Question

A friend says that she expects to earn 12.50 % on her portfolio with a beta of 1.50. You have a? two-asset portfolio including stock X and a? risk-free security. The expected return of stock X is 11.00 % and the beta is 1.25. The expected return on the? risk-free security is 3.50 %. You construct a portfolio to match your? friend's return. What is the beta of your? portfolio?

Answer 1

Answer:

Expected Portfolio Return = 12.50%

Expected Return on Stock X = 11.00%
Expected Return on Risk Free Security = 3.50%
Weight of Stock X = x
Weight of Risk Free Security = 1 – x

Portfolio Return = (Weight of Stock X * Return of Stock X) + (Weight of Risk Free Security * Return of Risk Free Security)
0.1250 = (x * 0.1100) + [(1 – x) * 0.0350]
0.1250 = 0.11x + 0.0350 – 0.0350x
0.09 = 0.075x
x = 1.20

Weight of Stock X = x = 1.20
Weight of Risk Free Security = 1 – x
Weight of Risk Free Security = 1 – 1.20 = -0.20

Portfolio Beta = (Weight of Stock X * Beta of Stock X) + (Weight of Risk Free Security * Beta of Risk Free Security)
Beta of Risk Free Security = 0
Portfolio Beta = (1.20 * 1.25) + (-0.20 * 0)
Portfolio Beta = 1.50 + 0
Portfolio Beta = 1.50