Dana has a portfolio of 8 securities, each with a market value of $5,000. The current beta of the portfolio is 1.28 and the beta of the riskiest security is 1.75. Dana wishes to reduce her portfolio beta to 1.15 by selling the riskiest security and replacing it with another security with a lower beta. What must be the beta of the replacement security? a. 1.21 b. 0.91 c. 0.73 d. 1.62

Option c. 0.73

Explanation:

Data provided in the question:

Market value of securities = $5,000

Current beta of the portfolio = 1.28

Beta of the riskiest security = 1.75

Required beta = 1.15

Now,

let the beta of the other security be 'x'

Portfolio beta = weighted average of individual betas in the portfolio

or

1.28 * 8 * $5000 = [ x * (8 - 1) * $5000 ] + [ 1.75 * $5000 ]

or

$51,200 = $35,000x + $8750

or

$35,000x = $42,450

or

x = 1.21

Thus,

If she wishes to reduce the beta to 1.15, by replacing the riskiest security,

let the beta of the replacement security be 'y'

Therefore,

1.15 * 8 * $5000 = [ 1.21 * (8 - 1) * $5000 ] + [ y * $5000 ]

or

$46,000 = $42,350 + $5,000y

or

$5,000y = $3,650

or

y = 0.73

Hence,

Option c. 0.73