How Bond Convexity Affects Rate Exposure and Embedded Options
Summary
The document compares positive and negative bond convexity from an investor’s perspective. Positive convexity generally means price gains accelerate more as yields fall than price losses accelerate when yields rise. The answer therefore favors greater positive convexity when considering convexity alone, while emphasizing that the bond’s position on the convexity curve and expectations about rates matter.
Negative convexity may signal an embedded option, such as an issuer’s call option, which leaves the investor short an option: the investor collects premium but is exposed to negative gamma and short volatility. These points are conceptual rather than supported by empirical comparisons. The discussion explicitly brackets other bond characteristics and cautions that interest-rate level, volatility expectations, and the bond’s place on the convexity spectrum can affect what is desirable; it does not provide a universal ranking for every market environment.
Key ideas
- Positive convexity can make a bond’s price respond more favorably to falling yields than to comparable yield increases.
- The desirability of convexity depends partly on the bond’s position on the convexity curve and rate expectations.
- Negative convexity can arise when a bond embeds an issuer call option.
- A bondholder exposed to an embedded call may effectively be short gamma and volatility in exchange for option premium.
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# In bond pricing, is negative convexity better than positive convexity? # In bond pricing, is negative convexity better than positive convexity? Say that I have two bonds and one of them has positive convexity and the other negative. Which one is better (assuming that you only care about convexity)? I understand that high convexity is desirable because the bondholder can benefit more from a drop in the interest rate than an identical increase in the interest rate. Does that mean negative convexity is bad, because investors are more affected by a raise in the interest rate? ## Answer by RndmSymbl (score 1) https://quant.stackexchange.com/a/15294 I am going to assume that the only thing you are interested in is convexity and the many other aspects as well as the suitability of focusing on a single measure are not addressed. In such a general setting more positive convexity provides, as you have already outlined, for the potential to increase prices at a faster rate as a response to interest rate declines. In addition you want to consider where your bond sits on the convexity spectrum and your interest rate expectations. Quote from comments to the article above with regard to expectations of rising interest rates: > It depends what side of the convexity curve your bond resides. For any given duration, you would want HIGH convexity if you are on the right hand (the flattening) part of the curve. In summary: high, absolute, positive convexity is most likely desirable while high, absolute, negative convexity is most likely less desirable given stable or falling interest rates. The distinction between level and direction of convexity are important as well the expectations regarding interest level and volatility, among other things such as the position in the covexity spectrum. ## Answer by slava (score 0) https://quant.stackexchange.com/a/15313 negative convexity, most likely, will imply that bond has embedded option. i.e. bond holder sells call option to bond issuer. therefore you'll have negative gamma position = collect option premium and short volatility.
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