# Optimal Hedge Ratio Calculator

URL: https://speedycalculator.com/calculators/finance/optimal-hedge-ratio/
Last updated: 2026-10-25

> The optimal hedge ratio calculator finds the minimum-variance hedge ratio from the volatility of spot and futures price changes and their correlation, and the number of futures contracts needed to hedge a position.

## Inputs

- Standard deviation of spot price changes (%)
- Standard deviation of futures price changes (%)
- Correlation coefficient
- Position size (units)
- Contract size (units)

## Results

- Optimal hedge ratio
- Futures contracts needed
- Hedge effectiveness (variance reduction)

## Formula

```
h* = ρ × σ_spot ÷ σ_futures
Contracts = h* × position size ÷ contract size
Hedge effectiveness = ρ²
```

## Explanation

When futures don't move exactly with the asset you own (basis risk), hedging one-for-one is not optimal. The minimum-variance hedge ratio uses the correlation and relative volatility to minimise the variance of the hedged position.

### How to use the Optimal Hedge Ratio Calculator

- **Standard deviation of spot price changes**
- **Standard deviation of futures price changes**
- **Correlation coefficient**
- **Position size (units)**
- **Contract size (units)**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Enter the standard deviations of spot and futures price changes, their correlation, your position size and the contract size.

### Tips

- Use the nominal annual rate and pick the compounding frequency your bank or broker states.
- Small differences in return or fees compound into large differences over decades.
- Run the calculation with a cautious, a central and an optimistic return to see the range of outcomes.
- Past returns do not guarantee future returns – nothing here is investment advice.

### Common mistakes to avoid

- Comparing an APR with an APY or effective rate.
- Ignoring inflation, taxes and fees when judging a real return.
- Entering a percentage as a decimal (5 instead of 0.05 is correct here).

### Inputs explained

FieldWhat to enterStandard deviation of spot price changesIn %Standard deviation of futures price changesIn %Correlation coefficientA numberPosition size (units)A numberContract size (units)A number

### What each result means

- **Optimal hedge ratio** = [Correlation coefficient]×[Standard deviation of spot price changes]÷[Standard deviation of futures price changes]
- **Futures contracts needed** = [Optimal hedge ratio]×[Position size (units)]÷[Contract size (units)]
- **Hedge effectiveness (variance reduction)** = [Correlation coefficient]^2×100

### Example values

How the main result changes when **Standard deviation of spot price changes** changes and everything else stays at the example values above:

Standard deviation of spot price changes (%)Optimal hedge ratio1.20.39431.80.59142.40.788630.98573.61.18294.81.5771

## Worked example

Inputs — Standard deviation of spot price changes: 2.4 %; Standard deviation of futures price changes: 2.8 %; Correlation coefficient: 0.92; Position size (units): 1,000,000; Contract size (units): 42,000.

Results — **Optimal hedge ratio = 0.7886**; Futures contracts needed = 18.8; Hedge effectiveness (variance reduction) = 84.64 %.

## FAQ

**What is the optimal hedge ratio?**
The ratio that minimises the variance of the hedged position.

**How many contracts do I need?**
Optimal ratio × position size ÷ contract size, rounded.

**What is hedge effectiveness?**
The share of variance removed: the correlation squared.

**What formula does the Optimal Hedge Ratio Calculator use?**
h* = ρ × σ_spot ÷ σ_futures.