A portfolio manager plans to use a Treasury bond futures...

A portfolio manager plans to use a Treasury bond futures contract to hedge a bond portfolio over the next 3 months. The portfolio is worth $$\$ 100$$ million and will have a duration of 4.0 years in 3 months. The futures price is 122 , and each futures contract is on $$\$ 100,000$$ of bonds. The bond that is expected to be cheapest to deliver will have a duration of 9.0 years at the maturity of the futures contract. What position in futures contracts is required? (a) What adjustments to the hedge are necessary if after 1 month the bond that is expected to be cheapest to deliver changes to one with a duration of 7 years? (b) Suppose that all rates increase over the next 3 months, but long-term rates increase less than short-term and medium-term rates. What is the effect of this on the performance of the hedge?

A portfolio manager plans to use a Treasury bond futures contract to hedge a bond portfolio over the next 3 months. The portfolio is worth $$\$ 100$$ million and will have a duration of 4.0 years in 3 months. The futures price is 122 , and each futures contract is on $$\$ 100,000$$ of bonds. The bond that is expected to be cheapest to deliver will have a duration of 9.0 years at the maturity of the futures contract. What position in futures contracts is required?
(a) What adjustments to the hedge are necessary if after 1 month the bond that is expected to be cheapest to deliver changes to one with a duration of 7 years?
(b) Suppose that all rates increase over the next 3 months, but long-term rates increase less than short-term and medium-term rates. What is the effect of this on the performance of the hedge?

Key Concepts

Duration

Duration is a measure of a bond’s sensitivity to changes in interest rates, representing the weighted average time until cash flows are received. It is crucial in hedging because matching the duration of assets and liabilities (or hedging instruments) determines how well the portfolio is protected against interest rate movements.

Hedge Ratio

The hedge ratio is used to determine the number of futures contracts necessary to offset interest rate risk in a bond portfolio. It involves matching the duration?adjusted value of the portfolio with the duration?adjusted value of the futures contracts, ensuring that the exposure to interest rate changes is balanced between the portfolio and the hedge.

Treasury Bond Futures Contract

Treasury bond futures contracts are standardized agreements to buy or sell Treasury bonds at a future date at a predetermined price. They allow investors to hedge or speculate on interest rate movements and are characterized by a specified notional value, price quotation, and maturity, all of which influence the size and effectiveness of the hedge.

Cheapest-to-Deliver (CTD) Bond

The cheapest-to-deliver bond is the one from the deliverable basket that minimizes cost for the seller when fulfilling the futures contract. Its characteristics, particularly duration, are essential in hedging strategies because the CTD bond’s duration is used in calculating the hedge ratio, and any changes in its attributes can impact the hedge’s accuracy.

Basis Risk

Basis risk refers to the risk that the futures price and the underlying asset’s price will not move perfectly in tandem, leading to an imperfect hedge. This risk is inherent in hedging when the instrument used (such as a futures contract) does not exactly match the characteristics of the asset being hedged, such as differences in duration or the effect of changing market conditions.

Yield Curve Effects

Yield curve effects describe how different segments of the yield curve may change asymmetrically, causing variations in the relative movements of short-, medium-, and long-term interest rates. This can impact the performance of a hedge, particularly when the portfolio and the hedging instrument have different sensitivities to these shifts, potentially altering the effectiveness of duration matching.

Hedge Adjustments

Hedge adjustments involve recalibrating the number of futures contracts or modifying the hedging strategy in response to changes in interest rates or the characteristics of the underlying assets, such as a change in the duration of the cheapest-to-deliver bond. These adjustments are critical for maintaining an effective hedge over time, particularly when market conditions or asset properties evolve.

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