Assume that both Apple and Yahoo plot on the SML. Apple has a beta of

Assume that both Apple and Yahoo plot on the SML. Apple has a beta of 2.6 and an expected return of 21.2%. Yahoo has a beta of 0.90 and an expected return of 9.3%.

The expected return on the market portfolio is 10%and the risk-free rate is 3%. If you wish to hold a portfolio consisting of Apple and Yahoo and have a portfolio beta equal to 1.5, what proportion of the portfolio must be in Apple? What is the expected return on the portfolio?

Apple Yahoo Market Portfolio Risk-free Asset
Beta 2.6 0.9 1.0 0.0
Expected Return 21.2% 9.3% 10.0% 3.0%
What will be an ideal response?

ANSWER

Answer:
βp = Σ βi ∗ wi =
1.50 = 2.6 ∗ wa + 0.9 * (1-wa)
.60 = 1.7wa
wa = 0.6/1.7 = 0.353 and wy = 0.647

E(rp) = rf + β[E(rm) – rf] × βp = 3.0% + 1.50 ∗ [10.0% – 3.0%] × 1.50 = 13.5%