Question

The following are estimates for two stocks.

Stock	Expected Return			Beta	Firm-Specific Standard Deviation
A		15%		0.60		26%
B		23		1.15		38

The market index has a standard deviation of 21% and the risk-free rate is 9%.

a.	What are the standard deviations of stocks A and B? (Do not round intermediate calculations. Enter your responses as decimal numbers rounded to 2 decimal places).

Stock A
Stock B

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

Stock A	0.35
Stock B	0.40
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 in numbers, not in percentage. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

  

	Standard Deviation
Expected return	%
Standard deviation	%
Beta
Nonsystematic standard deviation	%

Answer 1

Standard Deviation of Stock = Firm-specific StdDeviation+ Beta*Market StdDeviation

Stock A = 26% + 0.6*21% = 38.60%

Stock B = 38%+1.15*21% = 62.15%

cov(A,B) = beta(A)*beta(B)*variance(m) = 0.6*1.15*21% = 0.1449

Correlation(A,B) = Cov(A,B)/StdDev(A)*StdDev(B) = 0.1449/(0.386*0.6215) = 0.604

Portfolio:

Stock A	0.35
Stock B	0.40
T-bills	0.25

Expected Return = 0.35*15%+0.4*23%+0.25*9% = 16.70%

Standard Deviation = sqrt((0.35*38.6%)^2+(0.4*62.15%)^2+2*0.35*0.4*38.6%*62.15%*0.604) = 34.73%

Beta = 0.35*0.6+0.4*1.15+0.25*0 = 0.67

Nonsystematic standard deviation = 34.73% - 0.67*21% = 20.66%