Question

You wish to combine two stocks, Encor and Maestro, into a portfolio with an expected return of 16.7 percent. The expected return of Encor is 2.7 percent with a standard deviation of 1 percent. The expected return of Maestro is 26.4 percent with a standard deviation of 10.7 percent. The correlation between the two stocks is 0.4. What is the composition (weights) of the portfolio? (Round answer to 4 decimal places, e.g. 14.5125%.) Weight in Encor % Weight in Maestro % What is the portfolio standard deviation? (Round intermediate calculations to 7 decimal places, e.g. 0.5125129 and the final answer to 4 decimal places, e.g. 14.5125%.) Standard deviation %

Answer 1

Let Weight in Encor be W, then Weight in Maestro is (1-W).

Expected return on portfolio, Rp = 16.7%

Expected return of Encor , Re = 2.7%

Expected return of Maestro, Rm = 26.4%

Rp = W* Re + (1- W) * Rm

16.7% = W * 2.7% + (1-W) * 26.4%

16.7% = 2.7% W + 26.4% - 26.4% W

23.7% W = 9.7%

W = 0.4092 = 40.9282%= Weight in Encor

Weight in Maestro = (1- W) = 59.0717 %

Portfolio Standard deviation = (W ^2 *SD1^2 + W2^2* SD2^2 + 2* W1* W2* SD1*SD2* Correl(E,M) )^1/2

= (0.4092^2 * 0.01^2 + 0.5907^2 * 0.107^2 + 2* 0.4092 * 0.107 * 0.01 * 0.107* 0.4)^1/2

= 6.4952%