Question

The following are estimates for two stocks.

Stock	Expected Return			Beta	Firm-Specific Standard Deviation
A		10	%	1.00		35	%
B		16		1.50		44

The market index has a standard deviation of 21% and the risk-free (T-Bills are risk free) rate is 12%.

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	0.25
Stock B	0.50
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. The calculation of the standard deviation of Stock A and stock B is given below:

As we know that

The formula of Standard deviation is

= (Beta² * Std dev of market² + firm specific std deviation²)^0.5

So,

Std dev of stock A is

= (1² * 21² + 35²)^0.5

= 40.83%

Std dev of stock B = (1.50² * 21² + 44²)^0.5

= 48.78%

b. Provided that

Weight of stock A = 0.25

Weight of Stock B = 0.50

Weight of T-bill = 0.25

Now

Expected return of the portfolio is

= .25 * 10% + .50 * 16% + .25 * 12%

= 13.5%

Beta of the portfolio is

= .25 * 1 + .50 * 1.50 + .12 * 0

= 1

As we know that

Variance of the portfolio = Beta² * Std deviation of market² + Std deviation of portfolio²

^So,

Systematic component = Beta² * Std deviation of market²

And.

Non Systematic component = Std deviation of portfolio²

So,

Non Systematic Std deviation of portfolio² is

=  (0.25²* 35²) + (0.50²* 44²) + (0.25²*0)

=  560.56

Non Systematic Std deviation of portfolio= 23.68%

Now                                     

Std dev of portfolio² is

= (1² * 21² +560.56)^0.5

Std dev of portfolio = 31.65%