Consider a portfolio that consists of two assets which we call A and B. Let X be the annual rate of return from A and Y denote the annual rate of return from B. Let

E[X] = 0.15; E[Y] = 0.20; Var[X] = 0.052; Var[Y] = 0.072 and CORR[X, Y ] = 0.30

Use a spreadsheet to perform the following analysis.

1.Suppose the fraction of portfolio invested in asset B is f and the fraction invested in A is 1 - f. Let f vary from 0 to 1 in increments of 5% (i.e., f = 0.0; 0.05; 0.10; ... ; 1.0). Compute the mean and standard deviation of the annual rate of return of the portfolio. Plot the standard deviation as a function of the return.

2.Assume that the risk-free interest rate, r_F , is 0.05. For any portfolio P, let E[P] and SD[P ] denote its expected return and standard deviation of the return. The Sharpe-ratio for P is then given by (E[P] - r_F)/SD[P] . Which of the portfolios has the maximum Sharpe-ratio?

3.Repeat the above exercise but change CORR[X, Y ] to 0.1. Interpret the change in the output graph.