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Continuous Returns for Negative Roll-Adjusted Futures Series

Article Quant Q&A · Author: strimp099
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Summary

The document describes a continuous futures series built by adding a cumulative roll adjustment to settlement prices and applying the contract multiplier. With this additive adjustment, the resulting notional can become negative even when the underlying settlement price is positive. That makes ordinary logarithmic returns unusable at those observations, prompting a question about how to calculate continuous returns while retaining the effect of carry costs.

The answer notes that futures series can be adjusted in multiple ways and that the appropriate choice depends on the intended use. It points to a survey of adjustment methods and says a method discussed elsewhere in the exchange thread is likely suitable. It does not explain that method or provide a return formula, data comparison, or evidence that it preserves the desired carry effect. The discussion therefore identifies the source of the mathematical difficulty and the importance of the adjustment convention, but leaves the practical calculation unresolved.

Key ideas

  • An additive roll adjustment can produce negative adjusted futures values.
  • Log returns are undefined for negative values, so the usual continuous-return calculation fails.
  • The suitable futures adjustment method depends on the intended application.
  • The answer points toward an alternative method but does not describe or validate it.

Tags

FuturesCommoditiesStatisticsBacktesting
Full text
# Continuous returns for negative roll-adjusted futures data


# Continuous returns for negative roll-adjusted futures data












I've generated roll adjusted notional futures data by adding a roll adjustment to the settlement price then multiplying by contract multiplier through time. For example, for crude oil CL, on 15 March 2013, the settlement price of the CLJ3 contract was `93.45`. The cumulative roll adjustment was `-70.80` and the multiplier is `1,000`. My roll adjusted notional is then $(93.45-70.80)/*1,000=22,650$.

This is great but take for example 12 Feb 2009 where settlement price was `33.98` and cumulative roll adjustment was `-33.99`. This gives me a negative roll adjusted contract value of $(33.98-33.99)*1,000=-10$.

The implication of a negative roll adjusted notional value on futures is that you have literally lost money through the cost of carry for this product. I am using a method dictated by my client otherwise the ratio method, described here, may have been implemented. This person is intent on capturing potential loss due to carry, however.

I'm challenged in my attempt to compute continuous returns for the series because of the negative values. Taking the log of a negative number in MATLAB returns an imaginary number and Excel can't handle it at all.

Does anyone have experience or advice in computing continuous returns for negative roll-adjusted futures notionals?

## Answer by strimp099 (score 2, accepted)

https://quant.stackexchange.com/a/8213

Turns out there are many methods which people use to adjust futures time series. The method employed depends on the use. There's a real nice paper here that synthesizes each of the methods. Turns out the method Matt Wolf described will likely work the best.

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.