Question

Problem 12-10 Portfolio Weights (LO4, CFA2)

A stock has a beta of 0.9 and an expected return of 13 percent. A risk-free asset currently earns 4.4 percent.

a. What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b. If a portfolio of the two assets has a beta of 0.78, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

c. If a portfolio of the two assets has an expected return of 9.00 percent, what is its beta? (Do not round intermediate calculations.Round your answer to 4 decimal places.)

d. If a portfolio of the two assets has a beta of 1.01, what are the portfolio weights? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

Solution :-

Stock Beta = 0.90

Expected Return of Stock ( ER )= 13%

Return of Risk Free asset ( Rf ) = 4.4%

Beta of Risk Free Asset = 0

(a)

( 0.50 * ER ) + ( 0.50 * Rf )

= ( 0.50 *13% ) + ( 0.50 * 4.4% )

= 6.5% + 2.2%

= 8.7%

(b)

Let weight of stock be X

X * 0.90 + ( 1 - X ) * 0 = 0.78

X = 0.78 / 0.90 = 86.67%

Therefore Weight of stock = 86.67%

And Weight of Risk Free asset = ( 1 - 0.8667 ) = 13.33%

(c)

Let weight of stock be X

X * 13% + ( 1 - X ) * 4.4% = 9%

13%X + 4.4% - 4.4%X = 9%

8.6%X = 4.6%

X = 0.5349 = 53.49%

Weight of Risk Free asset = ( 1 - .5349 ) = 0.4651 = 46.51%

Now Portfolio Beta

= (53.49% * 0.90 ) + ( 46.51% * 0 )  

= 0.48

(D)

Let weight of stock be X

X * 0.90 + ( 1 - X ) * 0 = 1.01

X = 1.01 / 0.90

X = 1.122 = 112.22%

Stock = 112.22%

And Risk Free asset = -12.22%

Means we need to borrow risk free asset 12.22%

and invest in Stock

If there is any doubt please ask in comments

Thank you please rate ....