A stock has a beta of .7 and an expected return of 17 percent. A risk-free asset

Question

A stock has a beta of .7 and an expected return of 17 percent. A risk-free asset currently earns 4.8 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. Omit the "%" sign in your response.) Expected return %

b. If a portfolio of the two assets has a beta of .50, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) Portfolio Weight xS % xrf %

c. If a portfolio of the two assets has an expected return of 10.00 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.) Beta

d. If a portfolio of the two assets has a beta of 1.27, what are the portfolio weights? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) Porfolio Weight xS % xrf %

Explanation / Answer

a. Return on the stock will be as follows: Rs*Ws + Rf*Wf

wher Rf = 4.8 and Rs = 17 and Ws = Rs = 0.5. hence return is 4.8*0.5 + 17*0.5 = 10.9%

b.Now the risk free asset will have bet of 0. Hence the equation is given as follows

Beta = 0.5 = W*0.7 + (1-W)*0

0.5 = W*0.7

W = 0.5/0.7 = 0.71428

Therefore Weight of Asset 1 (Stock)= W1 = 0.71428

Weight of asset 2 (Risk free asset)= W2 = 1 - W = 1 -0.71428 = 0.28572

c.When Expected return is 10% we have the equation as :

10 = 17*W + 4.8*(1-W)

10 = 17W + 4.8 - 4.8W

5.2 = 12.2 W

Hence W = 0.4262

Hence Weight is Asset 1 (Stock) = W1 = 0.4262

Hence weight in Asset 2 (Risk free asset) = W2 = 1-0.4262 = 0.5738

c, When Beta is 1.27

1.27 = 0.7*W + (1-W)*0

W = 1.8143. T

weight of Stock w1 = 1.8143

and weight of Risk free asset w2 = 1-1.8143 = -0.8143

This indicates that we cannot have a a portfolio with a beta of 1.27.

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