How’s negative convexity compared with positive convexity?
We know when the convexity is zero, duration can explain everything. If the curve is not straight, we need to add convexity. For a bond, with positive convexity, the value increases faster when the interest rate drops than the value decreases when the interest rate increases. The opposite is for the negative convexity one. So as an investor, looks like positive convexity is better. Is that true? Any other effects we have to consider? Thanks!
Hi Fiona, good question. Yes, from an investor’s perspective, positive convexity is better than negative convexity because the loss is more than gain for the same delta basis point. But what makes negative convexity terrible is not just that. In extreme case, price/yield curve with negative convexity can turn a profitable position into a loss position. For example, if the shape is “n” shape (or let me call it up-side-down U). You can see this has negative convexity. You can choose a point on the n such that when the yield increases, the price decreases and when the yield decreases, price increases. But if the yield keeps decreasing, the price will eventually decrease also!
Actually that’s what happened to some subprime mortgage! People just didn’t expect the yield can move so much to that undesirable point! And their hedging strategies fail completely!