Why Minimum-Variance Hedge Ratios Use Percentage Changes

Summary

The document addresses why cross-hedging calculations often estimate a minimum-variance hedge ratio by regressing percentage changes in spot prices on percentage changes in futures prices, rather than regressing absolute price changes. The explanation is that the spot-to-futures price relationship is not stationary: it can vary over time as factors such as interest rates and storage costs change. Comparing percentage changes helps control for differences in price levels and makes the estimated relationship more suitable for a hedge ratio across observations.

The response offers a concise rationale for using returns in the regression, even when futures contracts are settled daily. It does not derive the hedge ratio or compare empirical performance of return-based and absolute-change regressions. The choice of transformation still depends on the data and hedging objective, and the brief answer does not address other sources of instability or model diagnostics.

Key ideas

• The spot-to-futures price ratio can change over time as rates and carrying costs vary.
• Regressing percentage changes helps account for differences in the price levels of the two instruments.
• A minimum-variance cross-hedge ratio can be estimated from the relationship between spot and futures returns.
• Daily futures settlement does not by itself determine whether price changes or percentage changes are the appropriate regression inputs.
• The explanation gives intuition but no empirical comparison or diagnostic procedure.

Tags

# Minimum hedge variance ratio


# Minimum hedge variance ratio












If futures contracts are being settled daily, why do we regress percentage changes in spot price over percentage changes in future price to get the minimum variance hedge ratio when cross hedging? Like why not regress absolute changes here?

Hull does this and I have no idea why.

## Answer by Evan Semet (score 1)

https://quant.stackexchange.com/a/80495

Hull (and others) do this because the ratio of spot to the future is non stationary. Even if we were to simplify this down and only look back in time when the future is exactly X time away from expiration, there would be many differences in the ratio of spot to future (interest rate changes, storage costs, ...). Changing each to the percent helps to control for this.

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.