Stock A has an expected return of 8 percent and an 18 percent volatility. Stock

Question

Stock A has an expected return of 8 percent and an 18 percent volatility. Stock B has an expected return of 16 percent and a 30 percent volatility. The correlation coefficient between the returns of stock A and stock B is 0.30.

a. What is the expected return of portfolio P1 with 25 percent of funds in stock A and the balance in stock B?

b. What is the covariance between the returns of stock A and those of stock B?

c. What is the volatility of the portfolio P1?

d. What are the expected return and volatility of the minimum risk portfolio?

e. Portfolio P2 has an expected return of 14 percent and a 25 percent volatility. Is it an efficient portfolio? Explain. What expected return should portfolio P2 offer to be efficient?

Explanation / Answer

a. Expected return on portfolio = 0.25 * 8 + 0.75*16 = 14%

b. the covarince between the returns of A and B = Cov (A, B) = Correlation * SD1 * SD2 = 0.3 * 0.18 *0.30 = 0.0162

c. The std deviation = sqrt(w1^2*sd1^2 + w2^2 * Sd2^2 + 2*w1*w2*sd1*sd2) = sqrt(0.25^2 *0.18^2 + 0.75^2 * 0.3^2 + 2*0.25*0.75*0.3*0.18*0.30) = 0.2423 = 24.23%

d. The weights for minimum risk portfolio is as follows

W1 = (sd2^2 - Corr*sd1*ds2)/(sd1^2 + sd2^2 -2*Corr*sd1*sd2)

W1 =( 0.3^2 - 0.3*0.18*0.3)/(0.18^2 + 0.3^2 - 2*0.3*0.18*0.3) = 0.0738/0.09 = 0.82

W2 = 1-0.82 0.18

Expected return = 0.82*8 + 0.18*16 = 9.44%

Std deviation = sqrt(w1^2*sd1^2 + w2^2 * Sd2^2 + 2*w1*w2*sd1*sd2) = sqrt(0.82^2 *0.18^2 + 0.18^2 * 0.3^2 + 2*0.82*0.18*0.3*0.18*0.30) = 0.1717 = 17.17%

e. The Volatilty of P2 (25%)is higher than P1(24.23%) and hence it shoudl generate a return greater than 14% to be efficient

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