Question

# The following are estimates for two stocks. Stock Expected Return Beta Firm-Specific Standard Deviation A 11...

The following are estimates for two stocks.

 Stock Expected Return Beta Firm-Specific Standard Deviation A 11 % 0.90 32 % B 16 1.40 40

The market index has a standard deviation of 19% and the risk-free rate is 11%.

a. What are the standard deviations of stocks A and B?

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.)

Solution:

a. Since beta of stock A, = 0.90 and beta of stock B, = 1.40, firm-specific standard deviation of stock A, = 0.32, firm-specific standard deviation of stock B, = 0.40

The standard deviation of individual stock is given by:- The standard deviation of stock A, is given by:- = 36.28% The standard deviation of stock A, is given by:- = (1.40^2 x 19^2 + 40^2)^(1/2) = 48.04%

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b. The expected return of the portfolio is given by:-  = 0.40*11% + 0.40*16% + 0.20*0 = 0.108 or 10.8%

The beta of the portfolio is given by:-  = 0.40*0.90 + 0.40*1.40 + 0.20*0 = 0.92

The variance of this portfolio are   = (0.40)^2*(40)^2 + (0.40)^2*(32)^2+ (0.20)^2*0 = 419.84

Hence, the total variance of the portfolio is = (0.92)^2 (19)^2 + 419.84 = 725.39

Standard deviation of the portfolio is = 26.93

The standard deviation of the portfolio is