Optimal Hedge Ratio

What is the Optimal Hedge Ratio?

The key to any effective hedging is to find the perfect security to be used for Hedging. One way to find it is to use the it. We can account for an imperfect relationship between the spot and future positions through the ratio as it considers the correlation between the two rates.

Example:

The optimal Hedge Ratio is calculated using the following formula:
$ ρ= \frac{COV_{S,F}}{\sigma_{S}\sigma_{F}} $

Where,
ρ is the correlation between S and F
σ_S is the standard deviation of the spot price
σ_F is the standard deviation of future price

Let’s take an example of hedging security with covariance as 2, S as 1.2, and F as 1.5. Using the formula given above to calculate the optimal hedge ratio as below:

$ ρ= \frac{2}{1.2*1.5}= 1.11 $

Why is it important?

This assists the investors in minimising the variance of the combined hedging position hence minimizing the risk and making the hedge more effective and efficient.

In addition to minimising the risk and making the hedge more effective, calculating the optimal hedge ratio can also help investors determine the appropriate amount of security for hedging. A high hedge ratio means a large amount of security is necessary to hedge the underlying asset. In contrast, a low hedge ratio means smaller security is necessary. By using the this, investors can determine the most cost-effective way to hedge their positions, thereby maximising their returns.

Moreover, it is useful as a benchmark for evaluating the effectiveness of a hedging strategy. If the actual hedge ratio used by an investor is close to the optimal hedge ratio, it suggests that the hedging strategy is efficient and effective. On the other hand, if the actual hedge ratio deviates significantly from the optimal hedge ratio. It may indicate that the hedging strategy needs to re-evaluate.