Question

Stocks A and B have the following probability distributions of expected future returns: Probability     A     B 0.1 (5 %) (22 %) 0.1 5 0 0.6 11 23 0.1 19 30 0.1 32 39 Calculate the expected rate of return, , for Stock B ( = 11.70%.) Do not round intermediate calculations. Round your answer to two decimal places.   % Calculate the standard deviation of expected returns, σA, for Stock A (σB = 16.30%.) 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? 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. -Select-IIIIIIIVVItem 4 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 four decimal places. Stock A: Stock B: Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b? 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. 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. 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. 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. 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. -Select-IIIIIIIVVItem 7

Answer 1

(a) Expected rate of return = Return₁ x Probability₁ + Return₂ x Probability₂ + ...... + Return_n x Probability_n

(b) Standard Deviation of expected returns

Standard Deviation (σ) = √ΣProbability x (Given Return - Expected Return)2

Stock A:

Stock B:

Coefficient of Variation (CV) = Coefficient of Variation measures Risk Per Unit Of Return. It is a relative measure of Risk

CV = Standard Deviation / Expected Return

Stock A: 8.90% / 11.70% = 0.76

Stock B: 16.30% / 18,50% = 0.88

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

Yes, 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.

(c)

Sharpe Ratio = (Expected Return - Risk Free Return) / Standard Deviation

Stock A: (11.70% - 2.5%) / 8.90% = 1.0337

Stock B: (18.50% - 2.5%) / 16.30% = 0.9817

The higher a Sharpe Ratio, the better the investment