Question

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

Probability	A	B
0.1	(8%)	(36%)
0.3	3	0
0.3	12	20
0.2	18	25
0.1	33	48

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 10.60%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 21.36%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

4. Is it possible that most investors might regard Stock B as being less risky than Stock A?  

   1. 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.
   2. 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.
   3. 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.
   4. 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.
   5. 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.

Answer 1

a)
Probability	B	Expected Return= Prob. X Return
0.1	-36.00%	-3.60%
0.3	0.00%	0.00%
0.3	20.00%	6.00%
0.2	25.00%	5.00%
0.1	48.00%	4.80%
Expected Return		12.20%
b)
Probability	A	Return - Expected Return (10.60%)	(Return - Expected Return)^2	(Return - Expected Return)^2 X probability
0.1	-8.00%	-18.60%	0.034596	0.0034596
0.3	3.00%	-7.60%	0.005776	0.0017328
0.3	12.00%	1.40%	0.000196	0.0000588
0.2	18.00%	7.40%	0.005476	0.0010952
0.1	33.00%	22.40%	0.050176	0.0050176
			Variance	0.011364
			Standard Deviation=sqrt(variance)	10.66%
c)
Coefficient of variation = SD/Expected Return
Coefficient of variation of B = 21.36%/12.20%	1.75
d)
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.