Question

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

Probability	A		B
0.1	(7	%)	(22	%)
0.2	5		0
0.5	14		19
0.1	22		27
0.1	30		36

1. Calculate the expected rate of return, for Stock B ( = 12.50%.) 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 = 15.70%.) 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 1.5%. 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 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.

   -Select-IIIIIIIVVItem 7

Answer 1

D2 : V fc =+A2-$C$8 X в А F 1 Returns A Probability [(P(r)] Expected return [rxP(r)=u] -0.7% -19.50% (r-u)^2 P(r)x(r-u)^2 0.38% N -7% 0.10 3.80% Sharpe ratio Sharpe ratio (Mean-Risk free rate)/SD 1.1591 5% 14% 0.20 0.50 0.10 0.101 co out w 1.0% 7.0% 2.2% 3.0% -7.50% 1.50% 9.50% 17.50% 0.56% 0.02% 0.90% 3.06% 0.11% 0.01% 0.09% 0.31% =(12.5%-1.5%)/9.49% 22% 30% Coefficient of variation Standard deviation+Mean | Coefficient of variation 0.76 =9.49%/12.5% 12.50% 8 Expected return 9 0.90% Variance (o^2) Standard deviation (o) 9.49% 12 Returns B -22% 0% Probability [(P(r)] 0.10 0.20 Expected return [rxP(r)=u] -2.2% -35.60% 0.0% -13.60% (r-u)^2 12.67% 1.85% P(r)x(r-u)^2 1.27% 0.37% Sharpe ratio Sharpe ratio 19% 0.50 27% 9.5% 2.7% 3.6% 0.10 0.10 5.40% 13.40% 22.40% (Mean-Risk free rate)/SD 0.7707 = (13.6%-1.5%)/15.7% 0.29% 1.80% 5.02% 0.15% 0.18% 0.50% 36% Coefficient of variation Standard deviation+Mean Coefficient of variation Susriation 1.15 = 15.7%/13.6% 19 Expected return 13.60% 20 Variance (o^2) 2.46% Standard deviation (o) 15.70% 22 Correct option is "If Stock B is less highly correlated with 25 the market than Stock A, then it might have a lower beta

a) Expected return for Stock B 13.60% Standard deviation for Stock A Coefficient of variation for Stock B Correct option is III 9.49% 1.15 c) Sharpe ratio for Stock A Sharpe ratio for Stock B Correct option is III 1.1591 0.7707

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