Stocks A and B have the following probability distributions of expected future r

Question

Stocks A and B have the following probability distributions of expected future returns: Probability 0.1 0.3 0.3 0.2 0.1 (12%) 4 14 (31%) 0 19 27 49 28 a. Calculate the expected rate of return, rB, for Stock B (rA-11.40%.) Do not round intermediate calculations. Round your answer to two decimal places. b. Calculate the standard deviation of expected returns, oA, for Stock A (OB- 20.59%.) Do not round intermediate calculations. Round your answer to two decimal places. c. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places. d. Is it possible that most investors might regard Stock B as being less risky than Stock A? I. If Stock B is less highly correlated with the market than A, then it might have a II. If Stock B is more highly correlated with the market than A, then it might have a III. If Stock B is more highly correlated with the market than A, then it might have a IV. If Stock B is more highly correlated with the market than A, then it might have V. If Stock B is less highly correlated with the market than A, then it might havea higher beta than Stock A, and hence be more risky in a portfolio sense. higher beta than Stock A, and hence be less risky in a portfolio sense. lower beta than Stock A, and hence be less risky in a portfolio sense. the same beta as Stock A, and hence be just as risky in a portfolio sense. lower beta than Stock A, and hence be less risky in a portfolio sense.

Explanation / Answer

Solution: a. Expected rate of return ,rB , for Stock B 12.90% Working Notes: Expected return of Stock B (ErB)= Sum of (Returns x probability of return) =-31% x 0.10 + 0% x 0.30+19% x 0.30 + 27% x 0.20 + 49% x 0.10 =0.129 =12.90 % b. Standard deviation of expected returns,(s.d. A) for Stock A 11.10% Working Notes: Expected return of Stock A (ErA)= Sum of (Returns x probability of return) = -12% x 0.10 + 4% x 0.30+14% x 0.30 + 22% x 0.20 + 28% x 0.10 =0.114 Which is given =11.40 % Standard deviation of expected returns,(s.d. A) for Stock A Standard deviation of return = Square root of ( Sum of (Prob. x (return - expected return )^2)) Standard deviation = Square root of ( (-12% -11.40%)^2 x 0.10 + (4% -11.40%)^2x 0.30+ (14% -11.40%)^2x 0.30 + (22% -11.40%)^2 x 0.20 + (28% -11.40%)^2 x 0.10) Standard deviation of return = Square root of ( 123.24) Standard deviation of return = (123.24)^(1/2) Standard deviation of return = 11.10135% Standard deviation of return = 11.10% C. Coefficient of variation for Stock B 1.60 Working Notes: Coefficient of Variation = Standard Deviation of stock B / Expected return of stock B =20.59%/12.90% =1.59612 =1.60 D. Answer is V. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense. Working Notes: Stock A Stock B Expected return 11.40% 12.90% Standard deviation of return 11.10% 20.59% Coefficient of Variation 0.97 1.60 Coefficient of Variation = Standard Deviation of stock A / Expected return of stock A =11.10%/11.40% =0.97368 =0.97 Though standard deviation of stock B is higher than stock A , so more risky than stock A. Stock B can be less risky than stock A, if Stock B coefficient of correlation with markets lower than stock A , overall result lower beta for stock B than stock A, lower the beta , result less risky than stock A . Please feel free to ask if anything about above solution in comment section of the question.

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