Convexity Risk in DV01-Neutral Yield-Curve Trades
Summary
The document explains why a DV01-neutral 2s10s steepener can still carry convexity risk. DV01 neutrality balances the position using current rate sensitivities; when yields move, those sensitivities change, so the trade may no longer be balanced. The shift in the relative DV01s creates changing exposure even without an initial first-order net sensitivity.
The example focuses on a rise in 10-year rates, which lowers the 10-year DV01 and changes the hedge balance. Whether that convexity effect helps or hurts depends on whether the 10-year position is long or short. The discussion also describes interest-rate gamma: rate sensitivity changes as rates move. For swaps, cross-gamma by tenor may be mostly negligible, while a risk-weighted aggregate gamma can help explain P&L, particularly at longer maturities. The source frames gamma reporting as potentially useful for P&L attribution, while questioning its value for routine risk hedging.
Key ideas
- Initial DV01 neutrality uses sensitivities measured at current yield levels.
- Yield changes alter DV01s, so a curve trade can become unbalanced as the market moves.
- The sign of the convexity benefit or cost depends on the direction of the position in the affected tenor.
- Interest-rate gamma describes how rate sensitivities change with rate movements.
- A weighted gamma measure may aid P&L explanation even when tenor cross-gammas are not useful for routine swap risk management.
Tags
Full text
# Convexity in a DV01 neutral trade # Convexity in a DV01 neutral trade I have got a question about DV01 neutral trades. Generally speaking: if you perform a 2s10s steepener on a generic govt yield curve, would convexity be a risk? If so, in what measures? Technically, as we are DV01 neutral, I imagine that convexity is also somewhat mitigated, yet I fail to understand where this convexity risk might arise from. Might you be provide me with an example? Thank you in advance for all your replies. ## Answer by dm63 (score 7) https://quant.stackexchange.com/a/61476 Let’s say you do a 2s-10s steepener, dv01 neutral. What does this mean ? It means you are using the current dv01s of the 2s and 10s, which are approximately 1.99 and 9.12, to weight the relative principal amounts of the bonds. Now, the key point is, when the market moves, these dv01s move and you no longer have a balanced trade. That is the convexity risk. For example , 10yr rates go up, so the dv01 of 10s goes down, so you have to make your position larger if you want to restore the balance. If you are long the 10s this effect will be a benefit (long convexity ) and if you are short it will be a cost (short convexity ). ## Answer by Dimitri Vulis (score 2) https://quant.stackexchange.com/a/61460 An intuitive explanation of why we have IR gamma: when rates are 10 bps, then 1 bp change is a somewhat bigger deal then when rates are 1,000 bps. (Maybe if instead of dv01 being a sensitivity to a 1bp move, we used some bump size dependent on rate level, we'd have less gamma.) If you have an IR swap then: - you can calculate a matrix of cross-gammas between all the tenors of your swap curve. Most of its entries will be close enough to 0 to be indistinguishable from numeric noise. Not at all useful for a swap, in my opinion, but may be useful for non-linear products. - more useful, you can calculate a single number for the gamma, risk-weighted by the tenors where you have the IR delta. This is helpful not for risk management, but if you are trying to achieve P&L explain with little unexplained residual, especially in longer maturities than 10 years. For risk management, put the risk amount on the risk report, see how much P&L it causes, so everyone can see that it's not worth hedging. Edit: as @dm63 points out, you can also see how much your IR deltas by tenor bucket have changed because of the IR gamma $\times$ rate change.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.