Choosing Commodity Futures and Hedge Ratios by Tenor, Risk, and Cost
Summary
The document explains how to choose a futures contract to hedge a commodity exposure, using natural gas as an example. It distinguishes next-day spot from near-term delivery positions: a longer-dated future may be a poor hedge for immediate spot exposure, while a contract matching the delivery period is generally available for nearer-term positions. When an exact contract is illiquid, shorter-dated futures can serve as proxy hedges, though effectiveness tends to decline as the tenor gap widens.
Hedge sizing should minimize the combined portfolio variance, taking account of the position and futures volatilities and their correlation. The document also emphasizes that correlation depends on the relationship and horizon being measured, so it should not be treated as the sole selection criterion. Bid-ask costs matter, especially when a long-dated hedge requires repeated rolls. The proposed objective is to minimize loss at a chosen confidence level while balancing hedge effectiveness against cost. No empirical comparison or specific calculation procedure is provided, so the guidance is conceptual and must be adapted to the instrument and risk horizon.
Key ideas
- Match the futures delivery tenor to the exposure when a suitable liquid contract exists.
- Proxy hedge effectiveness generally falls as the difference between exposure and hedge tenors grows.
- A minimum-variance hedge ratio depends on position and hedge volatility as well as their correlation.
- Include bid-ask costs and repeated roll costs when comparing hedge contracts.
- Choose a hedge by balancing its effectiveness and cost against a defined loss criterion.
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# Hedge Ratio Calculation
# Hedge Ratio Calculation
My question is if I have a spot position of a commodity e.g Naturals Gas I want to hedge, how would I determine, which futures e.g. quarterly, yearly I should pick. Should I just take the one it is the most correlated with? And when I calculate the correlation should I take it over the whole time period i.e 10 years? And lastly should I take daily, weekly or monthly returns as the correlation is going to change depending on the frequency?
## Answer by ZRH (score 2)
https://quant.stackexchange.com/a/54371
You are referring to the position to be hedged, as "spot position", which in gas markets means next day delivery. Hedging this with a longer-dated futured contract does not make sense, since the correlation will be rather low.
If by spot you mean near-term deliveries, such as e.g. next month, next quarter etc. then a matching traded contract will usually be available in the market, so there is no problem.
Generally, proxy-hedging will be required when long-dated illiquid contracts have to be hedged with shorter-dated contracts. In terms of hedge effectiveness, the correlation will decrease, as the tenor difference between the position and the hedge increases. For most commodities, volatilities are also tenor-dependent. The optimal hedge size $Q_{hedge}$ against a position of size $Q_{pos}$ and volatility $\sigma_{pos}$ is the quantity that results in minimal portfolio variance given hedge volatility $\sigma_{hedge}$ and correlation $\rho_{hedge,pos}$. Besides the variance of the portfolio of position and hegde, the hedging cost (bid-ask) needs to be taken into account. When hedging very long-dated positions, the hedge may have to be rolled over multiple times, i.e. bid-ask will be incurred multiply.
The optimal hedge would then be defined as the hedge with the lowest loss at a defined confidence level. This is defined by the tradeoff between hedge effectiveness and cost of hedgingShown 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.