Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.30 and σ_M was 0.16, the β of the portfolio would be approximately A) 0.64. B) 1.80. C) 1.88. D) 1.56.

Question

Quizplus · Accepted Answer

The beta of a portfolio is calculated as the covariance of the portfolio's returns with the market's returns, divided by the variance of the market's returns. In this case, the covariance of the portfolio's returns with the market's returns is not given, but we can use the single index model to calculate it. The single index model states that the covariance of a portfolio's returns with the market's returns is equal to the beta of the portfolio multiplied by the variance of the market's returns. Therefore, we can calculate the beta of the portfolio as follows:```beta = covariance of portfolio's returns with market's returns / variance of market's returns``````beta = (0.30 * 0.16) / (0.16 * 0.16)``````beta = 1.88```Therefore, the beta of the portfolio is approximately 1.88.

Suppose You Held a Well-Diversified Portfolio with a Very Large