Suppose you are considering owning a portfolio of two stocks -Stock A and Stock B. You are interested not only in the return and value of your portfolio, but also in the risk that comes with stock price volatility. Portfolio diversification is one way of managing risk, but what portfolio combinations work better than others? Let us suppose that the uncertainty associated with Stocks A and B is described by the following probability distribution of the stock prices of both stocks X and Y are the uncertain returns (in percent) to Stocks A and Y respectively 5.0 5.5 6.0 X: P(X) 0.25 0.25 0.25 0.25 4.5 Y: 4.0 5.0 6.0 7.0 P(Y) 0.25 0.25 0.25 0.25 1. Find the mean and standard deviation of each these stocks 2. Consider then a potential portfolio consisting of these stocks. The share of your money going to Stock A is a and that going to Stock B is (1-a). So the return on your portfolio Z aX (1-a)Y. Using the result that E(ax+ bY)-aE(X)+ bE(Y) and var(aX +bY)- a'var(X)+bvar(Y) 2abcov(X,Y), where a and b are constants, var(X) and var(Y) are the variances of returns, and cov(X,Y) is the covariance between the returns of the two stocks. Compare your portfolio under the following alternative scenarios. (i) You invest in only one stock. That this, either a 0 or a 1. (ii) You invest equally in both stocks (a 0.5) and the covariance between the two stocks in 0.592 (ii) You invest equally in both stocks (a-0.5) and the covariance between the two stocks is-0.592