Why Futures and Forward Prices Can Differ Through Interest-Rate Correlation

Summary

The document explains the link between the difference in futures and forward prices and the correlation between an underlying asset's price and interest rates. It asks whether negative rate correlation for stocks or bonds would make forwards more expensive than futures. The answer says that the adjustment is generally negligible for equity and bond futures because the traded contracts are short dated; it also notes that long-run equity-rate correlation is close to zero on average.

For bonds, the answer describes a strongly negative relationship with rates but still expects only a small correction for short-dated contracts. Eurodollar futures are offered as a contrasting case: their longer maturities and negative rate correlation make the convexity correction significant. The discussion is a concise qualitative comparison, not a numerical pricing method. Its conclusions are framed around contract maturities and correlations, so they do not imply that futures and forwards are identical in every market or at every horizon.

Key ideas

• Futures and forward prices can differ when the underlying price is correlated with interest rates.
• Short maturities make the correction negligible for the equity and bond futures discussed.
• Long-run equity-rate correlation is described as close to zero on average.
• The answer characterizes bond prices as negatively correlated with rates while still noting a small short-term correction.
• Long-dated Eurodollar futures illustrate a case where convexity adjustment is significant.

Tags

# the difference between forward price and future price


# the difference between forward price and future price












In Hull's book 'Options, Futures and Other derivatives', author said that when price of underlying asset S is strongly positively correlated with the interest rate, future price is slightly larger than forward price for same contract.

I understand his description under that assumption.

Then, in a real world, Is forward price for stock or bond larger than future price for the same underlying asset if two contracts are equal?

It's because as far as I know, bond price or stock price both are in general negatively correlated with interest rate.

Am I right?

(Actually, I think most investment assets are negatively correlated with interest rate, because people will take more risk to get an extra income when interest rate is low.)

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/24590

For equities, the futures contracts are so short dated that there is no significant correction between futures and forwards. In any case, the corrleation between equities and rates averages fairly close to zero over the long term.

For bonds, there is obviously a large negative correlation with rates. However once again, the futures contracts that are traded are so short dated that the correction is still negligible.

The Eurodollar contract is the futures contract where the convexity correction is highly significant. That's because the contracts are long dated, with a high negative correlation with rates.

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.