Question

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

Probability	A	B
0.3	(15%)	(30%)
0.2	3	0
0.2	11	20
0.1	24	26
0.2	33	40

1. Calculate the expected rate of return, , for Stock B ( = 7.30%.) 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 = 26.58%.) 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 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. 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. 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.
   4. 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.
   5. 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.
   
   
   -Select-IIIIIIIVVItem 4

3. Assume the risk-free rate is 2.5%. 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 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.
   2. 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.
   3. 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.
   4. 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.
   5. 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.

Answer 1

a. Expected rate of return = P1R1+P2R2+P3R3+P4R4+P5R5

expected rate of return on stock A=0.3*0.15+0.2*0.03+0.2*0.11+0.1*0.24+0.2*0.33

=16.30%

b.Standard deviation of expected return of stock A =0.3(15-16.3)^2+0.2(3-16.3)^2+0.2(11- 16.3)^2+0.1(24-16.3)^2+0.2(33-16.3)^2

=10.16%

Coefficient of variation for stock B= Standard deviation / expected rate of returns

=26.58%/7.30%

=3.64%

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 lower beta than Stock A, and hence be less risky in a portfolio sense.

c. Sharpe ratio for stock A & B=( return on portfolio- risk free rate)/ portfolio standard deviation

weight of stock A( WA)= SD of B/(SD of A+ SD of B)

= 26.58/(10.16+26.58)

= 0.72

weight of stock B(WB) = 1-WA =0.28

Expected return of portfolio= (WA * RA)^2 + (WB *RB)^2

= (0.72*16.30%)^2+(0.28*7.30%)^2

=1.42%

Covariance= submission of (probability*deviation of stock A* deviation of stock B)

=120.72

correlation = covariance/ SD of A* SD of B

=120.72/(10.16%*26.58%) = 0.45

Portfolio Standard deviation =(( WA* SDA)^2 + (WB*SDB)^2+2*WA*WB*SDA*SDB*correlation)^1/2

=((0.72*10.16)^2+(0.28*26.58)^2+2*0.72*0.28*10.16*26.58*0.45)^1/2

=78.95

Sharpe ratio =(1.42%-2.5%)/78.95

= -0.00014

V. 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.