Optimal Hedge Ratio Calculator

Compute the optimal hedge ratio using the standard deviations of spot and futures price changes and their correlation.

Std. Dev. (Spot Price Changes) — σₛ

Std. Dev. (Futures Price Changes) — σ𝒻

Correlation Coefficient — ρ

Optimal Hedge Ratio Calculator

In financial markets, investors and businesses often use hedging strategies to protect against price volatility. One of the most important concepts in hedging is the Optimal Hedge Ratio (OHR), which determines the ideal proportion of a position that should be hedged using futures contracts. By calculating the OHR, traders can minimize risk exposure while still participating in market opportunities.

Our Optimal Hedge Ratio Calculator helps you compute the ratio using three inputs:
Standard deviation of spot price changes (σₛ)
Standard deviation of futures price changes (σ𝑓)
Correlation coefficient (ρ) between spot and futures prices
This simple yet powerful tool allows you to calculate the exact hedge ratio to reduce portfolio risk effectively.

🔎 What is Optimal Hedge Ratio?

The Optimal Hedge Ratio (h*) is the proportion of an exposure that should be hedged using futures contracts to minimize risk.

👉 Formula:

Optimal Hedge Ratio = Correlation Coefficient × (Spot Price Std. Dev. ÷ Futures Price Std. Dev.)

A higher correlation increases hedge effectiveness, while differences in volatility between spot and futures prices adjust the hedge ratio accordingly.

📚 Examples

Example 1

Std. Dev. (Spot Price Changes), σₛ = 2.25
Std. Dev. (Futures Price Changes), σ𝑓 = 1.10
Correlation Coefficient, ρ = 0.55

Step 1 – Apply Formula:

h* = 0.55 × (2.25 ÷ 1.10)

Step 2 – Simplify:

h* = 0.55 × 2.045 = 1.125

✅ Optimal Hedge Ratio = 1.125

Example 2

Std. Dev. (Spot Price Changes), σₛ = 1.50
Std. Dev. (Futures Price Changes), σ𝑓 = 1.40
Correlation Coefficient, ρ = 0.90

Step 1 – Apply Formula:

h* = 0.90 × (1.50 ÷ 1.40)

Step 2 – Simplify:

h* = 0.90 × 1.071 = 0.964286

✅ Optimal Hedge Ratio = 0.964

Example 3

Std. Dev. (Spot Price Changes), σₛ = 3.00
Std. Dev. (Futures Price Changes), σ𝑓 = 4.00
Correlation Coefficient, ρ = 0.30

Step 1 – Apply Formula:

h* = 0.30 × (3.00 ÷ 4.00)

Step 2 – Simplify:

h* = 0.30 × 0.75 = 0.225

✅ Optimal Hedge Ratio = 0.225

✨ Features of Our Optimal Hedge Ratio Calculator

✅ Instant calculations using σₛ, σ𝑓, and ρ

✅ Provides accurate hedge ratio for minimizing risk

✅ Works seamlessly on desktop, tablet, and mobile devices

✅ Simple, intuitive interface with professional accuracy

✅ Completely free to use, no sign-up required

✅ Ideal for traders, portfolio managers, analysts, and students

👩‍💼 Who Should Use This Calculator?

Traders & Hedgers – To determine hedge levels in commodities, currencies, and equities

Portfolio Managers – To minimize volatility while maintaining returns

Risk Managers – To evaluate hedging strategies for businesses and funds

Researchers & Educators – To demonstrate the application of financial risk management

Students – To learn how correlation and volatility affect hedging effectiveness

💡 Why Optimal Hedge Ratio Matters

A hedge ratio of 1 means a perfect hedge, but in reality, different volatilities and correlations often result in ratios above or below 1.
A ratio above 1 means you should hedge more than your spot exposure.
A ratio below 1 means partial hedging is sufficient.
Understanding the OHR prevents both under-hedging (too much risk exposure) and over-hedging (too much cost with reduced returns).

✅ The Optimal Hedge Ratio Calculator is a must-have for traders, investors, and risk managers. It makes the complex calculation of hedge ratios fast, accurate, and simple.

👉 Try the Optimal Hedge Ratio Calculator today on Hive Calculator and master risk management with confidence!