Question

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

Probability	A		B
0.1	(13	%)	(37	%)
0.1	6		0
0.5	10		18
0.2	22		28
0.1	38		35

A.Calculate the expected rate of return,rb , for Stock B (rA = 12.50%.) 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 = 19.26%.) 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.

C. Assume the risk-free rate is 4.5%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to four decimal places.

Answer 1

Answer A.

Stock B:

Expected Return = 0.10 * (-0.37) + 0.10 * 0.00 + 0.50 * 0.18 + 0.20 * 0.28 + 0.10 * 0.35
Expected Return = 0.1440 or 14.40%

Answer B.

Stock A:

Variance = 0.10 * (-0.13 - 0.125)^2 + 0.10 * (0.06 - 0.125)^2 + 0.50 * (0.10 - 0.125)^2 + 0.20 * (0.22 - 0.125)^2 + 0.10 * (0.38 - 0.125)^2
Variance = 0.015545

Standard Deviation = (0.015545)^(1/2)
Standard Deviation = 0.1247 or 12.47%

Answer C.

Stock A:

Sharpe Ratio = (Expected Return - Risk-free Rate) / Standard Deviation
Sharpe Ratio = (0.1250 - 0.0450) / 0.1247
Sharpe Ratio = 0.6415

Stock B:

Sharpe Ratio = (Expected Return - Risk-free Rate) / Standard Deviation
Sharpe Ratio = (0.1440 - 0.0450) / 0.1926
Sharpe Ratio = 0.5140