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An insurance company must make payments to a customer of $10 million in 5 years and $25 million in 30 years. The yield curve

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Answer #1

Please see the table below. Please be guided by the second row to understand the mathematics.Figures in parenthesis, if any, mean negative values. All financials are in $ million.

Liabilities Term PV n x PV
L n L x 1.08^(-n)
10 5                  6.81           34.03
25 30                  2.48           74.53
Total                  9.29         108.56

Part (a)

The present value of the obligations = $ 9.29 million

Duration = 108.56 / 9.29 = 11.69 years

Part (b)

Maturity of the zero coupon bond (ZCB) = duration of the liabilities calculated above = 11.69 years

Part (c)

Face value of the ZCB that you will buy = 9.29 x (1 + 8%)11.69 =  22.84

When YTM changes to 9%;

PV of the bonds = 22.84 / (1 + 9%)11.69 =   8.34

and the PV of the obligations = 10 / (1 + 9%)5 + 25 / (1 + 9%)30 = 6.50 + 1.88 = 8.38

Hence, the net position = 8.34 - 8.38 = - $ 0.04 million

Thus the net position is a loss (reduction in value of) of $ 0.04 million

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