Question

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 0.18 and σM was 0.22, the β of the portfolio would be approximately:_______

a. 0.74.
b. 0.80.
c. 1.25.
d. 1.56.

Answer 1

B. 0.80

Step-by-step explanation:

A well diversified portfolio can be regarded as one which has different securities with their weight been small. Since the single index holds,

The single-index model (SIM) by William Sharpe, is a model that that provides the risk as well as the returns of stock.

Given:

the σ of your portfolio = 0.18

σM = 0.22,

the β of the portfolio= the σ of your portfolio/σM

the β of the portfolio==0.18/0.22

= 0.82

Therefore, the β of the portfolio would be approximately 0.80