question archive Stocks A and B have the following probability distributions of expected future returns: Probability A B 0
Stocks A and B have the following probability distributions of expected future returns: Probability A B 0
Subject:FinancePrice:3.86 Bought11
Stocks A and B have the following probability distributions of expected future returns:
| Probability | A | B | ||
| 0.1 | (7 | %) | (34 | %) |
| 0.1 | 6 | 0 | ||
| 0.5 | 12 | 21 | ||
| 0.2 | 18 | 30 | ||
| 0.1 | 28 | 39 | ||
a.Calculate the expected rate of return, , for Stock B ( = 12.30%.) Do not round intermediate calculations. Round your answer to two decimal places.
%
b.Calculate the standard deviation of expected returns, σA, for Stock A (σB = 19.47%.) 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.
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:
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The expected return for both the stock is given as
| Probabilty | Stock return A | Stock return B | ||
| P | A | B | P*A | P*B |
| 0.1 | -7% | -34% | -0.70% | -3.40% |
| 0.1 | 6% | 0% | 0.60% | 0.00% |
| 0.5 | 12% | 21% | 6.00% | 10.50% |
| 0.2 | 18% | 30% | 3.60% | 6.00% |
| 0.1 | 28% | 39% | 2.80% | 3.90% |
| Total | 12.30% | 17.00% |
Hence expected return for stock A= 12.3% and for B =17%
the standard deviation of stock A and B is given as
| Probabilty | Stock return A | Stock return B | ||||||
| P | A | B | P*A | P*B | A-expected return of A | P*(A-expected return of A)^2 | B-expected return of B | P*(B-expected return of B)^2 |
| 0.1 | -7% | -34% | -0.70% | -3.40% | -19% | 0.0037249 | -51% | 0.02601 |
| 0.1 | 6% | 0% | 0.60% | 0.00% | -6% | 0.0003969 | -17% | 0.00289 |
| 0.5 | 12% | 21% | 6.00% | 10.50% | 0% | 4.5E-06 | 4% | 0.0008 |
| 0.2 | 18% | 30% | 3.60% | 6.00% | 6% | 0.0006498 | 13% | 0.00338 |
| 0.1 | 28% | 39% | 2.80% | 3.90% | 16% | 0.0024649 | 22% | 0.00484 |
| Total | 12.30% | 17.00% | Sum(P*(A-expected return of A)^2) | 0.007241 | Sum(P*(B-expected return of B)^2) | 0.03792 |
standard deviation for stock A= (Sum(P*(A-expected return of A)^2))^0.5= 0.007241^0.5= 8.51%
standard deviation for stock A= (Sum(P*(B-expected return of B)^2))^0.5= 0.03792^0.5= 19.47%
Coeffiecient of variation for stock A= SD of A / Expected return of A=8.51%/12.30%=0.69
Coeffiecient of variation for stock B== SD of B / Expected return of B 19.47%/17%=1.15
Sharpe ratio for stock A=(Return of A- risk free rate)/Sd of A
=(12.30%-1.5%)/8.51%
=1.27
Sharpe ratio for stock B=(Return of B- risk free rate)/Sd of B
=(17.00%-1.5%)/19.47%
=0.80
