Question

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.)

Answer 1

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%

------------------------------------------------------------------------------------------------------------------------------------------------

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