A friend brags that she expects to earn a return of 10.25% on her portfolio with a beta of 0.825.Can you match her performance with Stock X (12% return and a beta of 1.1)and the risk free asset that earns a 5% return? With what portfolio weights?
A) Yes, 0.75 Stock X and 0.25 Risk Free Asset
B) Yes, 0.25 Stock X and 0.75 Risk Free Asset
C) Yes, 0.5 Stock X and 0.5 Risk Free Asset
D) No

Question

Quizplus · Accepted Answer

Let w be the weight of Stock X. β_p = w₁β₁ + . . . + w_nβ_n 0.825 = w(1.1) + (1 - w)0 0.825 = 1.1w w = 11ea7fdb_fc0a_73ca_a768_f58653142fa0_TB2902_11 = 0.75 Thus, the weight of the risk-free asset is 0.25. These weights yield the following portfolio expected return: E(k_p) = w₁ E(k₁) + w₂ E(k₂) + w_n E(k_n) E(k_p) = (0.75 × 0.12) + (0.25 × 0.05) = 0.1025 or 10.25% Yes, you can match her risk and return by investing 75% in asset X and the rest in the risk free asset.

A Friend Brags That She Expects to Earn a Return