Question 1

What is the minimum-variance hedge ratio (HR)?

Accepted Answer

The minimum-variance hedge ratio (h*) represents the optimal proportion of an underlying asset position that should be covered by derivative futures contracts to minimize the variance of the combined hedged portfolio.

Question 2

How do spot-futures correlation and volatility affect the optimal hedge?

Accepted Answer

Higher correlation (ρ) increases the hedge ratio toward 1.0. When spot volatility exceeds futures volatility (σ_S > σ_F), the hedge ratio increases above the correlation coefficient to compensate for the higher swings in the spot asset.

Question 3

Perfect 1:1 Hedge vs. Minimum-Variance Optimal Hedge: What is the difference?

Accepted Answer

A naive 1:1 hedge assumes spot and futures prices move identically in lockstep. A minimum-variance hedge accounts for basis risk and differences in volatility, preventing over-hedging or under-hedging.

Question 4

Can you provide a step-by-step worked numerical example of hedge ratio calculation?

Accepted Answer

Assume a $2,000,000 equity portfolio with 24% volatility (σ_S = 0.24). You hedge using E-mini S&P 500 futures with 20% volatility (σ_F = 0.20), correlation ρ = 0.85, and a single futures contract value of $250,000 (V_F). Step 1: h* = 0.85 × (0.24 / 0.20) = 1.02. Step 2: Total required hedge value = 1.02 × $2,000,000 = $2,040,000. Step 3: Exact contracts N* = $2,040,000 / $250,000 = 8.16 contracts (round to 8 contracts to short).

Question 5

What are the common risks and edge cases in cross-hedging?

Accepted Answer

Cross-hedging occurs when the asset being hedged differs from the futures contract deliverable. Basis risk (unexpected widening between spot and futures prices) and correlation breakdown during market crashes can reduce hedging effectiveness.

Question 6

Is my portfolio valuation and hedging strategy private?

Accepted Answer

Yes. All portfolio values, volatility inputs, contract sizes, and variance reductions are computed exclusively in client-side RAM with zero server transfers.

Question 7

What is an effective hedge ratio and variance reduction benchmark in risk management?

Accepted Answer

Hedge effectiveness equals R-squared (ρ²). A correlation of 0.90 yields an 81% reduction in total portfolio variance (0.90² = 0.81), leaving only 19% residual basis risk.

Scenario	Correlation (ρ)	Hedge Ratio (h*)	Contracts	Variance Reduction
Bearish Divergence (ρ = -0.80)	-0.80	-0.96	-8	64%
Weak Correlation (ρ = 0.20)	0.20	0.24	2	4%
Moderate Association (ρ = 0.50)	0.50	0.6	5	25%
Current Input Baseline	0.85	1.02	8	72.2%
Strong Alignment (ρ = 0.90)	0.90	1.08	9	81%
Perfect Linear Move (ρ = 1.00)	1.00	1.2	10	100%

Evaluation Criteria	ToolboxDock (Client-Side)	Traditional Online Calculators
Financial Data Privacy	100% Local (Never leaves device RAM)	Logged on remote servers and ad networks
Calculation Latency	Instant real-time update on keystroke	Full page reloads or API round-trips
Offline Usability	Works offline once cached in browser	Fails without active server connection
Cost & Paywalls	100% free with unlimited calculations	Usage caps or financial product paywalls

Scenario	Correlation (ρ)	Hedge Ratio (h*)	Contracts	Variance Reduction
Bearish Divergence (ρ = -0.80)	-0.80	-0.96	-8	64%
Weak Correlation (ρ = 0.20)	0.20	0.24	2	4%
Moderate Association (ρ = 0.50)	0.50	0.6	5	25%
Current Input Baseline	0.85	1.02	8	72.2%
Strong Alignment (ρ = 0.90)	0.90	1.08	9	81%
Perfect Linear Move (ρ = 1.00)	1.00	1.2	10	100%

Hedge Ratio Calculator

Hedging Parameters

1.02hedge ratio

Contracts to Trade

Total Hedge Notional

Variance Reduction

Correlation Sensitivity Matrix

What is the Hedge Ratio Calculator?

Financial Calculation Inputs

Output & Schedule Breakdown

How to Use the Hedge Ratio Calculator

1. Input Portfolio Value & Volatility

2. Configure Futures Contract Specifications

3. Review Optimal Contracts & Hedge Ratio

Financial Privacy & Architecture Comparison

Minimum-Variance Hedge Ratio Formula

Core Hedge Ratio Calculator Inputs & Terminology

Frequently Asked Questions

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