Answer:
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
