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

Expected rate of return on the portfolio is 8.46

Step-by-step 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