Question

An investor, who believes the economy is slowing down, wishes to reduce the risk of her portfolio. She currently owns 12 securities, each with a market value of $3,000. The current beta of the portfolio is 1.21 and the beta of the riskiest security is 1.62. What will the portfolio beta be if the riskiest security is replaced with a security of equal market value but a beta of 0.80

Answer 1

1.14

Step-by-step explanation:

Investors has number of securities = 12

Each with a market value = $3,000

Current beta of the portfolio (before replacement of riskiest security ) = 1.21

Beta of the riskiest security= 1.62

If the riskiest security is replaced = 0.80

Portfolio Beta before replacement of the riskiest security = Remaining number of securities / total number of securities * Beta of securities + Number of riskiest security / total number of securities * Beta of the riskiest security

Portfolio Beta before replacement of the riskiest security = Weight of securities*Beta of securities + Weight of riskiest security*Beta of riskiest security

Let the beta of securities be x.

1.21 =11/12 *x + 1/12 *1.62

1.21 =11/12 *x +0.135

1.21-0.135 = 11/12 x

1.075 =11/12 x

x = 1.075*12/11

x = 1.1727

Beta of securities = 1.17

Portfolio beta after the replacement of the riskiest security = 11/12*1.17 +1/12*0.8 = 1.0725 + 0.0666 = 1.1391 = 1.14