Fund one pension payment with 2y, 5y and 12y bonds and cash. Each year the curve shifts and twists: keep the asset duration on the liability's.
You start all in the 5-year bond, short of the 8-year liability. Match duration and keep it matched each year without overspending on trades.
Round 0/8 · 8 years to pay
Duration gap −3.29y (band ±0.25y)
| Line | Years left | Coupon | Face | Price | Value | Weight | DV01 |
|---|---|---|---|---|---|---|---|
| 5y bond | 5 | 5.00% | $676,839 | 100.00 | $676,839 | 100.0% | $293 |
| Cash | — | 5.00% | $0 | 100.00 | $0 | 0.0% | $0 |
| Liability | 8 | — | $1,000,000 | 67.68 | $676,839 | 100.0% | $516 |
| Twist \ parallel | −100 bp | −50 bp | −25 bp | 0 bp | +25 bp | +50 bp | +100 bp |
|---|---|---|---|---|---|---|---|
| +50 bp | −17.8k | −5.8k | 0.0k | +5.5k | +10.9k | +16.1k | +26.1k |
| 0 bp | −23.7k | −11.5k | −5.7k | 0.0k | +5.5k | +10.8k | +20.9k |
| −50 bp | −29.6k | −17.2k | −11.3k | −5.5k | +0.1k | +5.5k | +15.8k |
Instant change in surplus for a parallel move (columns) and a twist (rows), in bp.