Question

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

Probability	A	B
.1	(13%)	(40%)
.1	5	0
.5	15	21
.2	22	30
.1	33	48

a.) Calculate the expected rate of return for Stock B ( = 14.40%.) Do not round intermediate calculations. Round your answer to two decimal places.

b.) Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 22.17%.) Do not round intermediate calculations. Round your answer to two decimal places.

c.) Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. Round your answer to two decimal places.

d.) 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.

e.) Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?

Answer 1

- V D2 2 X B A E F G H fc =+A2-$C$8 C D Expected return [rxP(r)=u] -1.3% -27.40% Probability [(P(r)] 0.10 r-u 1 Returns A -13% (r-u)^2 P(r)x(r-u)^2 0.75% 7.51% Sharpe ratio Sharpe ratio 5% 15% 22% 33% 0.10 0.50 0.20 0.10 0.5% 7.5% 4.4% 3.3% -9.40% 0.60% 7.60% 18.60% 0.88% 0.00% 0.58% 3.46% (Mean-Risk free rate/SD 1.1306 =(14.4%-1.5%)/11.41% 0.09% 0.00% 0.12% 0.35% Coefficient of variation Coefficient of variation Standard deviation Mean 0.79 =11.41%/14.4% 8 Expected return 14.40% 1.30% Variance (o^2) Standard deviation (o) 11.41% 12 Returns B -40% 0% Probability [(PC)] 0.10 0.10 Expected return [rxP(r)= u r-u -4.0% -57.30% 0.0%-17.30% (r-u)^2 32.83% 2.99% P(r)x(r-u)^2 3.28% 0.30% Sharpe ratio Sharpe ratio 21% 30% 0.50 0.20 0.10 16 17 18 10.5% 6.0% 4.8% 3.70% 12.70% 30.70% 0.14% 1.61% 9.42% (Mean-Risk free rate)/SD 0.7127 =(17.3%-1.5%)/22.17% 0.07% 0.32% 0.94% 48% Coefficient of variation Standard deviation Mean 1.28 Expected return 17.30% Coefficient of variation =22.17%/17.3% Variance (o^2) Standard deviation (0) 4.92% 22.17% Correct option is "If Stock B is less highly correlated with 25 the market than Stock A, then it might have a lower beta

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