A portfolio consists of five securities that have individual betas of 1.38,0.87,1.02,1.49,and 0.67.You do not know the portfolio weight of each security.What do you know with certainty?
A)The portfolio beta will not be affected by any change in the portfolio weights.
B)The portfolio beta will not change if an additional security with a beta of 1 is added to the portfolio.
C)The portfolio beta will be greater than the market beta.
D)The portfolio beta will be less than 1.49 and greater than 0.67.
E)The optimal portfolio beta for any investor must be greater than 0 and less than 1.

Question

Quizplus · Accepted Answer

We know that the portfolio beta will be a weighted average of the individual betas, but we do not know the portfolio weights. Therefore, we cannot say for certain that the portfolio beta will be greater than or less than any specific value, except for the fact that it will fall between the smallest and largest individual betas in the portfolio. Thus, we can say with certainty that the portfolio beta will be less than 1.49 and greater than 0.67, which is the range of the individual betas. Options A, B, and E are not correct because they make assumptions about the impact of changes in portfolio weights or the optimal portfolio beta, which we cannot determine given the information provided. Option C is also incorrect because the portfolio beta could be less than, equal to, or greater than the market beta, depending on the specific portfolio weights.

A Portfolio Consists of Five Securities That Have Individual Betas