Hedge Ratio Calculator

Understanding Hedge Ratio in Financial Risk Management

The hedge ratio compares the value of a hedged position (such as futures or options contracts) against the total exposure of the underlying asset or portfolio. It measures the proportion of an asset or liability that is protected against adverse price movements.

The Optimal (Minimum Variance) Hedge Ratio Formula

In financial derivatives theory, the minimum variance optimal hedge ratio ($h^*$) minimizes the variance of the combined hedged portfolio value. It is calculated as:

$$h^* = \rho \times \left(\frac{\sigma_s}{\sigma_f}\right)$$

Where:

• $\rho$: Correlation coefficient between changes in spot price ($\Delta S$) and futures price ($\Delta F$).
• $\sigma_s$: Standard deviation of changes in spot price.
• $\sigma_f$: Standard deviation of changes in futures price.

Optimal Number of Futures Contracts

Once the optimal hedge ratio is calculated, the exact number of futures contracts ($N^*$) needed to hedge a portfolio value $V_A$ with contract value $V_F$ is:

$$N^* = h^* \times \left(\frac{V_A}{V_F}\right)$$