Question

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

Probability	A		B
0.1	(12	%)	(25	%)
0.2	4		0
0.5	13		19
0.1	19		29
0.1	38		49

1. Calculate the expected rate of return, r B, for Stock B (r A = 11.80%.) 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 = 18.66%.) Do not round intermediate calculations. Round your answer to two decimal places.

     %

   Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. 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 a lower 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 the same beta as Stock A, and hence be just as risky in a portfolio sense.
   3. 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. 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. 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.

   -Select-IIIIIIIVVItem 4

3. Assume the risk-free rate is 4.5%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to four 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.

   -Select-IIIIIIIVV

Answer 1

a) Expected return

Expected return = sum of ( probability x return)

Stock B = 0.1 x (-)25% + 0.2 x 0% + 0.5 x 19% + 0.1 x 29% + 0.1 x 49% = 14.80%

b) Standard deviation

Standard Deviation of A = 11.97%

Coefficient of Variation

Coefficient of Variation = Standard Deviation of B / Expected return of B = 18.66% / 14.80% = 1.26

Option III - 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

Sharpe Ratio = ( ER(i) - Rf ) / si

where, ER(i) = Expected return of stock, Rf = risk free rate, si = Standard deviation of stock

Stock A = (11.80% - 4.5%) / 11.97% = 0.61

Stock B = (14.80% - 4.5%) / 18.66% = 0.55

Option I - 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.