# Curve steepner and convexity

Can someone please explain why a curve steepener trade has a negative convexity? And are the gains from the steepness of the curve offset by the negative convexity?

• Hi ababoua, by steepner trade do you mean a CMS spread swap ? Or another payoff ? – Jiem Sep 4 '18 at 22:31
• @Jiem no, I don’t mean CMS spread swap. I meant a curve steepener like trading a 5s10s and expecting this part of the curve to steepen. – ababoua Sep 5 '18 at 6:16

For example using the number in the 20s30s link for a 100k steepening position the gamma cost is approximately $\frac{1}{2}\times 350^2 \times -100=6.125mm$ (OK its not really as much as this since the gammas/deltas decline, but we have held -100, with increasing rates but for small moves this linear approximation is reasonable - here it is an exaggerated example)