Hedging a Bond Book Before a Rate Decision
A dealer holds a $250 million portfolio of 10-year corporate bonds with an average duration of 7.5 years. The desk expects a central-bank decision in three days and wants to hedge rate risk using 10-year Treasury futures. The futures contract has a duration of about 8 years and a conversion factor of 0.85 for the cheapest-to-deliver bond. The desk's risk limit caps net duration at 2 years. A client simultaneously asks the desk to bid on a $40 million block of the same corporate bonds at a spread of 140 basis points over Treasuries, versus the desk's fair-value estimate of 125 basis points. The desk's funding cost has risen, and the firm's credit line to the desk is nearly fully utilized.
1. Calculate the approximate futures position needed to hedge the portfolio and explain the role of the conversion factor.
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The portfolio's dollar duration is $250 million times 7.5, or $1.875 billion in duration dollars. The futures contract's duration exposure per contract must be computed using the CTD bond's duration adjusted by the conversion factor. Using the stated futures duration of 8 years and conversion factor of 0.85, the effective duration per contract is 8 divided by 0.85, or about 9.41 years. If the contract's notional is, say, $100,000, the duration dollars per contract are about $941,000. Dividing $1.875 billion by $941,000 gives roughly 1,993 contracts, so about 2,000 contracts short.
The conversion factor adjusts for the deliverable bond's coupon and maturity relative to the notional coupon. Because the seller chooses which bond to deliver, the futures price tracks the cheapest-to-deliver bond, and the hedge ratio must reflect that bond's price sensitivity, not the notional contract's. The desk should also monitor basis risk: if the CTD changes before the decision, the hedge's effectiveness changes. The calculation is an approximation and should be refreshed as yields and the CTD change.
2. Should the desk take the client's block bid, and how do the hedge, the risk limit, and the credit line interact?
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The bid at 140 basis points over Treasuries is 15 basis points wider than fair value, which is compensation for the desk's risk and funding. But taking a $40 million block increases the portfolio to $290 million and raises duration dollars to about $2.175 billion, requiring the hedge to be increased to roughly 2,311 contracts to stay flat. The desk must check whether the added position and margin requirements fit within the net-duration limit of 2 years and within the available credit line. If the credit line is nearly exhausted, additional margin calls on the futures hedge could force deleveraging at the worst time, which is a liquidity risk, not just a market-risk issue.
The desk should also consider whether the client is selling because of information the desk lacks, and whether the 140 basis point spread truly compensates for the wider portfolio and funding cost. A disciplined answer is to size the block to what the credit line and limit can absorb, or to arrange a back-to-back sale or participation with another dealer before committing. The desk should not take the full block merely because the spread looks attractive; the constraint is the firm's ability to carry and hedge it through the event.