by Guangming Lang
2 min read


  • r

In a previous post, I showed how to calculate the global minimum variance portfolio using R and vanguard funds in my retirement account. It had an average annual return of 5.2% and volatility of 3.3% in the past 10 years. Because I’m holding those funds for a long term, at least 30 years. I don’t really mind a bigger volatility now. Instead, I really want a bigger return, say 10%. So I’ll set my target return as 10%, and find a portfolio that can achieve it. The resulting portfolio is called mean-variance efficient because it has the smallest volatility for the 10% target return.

Step 0. Load libraries and define helper functions.

## Error in library(tseries): there is no package called 'tseries'
download_data = function(symb, begin, end) {
        get.hist.quote(instrument=symb, start=begin, end=end, 
                       origin="1970-01-01", quote="AdjClose", 
                       provider="yahoo", compression="m", 

to_yearmon = function(data) {
        index(data) = as.yearmon(index(data))

Step 1. I choose assets from three broad classes: stocks, bonds, and commodities. For stocks, I choose funds that cover total US market, total international markets, and real estate. For bonds, I choose funds that invest in the total US bond market and inflation protected securities. For commodities, I choose funds that invest in gold and other precious metals and their mining companies and oil & gas and energy companies. First, I download the monthly adjusted closing price data of these funds between June 2000 and Oct 2014 from Yahoo.

# initialize the fund symbols 
stocks = c("VTSMX", "VGTSX", "VGSIX")
bonds = c("VIPSX", "VBMFX")
commodities = c("VGPMX", "VGENX")
symbols = c(stocks, bonds, commodities)

# download adj. price data
port = list()
for (symbol in symbols)
        port[[symbol]] = download_data(symbol, "2000-06-29", "2014-10-31")
## Error in get.hist.quote(instrument = symb, start = begin, end = end, origin = "1970-01-01", : could not find function "get.hist.quote"
# change the class of the time index to yearmon
lapply(port, to_yearmon)

# put both all price data in one data frame
prices ="cbind", port)
colnames(prices) = symbols
## Error in `colnames<-`(`*tmp*`, value = c("VTSMX", "VGTSX", "VGSIX", "VIPSX", : attempt to set 'colnames' on an object with less than two dimensions

Step 2. Calculate monthly continuously compounded returns as difference in log prices. = diff(log(prices))
## Error in log(prices): non-numeric argument to mathematical function
# inspect the return data
cat("Start: ", as.character(start(, "  End: ", as.character(end(
## Error in start( object '' not found
head(, 3)
## Error in head(, 3): object '' not found

Step 3. Calculate annualized sample average returns of the underlying assets and the sample covariance matrix of the returns.

mu.hat.annual = apply(, 2, mean) * 12   
## Error in apply(, 2, mean): object '' not found
cov.mat.annual = cov( * 12 
## Error in object '' not found

Step 4. Calculate the efficient portfolio with 10% as target return using a helper function written by Eric Zivot and Hezky Varon from U of Washington.

helper = "~/Coding/R-related/R/portfolio-optim/portfolio_noshorts.r"
## Warning in file(filename, "r", encoding = encoding): cannot open file '/
## Users/gmlang/Coding/R-related/R/portfolio-optim/portfolio_noshorts.r': No
## such file or directory
## Error in file(filename, "r", encoding = encoding): cannot open the connection
effi.port = efficient.portfolio(mu.hat.annual, cov.mat.annual, 0.1, F)
## Error in efficient.portfolio(mu.hat.annual, cov.mat.annual, 0.1, F): could not find function "efficient.portfolio"
## Error in eval(expr, envir, enclos): object 'effi.port' not found
# port weights
## Error in plot(effi.port): object 'effi.port' not found