Both assets B and C plot on the SML. Asset B has a beta of 1.3 and an expected return of 13.1%. Asset C has a beta of .50 and an expected return of 7.50%. The risk-free rate is 4% and the expected return on the market portfolio is 11%. If you wish to hold a portfolio consisting of assets B and C, and have a portfolio beta equal to 1.0, what proportion of the portfolio must be in asset C?
A) 0.375
B) 0.50
C) 0.625
D) 0.75

Question

Quizplus · Accepted Answer

The formula for portfolio beta is:
Portfolio Beta = Proportion of investment in Asset B * Beta of Asset B + Proportion of investment in Asset C * Beta of Asset C

We are given that the portfolio beta should be 1.0. Hence, we can write:
1 = Proportion of investment in Asset B * 1.3 + Proportion of investment in Asset C * 0.5

We need to solve for the proportion of investment in Asset C. Let x be the proportion of investment in Asset C. Then, the proportion of investment in Asset B would be (1-x). Substituting these values in our equation, we get:
1 = (1-x)*1.3 + x*0.5
Simplifying, we get:
1 = 1.3 - 1.3x + 0.5x
0.3 = 0.2x
x = 0.3/0.2
x = 1.5

Hence, the proportion of investment in Asset C is 0.375 or 37.5%.

Both Assets B and C Plot on the SML