Question

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

Probability	A	B
0.4	(11%)	(28%)
0.2	3	0
0.1	15	23
0.1	23	26
0.2	36	45

1. Calculate the expected rate of return, , for Stock B ( = 7.20%.) 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 = 28.84%.) Do not round intermediate calculations. Round your answer to two decimal places.
     %

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

   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 the same beta as Stock A, and hence be just as risky in a portfolio sense.
   2. 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.
   3. 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.
   4. 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.
   5. 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.
   
   
   -Select-IIIIIIIVVItem 4

3. Assume the risk-free rate is 3.0%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to two decimal places.

   Stock A:

   Stock B:

   Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?

   1. In a stand-alone risk sense A is less risky than B. 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.
   2. In a stand-alone risk sense A is less risky than B. 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.
   3. In a stand-alone risk sense A is more risky than B. 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.
   4. In a stand-alone risk sense A is more risky than B. 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.
   5. In a stand-alone risk sense A is less risky than B. 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.

Answer 1

1.
=0.4*(-28%)+0.2*0%+0.1*23%+0.1*26%+0.2*45%=2.700%

2.
=sqrt(0.4*(-11%-7.2%)^2+0.2*(3%-7.2%)^2+0.1*(15%-7.2%)^2+0.1*(23%-7.2%)^2+0.2*(36%-7.2%)^2)=18.247%

3.
=28.84%/2.7%=10.68148148

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.
Stock A=(7.2%-3%)/18.247%=0.23

Stock B=(2.7%-3%)/28.84%=-0.01

6.
In a stand-alone risk sense A is less risky than B. 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.