Jackie has one risk-free asset and one risky stock in her portfolio. The risk-free has an expected return of 3.2 percent. The risky asset has a beta of 1.3 and an expected return of 14.9 percent. What is the expected return on the portfolio if the portfolio beta is 0.975?

Portfolio Return = 11.975%

Explanation:

The portfolio return is calculated by taking the weights of individual securities in a portfolio and multiplying them by the return of individual securities. The formula can be written as,

Portfolio return = wA * rA + wB * rB

Where,

wA is the weight of security A rA is the return on security A wB is the weight of security B rB is the return on security B

The risk free asset has a beta of zero.

Let the weight of risk free asset be x. The weight of risky asset is 1-x.

Portfolio beta = 0.975 = x * 0 + (1-x) * 1.3

0.975 = 1.3 - 1.3x

0.975 - 1.3 = - 1.3x

-0.325 / - 1.3 = x

x = 0.25

Portfolio return = 0.25 * 0.032 + (1-0.25) * 0.149 = 0.11975 or 11.975%