6. This problem uses daily stock price data in the file Stock_Bond.csv on the book’s website. In this exercise, use only the first 500 prices on each stock.

The following R code reads the data and extracts the first 500 prices for five stocks. “AC” in the variables’ names means “adjusted closing” price.

dat = read.csv("Stock_Bond.csv", header = T)

prices = as.matrix(dat[1:500, c(3, 5, 7, 9, 11)])

(a) What are the sample mean vector and sample covariance matrix of the 499 returns on these stocks?

(b) How many shares of each stock should one buy to invest $50 million in an equally weighted portfolio? Use the prices at the end of the series, e.g., prices[,500].

(c) What is the one-day VaR(0.1) for this equally weighted portfolio? Use a parametric VaR assuming normality.

(d) What is the five-day Var(0.1) for this portfolio? Use a parametric VaR assuming normality. You can assume that the daily returns are uncorrelated.