Duration Overlay with Treasury Futures and Credit Spread Risk
Northbridge Insurance has a $240 million fixed-income portfolio with a modified duration of 5.1 years. Its actuarial team estimates that the present value of liabilities is $260 million with a modified duration of 8.3 years. The investment committee does not want to buy long-dated bonds because of liquidity and capital charges; instead it authorizes a Treasury futures overlay to raise the asset portfolio's modified duration to 7.5 years, not fully match liabilities. The chosen contract is a 10-year Treasury note future priced at 118.50, with a $100,000 contract size. The cheapest-to-deliver note has a modified duration of 7.8 years and a conversion factor of 0.82. The portfolio's credit spreads are expected to widen by 40 basis points over the next quarter, while Treasury yields are expected to fall by 60 basis points. The CIO asks how many contracts to trade, whether to buy or sell, and what the hedge will and will not achieve.
1. Calculate the number and direction of futures contracts needed to raise the asset modified duration to 7.5. Show the DV01 calculation.
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Current and target DV01. Portfolio DV01 = modified duration x market value x 0.0001 = 5.1 x $240,000,000 x 0.0001 = $122,400 per basis point. Target DV01 = 7.5 x $240,000,000 x 0.0001 = $180,000 per basis point. DV01 gap = $180,000 - $122,400 = $57,600 per basis point.
Futures DV01. Futures modified duration is commonly estimated as CTD duration divided by the conversion factor: 7.8 / 0.82 = 9.512. The contract value is 118.50% of $100,000 = $118,500. Futures DV01 = 9.512 x $118,500 x 0.0001 = $112.72 per basis point per contract.
Number of contracts. $57,600 / $112.72 = 511 contracts.
Direction. The asset duration is below the target, so the portfolio needs more duration. Buy 511 futures contracts (long futures).
Approximate effect. If Treasury yields fall 60 basis points, the futures gain is approximately 511 x $112.72 x 60 = $3.456 million. The asset portfolio's own gain from the 60 bp fall would be about $122,400 x 60 = $7.344 million before credit-spread effects. The overlay raises total rate sensitivity toward the 7.5-year target but does not change the portfolio's cash bonds.
2. Estimate the net effect of a 60 bp fall in Treasury yields and a 40 bp widening in credit spreads. State your assumptions and limitations.
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Assumption. Use the portfolio's modified duration of 5.1 as a proxy for spread duration. This is an approximation; actual spread duration may differ by sector and security.
Treasury-rate gain on cash bonds. 5.1 x $240,000,000 x 0.0060 = $7.344 million.
Credit-spread loss. 5.1 x $240,000,000 x 0.0040 = $4.896 million.
Net cash-bond effect. $7.344 million - $4.896 million = +$2.448 million.
Futures overlay gain. 511 x $112.72 x 60 = approximately +$3.456 million.
Combined estimate. About +$5.904 million, before basis, convexity, and timing effects. This is not a clean duration match: the futures hedge addresses Treasury rate risk, while credit spreads remain largely unhedged. If spread duration is lower than 5.1, the credit loss is smaller; if higher, the loss is larger. The estimate also ignores convexity, changes in the CTD bond, financing and margin costs, and the possibility that Treasury and credit spreads do not move as assumed.
3. Why might the committee choose a 7.5-year target rather than matching the 8.3-year liability duration? What risks remain?
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Reasons for a partial hedge. Matching 8.3 would require more futures and more margin, variation margin liquidity, and roll risk. The committee may also want to retain some asset-liability duration gap because liability cash flows are uncertain, because long-dated bond purchases are costly, or because it expects asset yields to rise. A 7.5 target reduces accounting and capital volatility without fully locking the portfolio into a synthetic long-duration position.
Remaining risks. The hedge has basis risk because the futures contract tracks the cheapest-to-deliver Treasury, not the insurance portfolio's credit bonds. Credit spread widening is not hedged by Treasury futures. The conversion factor and CTD bond can change, altering the hedge ratio. Futures require daily margin and can force cash sales if rates move adversely. The overlay must be rolled before expiry, creating roll risk. Liability duration is an estimate and may change with interest rates and actuarial assumptions. Finally, a 7.5 target deliberately leaves a 0.8-year duration gap, so the portfolio remains exposed to falling rates.
Supervisory point. The committee should document why 7.5 is appropriate, set a tolerance band, monitor hedge effectiveness, and stress test both rate and credit-spread shocks.