Question

Expected returns

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

Probability	A	B
0.1	-12%	-33%
0.3	6	0
0.3	16	20
0.2	23	26
0.1	36	40

A. Calculate the expected rate of return, rB, for Stock B (rA = 13.60%.) Do not round intermediate calculations. Round your answer to two decimal places.
_______ %

B. Calculate the standard deviation of expected returns, ?A, for Stock A (?B = 19.56%.) 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?

If Stock B is more 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.

If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.

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.

If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.

If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.

Answer 1

answer a

expected rate of return= probability (weights) x return

expected rate of return for stock A= 0.1x-33 +0.3x0+0.3x20+0.2x26+0.1x40 = 0.7%

answer b

mean of stock A= (-12+6+16+23+36)/5=13.8%

square of standard deviation= 0.2(-12-13.8)² +0.3(6-13.8)²+0.3(16-13.8)²+0.2(23-13.8)²+0.1(36-13.8)²

=217.496

So standard deviation= square root of 217.496= 14.74%

answerc

mean of stock B= (-33+0+20+26+40)/5= 10.6%

square of standard deviation= 0.2(-33-10.6)² +0.3(0-10.6)² +0.3(20-10.6)²+0.2(26-10.6)²+0.1(40-10.6)²

=574.156

So standard deviation = square of 574.156= 23.96%

covariance= std deviation/mean x 100

= 23.96/10.6 x100= 226.03%

answer d

If stock B is highly correlated with market than A, then it might have a higher beta than stock A and hence more risky in portfolio sense