Question

he following are estimates for two stocks.

Stock	Expected Return			Beta	Firm-Specific Standard Deviation
A		8	%	1.10		25	%
B		16		1.60		36

The market index has a standard deviation of 18% and the risk-free rate is 6%.

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

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

Stock A	0.30
Stock B	0.45
T-bills	0.25

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.)

Answer 1

a). Standard deviation of a stock is given by:

where

= stock beta; = Market stand deviation; and, = firm-specific standard deviation

Standard deviation of stock A = [(1.10^2*18%^2)+25%^2]^(1/2) = 31.89%

Standard deviation of stock B = [(1.60^2*18%^2) + 36%^2]^(1/2) = 46.10%

b). Expected return of the portfolio = sum of weighted returns

= wA*ErA + wB*ErB + wf*rf = (0.30*8%) + (0.45*16%) + (0.25*6%) = 11.10%

Beta of the portfolio =  sum of weighted betas

= wA*betaA + wB*betaB + wf*betaf

= (0.30*1.10) + (0.45*1.60) + (0.25*0.0) = 1.05

Non-systematic variance of the portfolio = (weight of A*firm-specific standard deviation)^2 + (weight of B*firm-specific standard deviation)^2 + (weight of T-bills*standard deviation of T-bills)^2

= (0.30*25%)^2 + (0.45*36%)^2 + (0.25*0)^2 = 3.19%

Non-systematic standard deviation = non-systematic variance^(1/2) = (3.19%)^(1/2) = 17.85%

Portfolio variance = (portfolio beta*market standard deviation)^2 + non-systematic variance

= (1.05*18%)^2 + 3.19% = 6.76%

Portfolio standard deviation = portfolio variance^(1/2) = 6.76%^(1/2) = 26.00%