Suppose your firm has an obligation to pay $500,000 in one year, $600,000 in two

Question

Suppose your firm has an obligation to pay $500,000 in one year, $600,000 in two years, and $700,000 in three years. It has valued this using a risk-free rate according to the current Treasury yield curve, which is flat at 4%. The duration of this obligation is given at 2.085 years, and your firm has purchased risk-free zero-coupon bonds that mature in 2.085 years to fund and immunize the obligation. If the yield curve immediately shifts to a flat 3.90%, what will be the net position (that is, the difference between the present values of the obligation and bonds)? Is the obligation now under- or overfunded? Is this a material amount?

Explanation / Answer

As is clear, the obligation is now overfunded by $3.3. And obviously it is not a very significant amount,  

1 2 3 t+1 t+2 t+3 Cash Flows from Obligation -500 -600 -700 Cash flow from bond 500 600 700 Present Value at 4 % 480.7692 554.7337 622.2975 1657.8 Present Value at 3.9% 481.232 555.8021 624.096 1661.13

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