Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds.If the $\sigma$ of your portfolio was 0.18 and $\sigma$_Mwas 0.22, the $\beta$ of the portfolio would be approximately A)0.64. B)1.19. C)0.82. D)1.56.

Question

Quizplus · Accepted Answer

Using the single index model, we know that the formula for the beta of a portfolio is:

beta = covariance of portfolio with market / variance of market

In this case, we are given that the variance of the market (represented by the index) is 0.22. We are also given the covariance of the portfolio with the market, which is equal to the F1F1F1S1F1F1F10, or 0.18. Therefore, the beta of the portfolio would be:

beta = 0.18 / 0.22 = 0.82

Thus, the best choice is C.

Suppose You Held a Well-Diversified Portfolio with a Very Large σ\sigmaσ

Suppose You Held a Well-Diversified Portfolio with a Very Large $\sigma$