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Why Minimum Variance Hedge Ratios Do Not Require Matching Price Units

Article Quant Q&A · Author: ConnieTraveller
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Summary

The document addresses whether a minimum variance hedge ratio requires spot and futures prices to use the same physical units. Its example compares spot prices quoted in dollars per barrel with futures prices quoted in dollars per million British thermal units, raising the possibility of converting between barrels and energy units before calculating the ratio.

The response explains that the standard inputs are typically the standard deviations of daily log-price changes, or returns, along with the correlation between the two instruments. Returns and correlation are dimensionless, so the price quotation units do not need to be converted just to calculate the hedge ratio. This is also what allows cross-commodity hedges, such as using one fuel to hedge another. The note is brief and does not derive the hedge-ratio formula or discuss contract multipliers and practical position sizing, which still matter when translating a statistical ratio into trade quantities.

Key ideas

  • Minimum variance hedge calculations commonly use standard deviations of log returns rather than price levels.
  • Log returns and correlation are dimensionless, so the quoted physical units need not match.
  • A hedge may use a different but related commodity, such as one fuel hedging another.
  • Converting the statistical hedge ratio into contracts still requires attention to contract specifications.

Tags

CommoditiesFuturesStatisticsRisk management
Full text
# Units of measurement for Minimum Variance Hedge Ratio


# Units of measurement for Minimum Variance Hedge Ratio












The minimum variance hedge ratio is given by $h=p*\frac{\sigma_S}{\sigma_F}$.

I was wondering if you wanted to calculate the S.D yourself and the spot prices were in Dollars per barrel while futures prices were in Dollars per million BTU, would you have to change barrels into million BTU (ie. multiply 5.4)?

## Answer by ogukku (score 1)

https://quant.stackexchange.com/a/46972

Since SD in this case is usually the 1-day difference of log prices (i.e. 1-day returns) and corr is a dimensionless number, you shouldn't have to keep the units the same. After all that's how you're able to hedge a position using a different commodity that you have access to, for example jet fuel.

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.