Both assets B and C plot on the SML.Asset B has a beta of 1.1 and an expected return of 12.1%.Asset C has a beta of .80 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)0.333
B)0.50
C)0.625
D)0.75

Question

Quizplus · Accepted Answer

The correct answer is A.The portfolio beta is a weighted average of the betas of the individual assets in the portfolio. In this case, we want the portfolio beta to be 1.0, so we can set up the following equation:1.0 = (weight of asset B * beta of asset B) + (weight of asset C * beta of asset C)We know that the beta of asset B is 1.1 and the beta of asset C is 0.80. We also know that the weight of asset B plus the weight of asset C must equal 1.0. So, we can substitute these values into the equation and solve for the weight of asset B:1.0 = (weight of asset B * 1.1) + (1.0 - weight of asset B * 0.80)1.0 = 1.1 * weight of asset B + 0.80 - 0.80 * weight of asset B1.0 = 0.30 * weight of asset B + 0.800.20 = 0.30 * weight of asset Bweight of asset B = 0.6666666666666666Therefore, the proportion of the portfolio that must be in asset B is 0.6666666666666666, or 66.67%.

Both Assets B and C Plot on the SML