Revision as of 00:30, 5 December 2023 by Admin (Created page with "You manage a pension fund, and your liabilities consist of two payments as follows: {| class="table table-bordered" ! Time !! Payment |- | 10 Years || $20 million |- | 20 Years || $30 million |} Your assets are $18 million. The term structure is currently flat at 5%. Compute an approximate change in the present value of your liabilities, using duration, when interest rates fall by 0.25%. <ul class="mw-excansopts"> <li>0.8M</li> <li>0.85M</li> <li>0.9M</li> <li>0.95...")
Dec 05'23
Exercise
You manage a pension fund, and your liabilities consist of two payments as follows:
| Time | Payment |
|---|---|
| 10 Years | $20 million |
| 20 Years | $30 million |
Your assets are $18 million. The term structure is currently flat at 5%.
Compute an approximate change in the present value of your liabilities, using duration, when interest rates fall by 0.25%.
- 0.8M
- 0.85M
- 0.9M
- 0.95M
- 1M
References
Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.
Dec 05'23
Solution: A
[[math]]\begin{gathered}P V=\frac{20}{(1+5 \%)^1 0}+\frac{20}{(1+5 \%)^3 0}=12.28+6.94=19.22 \text { million } \\ D=\frac{12.28 * 10+6.94 * 30}{19.22}=17.22 \\ M D=\frac{D}{1+y}=16.40\end{gathered}[[/math]]
When rates drop by 0.25%, the PV of liabilities will go up by
0.25% ∗ MD ∗ PV = 0.7881 million
References
Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.