Question

A stock has a beta of 1.24, an expected return of 13.68 percent, and lies on the security market line. A risk-free asset is yielding 2.8 percent. You want to create a $6,000 portfolio consisting of Stock A and the risk-free security such that the portfolio beta is 0.65. What rate of return should you expect to earn on your portfolio?

Answer 1

Answer:

Expected rate of return on the portfolio is 8.46

Explanation:

RR: Rate of return

Stock has $RR_{1}$ = 13.68, $Beta_{1}$ = 1.24

Risk-free asset has $RR_{2}$ = 2.8, $Beta_{2}$ = 0

(Yield can be considered equivalent to RR here)

Let $x_{i}$ be the weight of the assets.

Portfolio's beta is given by:

Beta = $\sum{x_{i} \beta _{i}}$  = 0.65

=> $1.24x_{1} + 0x_{2} = 0.65$

=> $x_{1}$ = 0.52

=> $x_{2}$ = 1 - 0.52 = 0.48

Rate of return of the portfolio is given by

RR= $\sum{x_{i}RR _{i}}$ = (0.52 * 13.68) + (0.48 * 2.8) = 8.46