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, and since we do not know the weights, we cannot know the exact value of the portfolio beta. 
However, we do know that it will be a number between the smallest and largest individual betas (0.67 and 1.49), since the weights must add up to 1. Therefore, we can say with certainty that the portfolio beta will be less than 1.49 and greater than 0.67.

A Portfolio Consists of Five Securities That Have Individual Betas