The stock market consists of only 2 stocks, X and Y Their market capitalizations are $1.5bn and $8.5bn respectively. Their returns are uncorrelated. The mean return of X is 6% and that of Y is 11%. The standard deviations of X and Y are 25% and 40% respectively. Assume that the risk-free rate is 5.63%. 

i. What are the mean return, the return standard deviation, and the Sharpe ratio of the market portfolio? Explain each step in your analysis. Compare these numbers to those for X and Y and explain any patterns that you see. 

ii. Derive the precise numerical form of the Capital Asset Pricing Model (CAPM) equation that holds in this economy and interpret it. 

ii. Compute and comment upon the CAPM betas of the two stocks. Plot the Security Market Line, explain its implications, and on that line show each of the stocks. 

b. Explain the intuition as to why the CAPM tells us that it is covariances that determine the risk of individual securities rather than their variances.