Hedging Interest Rate Risk: Duration and DV01

Interest rate risk is measured in DV01

When rates rise, bond prices fall, and the longer the duration, the bigger the drop. DV01 (basis point value) = market value × duration × 0.01%: a $10 million portfolio with duration 7 loses about $7,000 for every 1 basis point rise in rates.

Balance by sensitivity, not by market value

Treasury futures have a different duration from your portfolio, so selling 1:1 by market value under- or over-hedges. For a duration hedging, contracts = portfolio DV01 ÷ DV01 per futures contract; you can also cut duration to just a target value.

Duration is only a straight-line approximation

The relationship between price and rates is curved; this is convexity (bond). For small moves a DV01 hedge is accurate; when rates jump 200 basis points at once, the two sides no longer line up. That's why duration hedges are recalculated and rebalanced regularly as rates change.

Key takeaways

• DV01 = market value × duration × 0.01%: roughly how much the position gains or loses for each 1 basis point move in rates.
• Number of Treasury futures = portfolio DV01 ÷ DV01 per futures contract. To reduce only part of the risk, size it to a target duration.
• Hedging 1:1 by market value leaves you under- or over-hedged, because the two sides have different durations.
• Duration is only a straight-line approximation: big rate moves bring convexity errors, so recalculate and rebalance regularly.

Try it yourself

You can do these exercises in this lesson's interactive simulation:

1. Click "Example: duration 7 · rates +100bp": how many Treasury futures do you need to sell? How much does the portfolio lose, how much do the short futures make, and what's left in total?
2. Switch to "By market value": after selling 91 contracts, what's the "Residual duration"? Then drag the portfolio duration to 4: what's the residual duration now, and is that under-hedged or over-hedged?
3. Go back to "By DV01," duration 7, and drag the rate change to +200bp and −200bp: how much is left in total? Why isn't it exactly zero?
4. Switch to "Target duration" and set it to 3: how many contracts do you need to sell? With rates +100bp, roughly what fraction of the unhedged result is the total?

Quiz and explanations

1. A portfolio is worth $20 million with a duration of 6, and each Treasury futures contract has a DV01 of $80. Roughly how many contracts must you sell to fully hedge by DV01?

Answer: 150.Portfolio DV01 = $20 million × 6 × 0.01% = $12,000, and ÷ $80 = 150 contracts.

2. A $10 million portfolio has a duration of 8 and you want to bring it down to 3. Each futures contract is worth $110,000 with a duration of 6.5. Roughly how many do you sell?

Answer: 70.(8 − 3) × $10 million ÷ ($110,000 × 6.5) ≈ 69.9, about 70 contracts.

3. Why does selling Treasury futures 1:1 by market value often hedge inaccurately?

Answer: The portfolio and the futures have different durations, so they react differently to rates.To make both sides equally sensitive to rates, balance them by DV01 (or duration × market value).

Terms in this lesson

• convexity (bond) (Convexity): How much a bond's price curves against rates; duration is only a straight-line estimate, so the bigger the rate move, the bigger the convexity error and the less accurate a duration hedge.
• duration (Duration): How sensitive a bond's price is to interest rates: a 1% rate move changes the price by roughly “duration” percent.
• duration hedging (Duration Hedging): Selling instruments like Treasury futures based on rate sensitivity (duration or DV01) rather than 1:1 by market value, so a bond portfolio stops reacting to rate moves.
• DV01 (basis point value) (DV01 / Basis Point Value): Roughly how much a position's value changes when yields move 1 basis point (0.01%) ≈ market value × duration × 0.0001.