P8-15 Correlation, risk, and return Nikki Williams wishes to evaluate the risk and return behaviors associated with various combinations of assets X and Y under three assumed degrees of correlation: perfectly positive, uncorrelated, and perfectly nega- tive. The expected returns and standard deviations calculated for each of the assets are shown in the following table. Asset Expected return, 10% 15 Standard deviation, 5% 8 X Y a. If the returns of assets X and Y are perfectly positively correlated (correlation coefficient = +1), describe the range of (1) expected return and (2) risk associ- ated with all possible portfolio combinations. b. If the returns of assets X and Y are uncorrelated (correlation coefficient = 0), describe the approximate range of (1) expected return and (2) risk associated with all possible portfolio combinations. c. If the returns of assets X and Y are perfectly negatively correlated correlation coefficient = -1), describe the range of (1) expected return and (2) risk associ- ated with all possible portfolio combinations. 3. You are going to invest $20,000 in a portfolio consisting of assets X, Y, and Z, as follows: Asset X Y Z Annual Return 10% 8% 16% Probability 0.50 0.25 0.25 Beta 1.2 1.6 2.0 Proportion 0.333 0.333 0.333 Given the information in Table, find a) expected annual return of this portfolio b) beta of portfolio c) Assuming the risk-free rate of 6 percent and the market return of 12 percent, compute the required rate of return of this portfolio