=r.free, b=sr.tan, col="green", lwd=2) # plot portfolio frontier with tangency portfolio sd.vals = sqrt(diag(covmat)) mu.vals = er plot(ef\$sd, ef\$er, ylim=c(0, max(ef\$er)), xlim=c(0, max(ef\$sd)), xlab="portfolio sd", ylab="portfolio er", main="Efficient Portfolios") text(sd.vals, mu.vals, labels=names(mu.vals)) abline(a=r.free, b=sr.tan) # # compute portfolio frontier with no short sales ef.ns <- efficient.frontier(er, covmat, alpha.min=0, alpha.max=1, nport=20, shorts=FALSE) attributes(ef.ns) ef.ns summary(ef.ns) plot(ef.ns) plot(ef.ns, plot.assets=TRUE, col="blue", pch=16) points(gmin.port.ns\$sd, gmin.port.ns\$er, col="green", pch=16, cex=2) points(tan.port.ns\$sd, tan.port.ns\$er, col="red", pch=16, cex=2) text(gmin.port.ns\$sd, gmin.port.ns\$er, labels="GLOBAL MIN", pos=2) text(tan.port.ns\$sd, tan.port.ns\$er, labels="TANGENCY", pos=2) sr.tan.ns = (tan.port.ns\$er - r.free)/tan.port.ns\$sd abline(a=r.free, b=sr.tan.ns, col="green", lwd=2) # plot portfolio frontier with tangency portfolio sd.vals = sqrt(diag(covmat)) mu.vals = er plot(ef.ns\$sd, ef.ns\$er, ylim=c(0, max(ef.ns\$er)), xlim=c(0, max(ef.ns\$sd)), xlab="portfolio sd", ylab="portfolio er", main="Efficient Portfolios") text(sd.vals, mu.vals, labels=names(mu.vals)) abline(a=r.free, b=sr.tan.ns)