How Bond Convexity Changes Gains and Losses

Summary

The document clarifies the relationship between a bond position, duration, and convexity. It distinguishes a long position in a conventional coupon bond, which has positive duration and convexity, from a short position, which has negative convexity exposure. Duration describes the bond price’s sensitivity to yield changes, while convexity affects how that sensitivity changes as yields move.

The explanation says negative convexity makes losses on a short bond position accelerate as yields fall, while gains diminish as yields rise. It answers the question about duration signs indirectly: the discussion concerns exposure and the change in price sensitivity, rather than claiming that a long bond’s duration is negative. The document is a brief conceptual answer and gives no equations, quantitative examples, or treatment of bonds with embedded options, whose convexity may differ from that of a vanilla bond.

Key ideas

• A long position in a conventional vanilla bond has positive duration and positive convexity exposure.
• A short bond position has negative convexity exposure.
• Negative convexity causes losses to accelerate as yields fall and gains to diminish as yields rise.
• Convexity describes how price sensitivity changes as yields move.

Tags

# Question About Negative and Positive Convexity


# Question About Negative and Positive Convexity












I read the following paragraph from investopedia: https://www.investopedia.com/terms/c/convexity.asp If a bond's duration increases as yields increase, the bond is said to have negative convexity. In other words, the bond price will decline by a greater rate with a rise in yields than if yields had fallen. Therefore, if a bond has negative convexity, its duration would increase—the price would fall. As interest rates rise, and the opposite is true.

If I understand correctly, for a vanilla bond with coupon, its duration is always a negative value, right? When investopedia says "If a bond's duration increases as yields increase", it is saying the absolute value of duration increases, is that right?

## Answer by Jan Stuller (score 1)

https://quant.stackexchange.com/a/54818

If you're long a normal Vanilla bond, you're always long Duration and long Convexity. You get negative convexity if you are short the bond.

Convexity has an effect on the rate at which you make or lose money:

Negative convexity (you are short the bond) means that the rate at which you lose money increases as yields decrease. And the rate at which you make money decreases as yields go up. So being short convexity is not as good as being long convexity.

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.