# 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?

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.