Northspread
Formula sheet/NISM Series XV: Research Analyst/Fundamental Analysis of Commodities
[ FUNDAMENTAL ANALYSIS OF COMMODITIES ]

Minimum Variance Hedge Ratio & Optimal Contracts

Hedge Ratio(h∗)=ρs,f×(σs/σf)\text{Hedge Ratio} (h*) = \rho_{s, f} \times ( \sigma_{s} / \sigma_{f} )
Optimal Quantity to Hedge(Qh)=h∗×QA\text{Optimal Quantity to Hedge} (Q_{h}) = h* \times Q_{A}
Number of Futures Contracts(N∗)=Qh/Contract Size=(h∗×QA)/Contract Size\text{Number of Futures Contracts} (N*) = Q_{h} / \text{Contract Size} = ( h* \times Q_{A} ) / \text{Contract Size}
Variables

ρs,f\rho_{s, f}: Correlation coefficient between changes in spot and futures prices. σs\sigma_{s}, σf\sigma_{f}: Standard deviation of changes in spot and futures prices; QAQ_{A}: Physical asset exposure.

Exam note

Minimizes basis risk and variance of the combined physical + derivative position.

Worked example
Minimum Variance Hedge Ratio & Futures Contracts

A cable manufacturing company needs to hedge 500 Metric Tonnes (MT) of copper procurement for next month. Statistical analysis reveals: correlation coefficient between spot and futures price changes (ρ) = 0.985, standard deviation of spot changes (σ_s) = 9.02, standard deviation of futures changes (σ_f) = 9.71. MCX Copper contract size is 2.5 MT. Calculate the optimal Hedge Ratio, quantity to hedge, and number of contracts.