Question

Assume the market risk is 8% and risk-free rate is 2%. You have a portfolio with $15,000 invested in Stock A with a beta of 1.2, $8,000 in Stock B with a beta of 1.8, and $12,000 in Stock C with a beta of 2.0. What is the beta and expected return of the portfolio?

Answer 1

Total investment = 15,000 + 8,000 = $23,000

Wa = 15,000/23,000 = 0.652173913

Wb = 8,000/23,000 = 0.347826087

The beta of the portfolio = Wa * Beta of Stock A + Wb * Beta of Stock B

The beta of the portfolio = 0.652173913 * 1.2 + 0.347826087 * 1.8

The beta of the portfolio =1.4086956522

CAPM

The expected return of Stock A

re = 0.02 + 1.2 * (0.08 - 0.06)

re = 0.044

The expected return of Stock B

re = 0.02 + 1.8 * (0.08 - 0.06)

re = 0.056

The expected return of the portfolio = Wa * The expected return of Stock A + Wb * The expected return of Stock B

The expected return of the portfolio = 0.652173913 * 0.044 + 0.347826087 * 0.056

The expected return of the portfolio = 0.04817391304

The expected return of the portfolio = 4.817391304%