Portfolio Management A particular firm’s portfolio is composed of two assets, which we will call" A" and "B." Let X denote the annual rate of return from asset A, and let Y denote the annual rate of return from asset B. Suppose that E(X) = 0.15, E(Y) = 0.20, SD (X) = 0.05, SD (Y) = 0.06, and CORR (X, Y) = 0.30.  (a) What is the expected return of investing 50% of the portfolio in asset A and 50% of the portfolio in asset B? What is the variance of this return?  (b) Replace CORR (X, Y) = 0.30 by CORR (X, Y) = 0.60, 0, -0.30, and -0.60 and answer the questions in part (a). What is the impact of correlation on the expected returns and its variance? Explain why this is so.  (c) Suppose that the fraction of the portfolio that is invested in asset B is f, and so the fraction of the portfolio that is invested in asset A is (1 – f). Let f vary from f = 0.0 to f = 1.0 in increments of 5% (that is, f = 0.0, 0.05, 0.10, 0.15, ...), and compute the mean and the variance of the annual rate of return of the portfolio (using the original correlation of 0.3). Construct a chart plotting the expected return as a function of the variance.  (d) Explain why there is such a relationship between the expected returns and variance in the chart in part (c)

Portfolio Management A particular firm’s portfolio is composed of two assets, which we will call" A" and "B." Let X denote the annual rate of return from asset A, and let Y denote the annual rate of return from asset B. Suppose that E(X) = 0.15, E(Y) = 0.20, SD (X) = 0.05, SD (Y) = 0.06, and CORR (X, Y) = 0.30. 

(a) What is the expected return of investing 50% of the portfolio in asset A and 50% of the portfolio in asset B? What is the variance of this return? 

(b) Replace CORR (X, Y) = 0.30 by CORR (X, Y) = 0.60, 0, -0.30, and -0.60 and answer the questions in part (a). What is the impact of correlation on the expected returns and its variance? Explain why this is so. 

(c) Suppose that the fraction of the portfolio that is invested in asset B is f, and so the fraction of the portfolio that is invested in asset A is (1 – f). Let f vary from f = 0.0 to f = 1.0 in increments of 5% (that is, f = 0.0, 0.05, 0.10, 0.15, ...), and compute the mean and the variance of the annual rate of return of the portfolio (using the original correlation of 0.3). Construct a chart plotting the expected return as a function of the variance.

 (d) Explain why there is such a relationship between the expected returns and variance in the chart in part (c)