The following are estimates for two stocks. Stock Expected Return Beta Firm-Spec

Question

The following are estimates for two stocks.

Stock Expected Return Beta Firm-Specific Standard Deviation
A 12 % 0.65 27 %
B 20 1.20 40

The market index has a standard deviation of 23% and the risk-free rate is 11%.

a. What are the standard deviations of stocks A and B? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Stock a = Stock b=

please put answer in %

b. Suppose that we were to construct a portfolio with proportions:

Stock A 0.40
Stock B 0.40
T-bills 0.20

Compute the expected return, standard deviation, beta, and nonsystematic standard deviation of the portfolio. (Do not round intermediate calculations. Enter your answer for Beta as a number, not a percent. Round your answers to 2 decimal places.)

expected Return= (in %)

Standard Deviation= (in %)

Beta=

Nonsystamatic Standard Deviation= (in %)

Explanation / Answer

a. sd of A = (sd of stock2 - sd of market2) ^(1/2) = (0.272 - 0.232)^(1/2) = (0.0729 - 0.0529)^(1/2) = 0.02^(1/2) = 0.1414 = 14.14%

sd of B = (sd of stock2 - sd of market2) ^(1/2) = (0.42 - 0.232)^(1/2) = (0.16 - 0.0529)^(1/2) = 0.1071^(1/2) = 0.3272 = 32.72%

b. expected return of portfolio = 0.4 * 12 + 0.4*20 + 0.2*11 = 15%

beta of portfolio = 0.4*0.65 + .4*1.2 = 0.74

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