Question

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

Probability	A		B
0.1	(14	%)	(30	%)
0.1	2		0
0.5	13		20
0.2	24		29
0.1	36		45

1. Calculate the expected rate of return, , for Stock B ( = 13.70%.) 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 = 19.01%.) 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 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 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?

   1. 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.
   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 lower beta than Stock A, and hence be less 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 higher beta than Stock A, and hence be more 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 lower beta than Stock A, and hence be less 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 higher beta than Stock A, and hence be more risky in a portfolio sense.

Answer 1

A E F G X V fic =+A2-$C$8 B C D Expected Probability return [(P(r)] [rxP(r)=u] r- 0.101 -1.4% -27.70%! (r-u)^2 1 Returns A -14% P(r)x(r-u)^2 0.77% 7.67% Sharpe ratio Sharpe ratio (Mean-Risk free rate)/SD 0.8812 =(13.7%-2.5%)/12.71% 2% 13% 24% 36% 0.10 0.50 0.20 0.10 0.2% -11.70% 6.5% -0.70% 4.8% 10.30% 3.6% 22.30% 1.37% 0.00% 1.06% 4.97% 0.14% 0.00% 0.21% 0.50% Coefficient of variation Standard deviation Mean Coefficient of variation 0.93 =12.71%/13.7% 8 Expected return 13.70% 1.62% Variance (012) Standard deviation (o) 12.71% 12 Returns B -30% 0% Probability [(P(r)] 0.10 0.10 Expected return [rxP(r)=u] -3.0% -47.30% 0 .0% -17.30% (r-u)^2 22.37% 2.99% P(r)x(r-u)^2 2.24% 0.30% Sharpe ratio Sharpe ratio 20% 29% 45% 0.50 0.20 0.10 10.0% 5.8% 4.5% 2.70% 11.70% 27.70% 0.07% 1.37% 7.67% 0.04% 0.27% 0.77% (Mean-Risk free rate)/SD 0.7785 = (17.3%-2.5%)/19.01% Coefficient of variation Standard deviation Mean Expected return 17.30% Coefficient of variation H 1.10 =19.01%/17.3% Variance (o^2) Standard deviation (0) a riance (0421tion cost 3.61% 19.01% 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 17.30% 12.71% Standard deviation for Stock A Coefficient of variation for Stock B Correct option is II 1.10 0.8812 c) Sharpe ratio for Stock A Sharpe ratio for Stock B Correct option is II 0.7785

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