How Correlation Affects Futures Convexity Adjustments

Summary

The document addresses whether futures-versus-forward convexity adjustments require a perfect correlation between a short rate and a forward rate. The question describes a possible mismatch: gains on a Eurodollar futures position might coincide with rising spot rates, so reinvesting gains could occur at a higher rate rather than a lower one. This challenges a simplified intuition about how rate movements and reinvestment interact.

The accepted answer says that suitable adjustment models let users choose the correlation instead of fixing it at one. It adds that implied correlations are often materially below one, particularly when the yield curve is volatile and forward rates move differently from the short end. The note offers a qualitative modeling point rather than a derivation, named model, or empirical dataset. It does not specify how to estimate correlation, how it varies through time, or how the adjustment changes numerically, so those details need to be established separately for an application.

Key ideas

• Convexity adjustment models can allow the correlation between spot and forward rates to vary rather than fixing it at one.
• Implied correlations may be below one, especially when the yield curve is volatile.
• Forward rates can move differently from short-end rates, affecting the reinvestment intuition behind the adjustment.
• The document provides no estimation procedure or quantitative model specification.

Tags

# Convexity adjustment


# Convexity adjustment












I have a problem with the underlying assumption in the future/forward convexity adjustment. If I understand correctly, the assumption is, if I am long ED, I earn money when rates go down and invest the money in a lower rate and vice versa. What I don't agree with is that the correlation between the spot rate and for example EDU5 is very far from 1, sometimes it is even negative (especially in a crisis). So I may earn money on long EDU5 and invest the earnings in a higher rate, as the spot rate is going high as well.

- Do most models assume 1 correlation between the spot rate and the forward rate?

- Any models thay take the correlation under consideration?

## Answer by dm63 (score 5, accepted)

https://quant.stackexchange.com/a/23146

I have traded those convexity adjustments for many years. Any decent model of these adjustments allows the user to vary the correlation as they please, rather than assuming something. If it is of interest, the implied correlations usually trade significantly under 1, especially in periods when the curve is volatile. ie when forward rates might be going in different direction to the short end.

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.