##--------------------------------------- ## Problem 5 ## Portfolio Means, Standard Deviations and Correlations ##--------------------------------------- install.packages("quantmod") library(quantmod) # load data from yahoo finance getSymbols('VUG', from = "2006-01-01") getSymbols('VTV', from = "2006-01-01") VUG # take a look to the data # pick daily closing price only VUG = VUG\$VUG.Close VTV = VTV\$VTV.Close # Plot the historical price of VUG vs VTV. par(mfrow = c(1,2)) plot(VUG) plot(VTV) # compute return of two ETFs VUG.return = dailyReturn(VUG) VTV.return = dailyReturn(VTV) # plot histogram of daily returns of two ETFs par(mfrow = c(1,2)) hist(VUG.return, breaks = 50) hist(VTV.return, breaks = 50) # Calculate the means and standard deviations of both ETFs. mean(VUG.return) mean(VTV.return) sd(VUG.return) sd(VTV.return) # Calculate the covariance between them. cov(VUG.return, VTV.return) # Suppose you decide on a 50-50 split portfolio, calculate mean and variance of your portfolio. portfolio_return = 0.5 * VUG.return + 0.5 * VTV.return hist(portfolio_return, breaks = 50) # compute mean and variance of return of the portfolio portfolio_mean_1 = 0.5 * mean(VUG.return) + 0.5 * mean(VTV.return) portfolio_var_1 = 0.5^2 * var(VUG.return) + 0.5^2 * var(VTV.return) + 2 * 0.5 * 0.5 * cov(VUG.return, VTV.return) portfolio_sd_1 = sqrt(portfolio_var_1) print(portfolio_mean_1) print(portfolio_var_1) print(portfolio_sd_1) # Which alternative portfolio best suits you? # the choice of portfolio depends on your own risk preference