Download to a spreadsheet the last 30 years of monthly adjusted stock prices for Occidental Petroleum (OXY), ONEOK (OKE), and Chevron (CVX). You can download the data from finance.yahoo.com.

a) Calculate the monthly returns of each stock.

b) Calculate 5-year rolling standard deviations of returns. Find the annualized standard deviations by multiplying by the square root of 12. Use the Excel function STDEVP. Plot the annualized 5-year rolling standard deviations over time.

c) Calculate 5-year rolling mean of the returns. Find the annualized mean by multiplying by 12. Plot the 5-year rolling annualized means over time.

d) Which statistic, the mean or the standard deviation, is more stable? e) For the following exercises use all the 30 years of monthly data. Use the Excel function CORREL to calculate the correlation coefficient between the monthly returns for each pair of stocks. Which pair provides the greatest gain from diversification? f) Calculate the annualized standard deviation and mean of each stock return. Calculate the standard deviation of returns for a portfolio with equal investments in the three stocks. g) If there is a risk-free asset with risk-free rate equal to zero, find the feasible set and the efficient frontier. Assume that the investment universe consists of the three stocks and the risk-free asset. You can use the historical means, standard deviations, and correlations. h) Suppose you want to construct an optimal portfolio that will have a 40% standard deviation. What would be the optimal weights in the stocks and the risk-free asset? What would be the expected return of that optimal portfolio? i) Obtain the market capitalization of the three stocks. Using these values, calculate the proportion of each market cap of the total market cap (sum of the market cap of the three stocks). Construct a portfolio with those proportions. Called this new portfolio asset E. j) Assume that there is a risk-free asset with rate equal to zero. Find the mix (weights) of asset E and the risk-free asset that has a 40% standard deviation. What are the weights in the stocks (each one) and risk-free asset that produce that mix? What is the expected return of the mix? k) Compare the weights in j) to the ones in h). Which weights, the ones in j) or h), would you use if you wanted to maximize your return given a 20% volatility? Why?