Normalizing Futures Prices and Estimating a Pairs Hedge Ratio

Summary

The document discusses how to compare two correlated futures contracts whose prices and tick sizes differ when building a pairs strategy. One suggested approach sets both starting prices to one, then compounds each instrument’s percentage price changes to create normalized price series. Their difference can then be examined as a candidate spread. This puts the series on a comparable relative scale, while the original tick sizes still matter when estimating realistic trading results.

A second suggestion is to regress one security’s price on the other and use the fitted slope as a hedge ratio. The answers offer practical starting points but do not explain how to test whether the relationship is stable, choose a lookback window, or define a significant deviation. Normalizing by percentage changes and estimating a regression hedge ratio are distinct choices; neither by itself establishes that a spread is mean-reverting or tradable. Tick value, contract multipliers, and execution costs also need consideration in a futures backtest.

Key ideas

• Rescaling both instruments to the same initial value allows comparison of their compounded percentage price changes.
• Different tick sizes affect realized spread behavior and should be accounted for in a backtest.
• A linear regression slope can serve as a candidate hedge ratio between two prices.
• Normalization and hedge ratio estimation do not by themselves establish a stable, tradable pairs relationship.

Tags

# pairs trading, normalization


# pairs trading, normalization












I am interested in implementing a simple pairs trading strategy using two correlated futures contracts. I am unsure what the best way to normalize the prices of the two instruments is.

Essentially right now I am iterating concurrently through the prices of two instruments however the prices are on very different scales and the two contracts have different minimum tick price increments.

What is the best way to normalize the prices so that I can compute the difference in between prices in order to determine if there is a significant spread present?

## Answer by Artem Korol (score 1)

https://quant.stackexchange.com/a/33557

Normalize by assuming both prices at t(1) = 1, and then multiply every t by (1 + price change in %) to get normalized price at t+1. Difference in tick size does not matter it will just make the spread volatility larger. However you will have to account for that tick size when you back test.

## Answer by user1130176 (score 0)

https://quant.stackexchange.com/a/38236

Do a linear regression of security 1 versus security 2 and the slope is the hedge ratio.

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