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 B?
A)0.375
B)0.50
C)0.625
D)0.75

Question

Quizplus · Accepted Answer

To find the proportion of the portfolio that must be in asset B, we need to use the formula for the beta of a portfolio:

Portfolio beta = Proportion of portfolio in asset B x Beta of asset B + Proportion of portfolio in asset C x Beta of asset C

We know that the portfolio beta must be 1.0, and we can substitute the given values for the betas of assets B and C and the expected return on the risk-free rate and market portfolio:

1.0 = x(1.3) + (1 - x)(0.5)
1.0 = 1.3x + 0.5 - 0.5x
0.5 = 0.8x
x = 0.625

Therefore, the proportion of the portfolio that must be in asset B is 0.625 or 62.5%.

Both Assets B and C Plot on the SML