Final answer:
The optimal hedge ratio requires the minimum-variance hedge ratio formula, considering the covariance and variances of spot and futures prices, which cannot be derived solely from the forward price formula provided (F₀ = S₀e⁽ʳ⁺ᵘ−ʸ⁾ᵀ).
Step-by-step explanation:
The optimal hedge ratio for energy commodities when hedging with futures on the same asset can be determined using the minimum-variance hedge ratio formula. This formula is based on the spot-futures covariance and the variances of spot and futures prices. However, the provided forward price formula F₀ = S₀e⁽ʳ⁺ᵘ−ʸ⁾ᵀ alone does not give us enough information to calculate the hedge ratio without additional data on spot and futures price variability and their covariance.
When constructing a hedge, one common method is to use the concept of the minimum-variance hedge ratio, which minimizes the variance of the value of the hedged position. While the exact formulation for this hedge ratio often involves statistical measures such as covariances or correlations between the spot and futures prices, the basic premise is to find a proportion of the position to be hedged that results in the lowest possible risk (variance). This involves a deep understanding of the market dynamics and the mathematical relationships between the hedging instruments.