Normalizing Futures Prices for Cointegration and Hedging

Summary

The document asks how to prepare E-mini S&P 500 and Nasdaq futures prices for a cointegration test when their contract multipliers differ. One proposed method multiplies each quoted price by its contract multiplier, producing notional values that can be treated like share prices. Another response argues that cointegration is generally tested on original price series and may not require normalization. A third suggestion shifts the question toward comparing risk-scaled moves: divide returns by a volatility estimate so changes have more comparable sizes.

These answers address different goals and do not establish a single required transformation. Contract-value scaling adjusts for dollar exposure, while volatility scaling standardizes return magnitudes; neither automatically resolves choices about cointegration specification. The discussion gives no empirical test or guidance on whether scaling affects a particular test's conclusions, so researchers should distinguish the economic question they want to answer from a desire to make the series numerically comparable.

Key ideas

• Multiplying futures prices by contract multipliers expresses each series in notional-value terms.
• Cointegration may be tested on original price series without normalizing them.
• Volatility-scaled returns can make the magnitude of moves more comparable across instruments.
• The appropriate transformation depends on whether the goal is dollar exposure, statistical testing, or comparable risk units.

Tags

# How to normalize Futures data(different leverage) for cointegration test?


# How to normalize Futures data(different leverage) for cointegration test?












For example I want to construct 2 time series, one for ES and the other for NQ and test for cointegration.

ES one point equal to 50$.

NQ one point equal to 20$.

If I have the following data:

ES[0]=1300;ES[1]=1307;ES[2]=1314...

NQ[0]=2700;NQ[1]=2692;NQ[2]=2715...

How do I normalize this data for cointegration test?

TX in advance!

## Answer by user508 (score 6, accepted)

https://quant.stackexchange.com/a/2268

Multiply each price series by its multiplier to get notional values. Then proceed as if the notional value were the price of 1 share.

## Answer by Ram Ahluwalia (score 3)

https://quant.stackexchange.com/a/2266

In a co-integration test you rely on the original price series -- not transformations of the price series such as rate of change and so on. Seems to me there is no need for normalization.

## Answer by Shane (score 1)

https://quant.stackexchange.com/a/2269

It sounds like you want to look at constant volatility series. Just divide the returns by some volatility measure on each series respectively (e.g. ($r_t * volatilitytarget)/\sigma(50 days)$). Then the change in one will be equivalent in size to the change in the other.

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