DV01 Neutrality and P&L in a 5s30s Curve Spread
Summary
The discussion explains how bond DV01s measure each bond’s approximate price sensitivity to a one basis point move in its own yield, under a parallel shift assumption. Because the 5-year and 30-year bonds respond to different points on the yield curve, a spread position needs leg weights that account for the separate DV01s. In the example, the 5-year leg has half the DV01 of the 30-year leg, so twice as much 5-year notional is used to create a DV01-neutral position.
For a position expressed in spread DV01, first-order P&L can be estimated by multiplying the spread move by the traded DV01, with sign determined by whether the spread widened or narrowed and which leg is bought or sold. The answer also notes that neutrality can be defined in other ways, such as using regression or principal component analysis. The calculation is an approximation: actual bond P&L can differ because of curve shape changes, convexity, carry, and other effects.
Key ideas
- A bond’s DV01 approximates its price change for a one basis point move in its own yield.
- Parallel curve shifts are assumed in the basic DV01 calculation.
- DV01-neutral curve spreads require weighting the two legs according to their sensitivities.
- First-order spread P&L is approximately the spread change multiplied by the position’s spread DV01.
- Regression and principal component methods can define alternative forms of curve neutrality.
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# DV01 Neutral Curve Spread # DV01 Neutral Curve Spread I'm struggling to understand making a curve spread BPV-neutral. Say I am looking at the 5Y and 30Y bond spread. I have 2 questions: - I understand that both of these have different DV01s, or sensitivities to changes in 'interest rates'. However, what 'interest rate' are we talking about in this case for each bond? For example, if the 5Y bond has a DV01 of 10 dollars and 30Y of 20 dollars, does that mean if the 5Y yield goes up by 1bp, then the 5Y bond loses 10 dollars in value, and if the 30Y yield goes up by 1bp, then the 30Y bond loses 20 dollars in value? It's weird because the sensitivity is referring to different interest rates, not like 1 common interest rate, correct? - If I want to calculate the PNL from holding a 5s30s curve BPV-neutral, then can I just subtract the 30Y yield - the 5Y yield, and see how much that moved? Then, I can multiply this number by the DV01 that I'm trading. However, online, people seem to imply that I need to scale each leg by its DV01. However, since I am in yield-space, isn't that already accounted for? ## Answer by user68819 (score 0, accepted) https://quant.stackexchange.com/a/81170 I wouldn't call the bond DV01s bond-spread DV01s unless you really do mean the DV01 of an ASW (?). They are just bond DV01s. - Yes you are correct. The underlying assumption in calculating these DV01s is that the curve moves in parallel. A naive weighting might say (giving the numbers you use): that one would need to 2x the notional of the 5y bond versus some notional of the 30y bond to be DV01 neutral. So for example for 100k 5s30s spread you would sell 50mn 30s and buy 100mn 5s. You can have all kinds of weightings to make you neutral: regression based, PCA based. - if you sold 100k DV01 of the spread (sell 30s buy 5s) at 15bps and it gets to 20bps, then yes, to a first order, your PNL is +500k.
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