Question

assume the single-factor model applies and that 70 percent of the funds in a portfolio are invested in a risky security and the remainder in the risk-free asset. the risky security has a beta of 1.4. the portfolio has a beta of:

Answer 1

The portfolio beta is calculated as 0.98, by using the weighted sum of the individual asset betas, based on their proportion in the portfolio. The portfolio beta is 0.98.

Step-by-step explanation:

To calculate the beta of a portfolio, we need to take into account the weight of each security in the portfolio and the beta of each security.

In this case, 70 percent of the funds are invested in a risky security with a beta of 1.4, and the remainder is invested in the risk-free asset, which has a beta of 0.

To calculate the portfolio beta, we multiply the weight of each security by its beta and then sum up the results:

Portfolio Beta = (Weight of Risky Security) x (Beta of Risky Security) + (Weight of Risk-Free Asset) x (Beta of Risk-Free Asset)

Plugging in the given values:

Portfolio Beta = (0.7) x (1.4) + (0.3) x (0)

Portfolio Beta = 0.98