Question

Stocks X and Y have the following probability distributions of expected future returns:

Probability	X	Y
0.1	-6%	-24%
0.2	5	0
0.4	15	20
0.2	22	25
0.1	35	35 Calculate the expected rate of return, rY, for Stock Y (rX = 14.30%.) Round your answer to two decimal places. % Calculate the standard deviation of expected returns, ?X, for Stock X (?Y = 16.32%.) Round your answer to two decimal places. % Now calculate the coefficient of variation for Stock Y. Round your answer to two decimal places. Is it possible that most investors might regard Stock Y as being less risky than Stock X? If Stock Y is more highly correlated with the market than X, then it might have a higher beta than Stock X, and hence be less risky in a portfolio sense. If Stock Y is more highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense. If Stock Y is more highly correlated with the market than X, then it might have the same beta as Stock X, and hence be just as risky in a portfolio sense. If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense. If Stock Y is less highly correlated with the market than X, then it might have a higher beta than Stock X, and hence be more risky in a portfolio sense. -Select-IIIIIIIVV

Answer 1

Expected rate of return for Stock Y=(0.1*(-24%)+0.2*0%+0.4*20%+0.2*25%+0.1*35%)=14.1%

Standard Deviation of Stock X=sqrt(0.1*(-6%-14.3%)^2+0.2*(5%-14.3%)^2+0.4*(15%-14.3%)^2+0.2*(22%-14.3%)^2+0.1*(35%-14.3%)^2)=10.65%

COefficient of Variation for Stock Y=Standard Deviation for Y/Expected returns for Y=16.32%/14.1%=1.157

If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.