Why Bond DV01 and Yield Delta Can Measure Different Risks
Summary
The document explains why a bond's DV01 or related interest-rate sensitivity may differ from what a trader calls its delta. These labels are often used loosely, so the first step is to establish the desk's definitions and methodology. Sensitivity can be measured by bumping a bond's yield, shifting an entire curve, or changing selected tenor buckets; the bumped inputs might be par rates, forward rates, or other curve points. The reported impact may be a price change or position-level profit and loss.
The answer notes that duration and key-rate duration are related measures, while credit-risky bonds add modeling uncertainty. A floating-rate bond and a below-par fixed-coupon bond may respond differently to a risk-free-rate move, depending on the pricing model and what is held constant. Consequently, yield-based sensitivity need not match the sum of curve-bucket sensitivities. The examples are conceptual, and the excerpt does not prescribe one universal definition or calculation; it advises confirming the exact measure with the relevant trader or desk documentation.
Key ideas
- DV01, PV01, yield sensitivity, and interest-rate delta may refer to different risk measures across desks.
- The sensitivity depends on which yield or curve rates are bumped and how the resulting impact is reported.
- Yield-based bond price sensitivity can differ from summed tenor-bucket sensitivities on a swap curve.
- Credit risk and bond pricing assumptions can make interest-rate sensitivity less straightforward than for a modeled swap.
- Confirm the desk's definitions and calculation methods before comparing risk numbers.
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Full text
# Difference between DVO1 and delta # Difference between DVO1 and delta I was speaking to this rates trader, and we were talking about how the delta of a swap spread has changed in both legs and now there is a mismatch in the delta between the bond and the swap. He made a comment that I hadn't heard before. He said delta and dvo1 are different for a given bond. Could someone please explain why they would be different and what each of them capture? Thank you ## Answer by Dimitri Vulis (score 4) https://quant.stackexchange.com/a/82107 Some people, including traders, use terms "dv01", "pv01", "yield01", "ir01", "interest rate delta / sensitivity / risk", etc rather loosely. You should find out exactly what they mean for this desk / trader. There ought to be a document defining the risk measures and the methodologies for calculating them for this desk. For example, the risk scenarios might bump: - the bond's yield - some curve shifted in parallel in its entirety - only a part of some curve (i.e. risk by tenor bucket); and you might bump the par rates, or the forward rates, or something else yet. The impact of the scenario might be the change in the price of the bond (quoted as a percentage of the face value in most markets), or the profit and loss of the current position (i.e. price times the notional times any factor etc). Durations / key rate durations are another way to quantify interest rate risk, although, in my opinion, less convenient. As Mr. Spock used to say, Infinite Diversity in Infinite Combinations. :) For a credit-risky bond, the interest rate sensitivity might be less clear-cut than for a swap being priced to model. For example, consider two credit-risky bonds: - a floater paying index + 700 bps, trading at par - a fixed-coupon bond, paying 900 bps and trading at 85%. how much would their bonds' prices change if we bump risk-free interest rates a little and nothing else changes? There are various bond pricing models that would predict the price change, and if you ponder these examples, you will realize that the estimation would not be as trivial as yield01. Thus, perhaps your trader meant "the bond price impact from bumping the yield 1 basis point isn't quite the same as the sum of impacts on model pv of bumping tenor buckets of par swap curve". Or perhaps they meant something different! My point is, every once in a while we see questions like "a trader said something, what does it mean", and people try to guess the best we can, but your trader would probabky prefer that you ask them for clarification because the guesses will sometimes be wrong.
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