Question

A stock has a beta of 1.4, an expected return of 17.2 percent, and lies on the security market line. A risk-free asset is yielding 3.2 percent. You want to create a portfolio that is comprised of the stock and the risk free and will have a portfolio beta of 0.6. What is the expected return on this portfolio?

Answer 1

the portfolio's return will be Ep(r)= 9.2 %

Step-by-step explanation:

if the stock lies on the security market line , then the expected return will be

Ep(r) = rf + β*( E(M)- rf)

where

Ep(r) = expected return of the portfolio

rf= risk free return

E(M) = expected return of the market

β = portfolio's beta

then

Ep(r) = rf + β*( E(M)- rf)

E(M) = (Ep(r) - rf ) / β + rf

replacing values

E(M) = (Ep(r) - rf ) / β + rf

E(M) = ( 17.2% - 3.2%) /1.4 + 3.2% = 13.2%

since the stock and the risk free asset belongs to the security market line , a combination of both will also lie in this line, then the previous equation of expected return also applies.

Thus for a portfolio of β=0.6

Ep(r) = rf + β*( E(M)- rf) = 3.2% + 0.6*(13.2%-3.2%) = 9.2 %

Ep(r)= 9.2 %