
Explanation:
$396 \times 1.08 = 427.68$ million.$308 \times 1.10 = 338.80$ million.$427.68 - 338.80 = 88.88$ million.$396 \times 30% = 118.8$ million.$308 \times 14% = 43.12$ million.This results in an interval of (USD -102.34 million, USD 280.1 million). Option D is correct.
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Q.34 A defined benefit scheme holds investments in high-quality corporate bonds as well as gilts (government bonds). An analyst reports the following information to the scheme’s manager:
| Scheme | Assets | Liabilities |
|---|---|---|
| Amount (USD million) | 396 | 308 |
| Expected annual growth | 8% | 10% |
| Modified duration | 12 | 8 |
| Annual volatility of growth | 30% | 14% |
To determine whether the scheme is sufficiently prepared to meet its obligations to members, the scheme’s manager wishes to estimates the possible surplus value at the end of one year. He makes the following assumptions:
I. Annual returns on assets and the annual growth of the liabilities are jointly normally distributed
II. The correlation coefficient between assets and liabilities is 0.63
Determine the 95% confidence interval for the surplus value:
A
(USD -88.88 million, USD 97.561 million)
B
(USD -102.34 million, USD 191.22 million)
C
(USD -88.88 million, USD 186.441 million)
D
(USD -102.34 million, USD 280.1 million)
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