Q: How do I hedge a multi-stock portfolio with index futures?

Step 1: Calculate the portfolio's weighted average beta — sum of (position weight × individual beta) for all holdings. Step 2: Apply the beta hedge formula: Contracts = Portfolio Beta × Portfolio Value / (Futures Price × Multiplier). Step 3: Short that number of index futures contracts. Example: $500,000 portfolio with weighted beta 1.35, E-Mini S&P 500 at $5,250 × 50 = $262,500/contract → 1.35 × $500,000 / $262,500 = 2.57 → short 3 contracts (rounded). The Portfolio tab calculates this automatically from a table of individual positions.

Q: What does 'effective beta after hedge' mean?

Effective beta after hedge is the portfolio's net market sensitivity after accounting for the short futures/ETF position. Due to the discrete rounding of contracts (you can only trade whole contracts, not fractional), the effective beta after hedge will usually differ slightly from the target beta. For example, targeting beta 0 with a $500,000 portfolio requiring exactly 2.38 contracts — rounding to 2 contracts leaves an effective beta of approximately 0.10 (10% market exposure remains). The quality indicator shows: Precise (effective beta within 0.05 of target), Approximate (within 0.15), or Rounding Error (more than 0.15 away).

Q: Is the Hedge Ratio Calculator free to use?

Yes. The Hedge Ratio Calculator Pro on StockToolHub is completely free with no registration, account, or subscription required. All five tabs — Beta Hedge, Min-Variance, Options, Portfolio, and Scenarios — are fully accessible with no limitations and no sign-up required.

Question 1

What is a hedge ratio?

Accepted Answer

A hedge ratio is the proportion of a position that is offset by a hedging instrument. A hedge ratio of 1.0 means fully hedged (100% of the position is offset); 0.5 means 50% hedged; 0 means unhedged. In practice, the hedge ratio determines how many contracts or units of the hedging instrument (index futures, ETF shares, put options) are needed to offset the risk of a portfolio or individual position. Different methodologies produce different optimal hedge ratios depending on the type of risk being hedged.

Question 2

What is the beta hedge ratio formula?

Accepted Answer

The beta hedge ratio formula for equity portfolios is: N = (β_target − β_portfolio) × (Portfolio Value / Contract Value), where Contract Value = Futures Price × Multiplier. For a full hedge (β_target = 0): N = −β_portfolio × Portfolio Value / Contract Value. The negative sign means you short the hedge instrument. Example: Portfolio value $500,000, beta 1.25, E-Mini S&P 500 futures at $5,250 × multiplier 50 = $262,500 per contract. Contracts = (0 − 1.25) × $500,000 / $262,500 = −2.38 → short 2 contracts.

Question 3

What is the minimum variance hedge ratio (MVHR)?

Accepted Answer

The Minimum Variance Hedge Ratio (MVHR), introduced by Johnson (1960) and Stein (1961), minimizes the variance of a hedged position by finding the optimal proportion of the hedge instrument to hold. Formula: h* = ρ × (σ_S / σ_F), where ρ is the correlation between the spot asset and futures returns, σ_S is the standard deviation of spot returns, and σ_F is the standard deviation of futures returns. MVHR equals the OLS regression slope when you regress spot returns on futures returns. Hedge effectiveness is measured by ρ² — the proportion of spot variance eliminated by the optimal hedge.

Question 4

How do I calculate the number of put options for delta hedging?

Accepted Answer

Delta hedge contracts = (Shares × Coverage%) / (|Delta| × Contract Size). For standard equity options where contract size = 100 shares: with 1,000 shares, ATM put delta = 0.50, and 100% coverage: Contracts = (1,000 × 100%) / (0.50 × 100) = 20 put contracts. The position delta (long shares) is +1,000; the hedge delta is −(20 × 0.50 × 100) = −1,000; net delta = 0 (delta-neutral). The hedge cost = contracts × option premium × contract size.

Question 5

What is the difference between beta hedging and minimum variance hedging?

Accepted Answer

Beta hedging is designed for equity portfolios and uses the portfolio's systematic risk (beta) to determine how many index futures contracts to short. It focuses on eliminating market risk (systematic risk). Minimum variance hedging (MVHR) uses historical return data to find the hedge ratio that minimizes the total variance of the hedged position — it is driven by the correlation and relative volatility between the spot asset and the hedge instrument. MVHR is used more for commodity, currency, and fixed income hedging where beta is not the relevant risk measure. MVHR is always statistically optimal for variance minimization; beta hedging is more intuitive for equity portfolio management.

Question 6

What is hedge effectiveness and how is it measured?

Accepted Answer

Hedge effectiveness measures how much of the position's risk is eliminated by the hedge. For the minimum variance hedge, effectiveness = ρ² (the square of the correlation between spot and hedge instrument returns). At ρ = 1.0 (perfect correlation), effectiveness = 100% — all variance is eliminated. At ρ = 0.9, effectiveness = 81%. Below ρ = 0.7 (effectiveness < 49%), the hedge instrument is a poor fit for the position being hedged and should be reconsidered. For accounting purposes (ASC 815, IFRS 9), a hedge must demonstrate effectiveness above 80% to qualify for hedge accounting treatment.

Question 7

How do I hedge a multi-stock portfolio with index futures?

Accepted Answer

Step 1: Calculate the portfolio's weighted average beta — sum of (position weight × individual beta) for all holdings. Step 2: Apply the beta hedge formula: Contracts = Portfolio Beta × Portfolio Value / (Futures Price × Multiplier). Step 3: Short that number of index futures contracts. Example: $500,000 portfolio with weighted beta 1.35, E-Mini S&P 500 at $5,250 × 50 = $262,500/contract → 1.35 × $500,000 / $262,500 = 2.57 → short 3 contracts (rounded). The Portfolio tab calculates this automatically from a table of individual positions.

Question 8

What does 'effective beta after hedge' mean?

Accepted Answer

Effective beta after hedge is the portfolio's net market sensitivity after accounting for the short futures/ETF position. Due to the discrete rounding of contracts (you can only trade whole contracts, not fractional), the effective beta after hedge will usually differ slightly from the target beta. For example, targeting beta 0 with a $500,000 portfolio requiring exactly 2.38 contracts — rounding to 2 contracts leaves an effective beta of approximately 0.10 (10% market exposure remains). The quality indicator shows: Precise (effective beta within 0.05 of target), Approximate (within 0.15), or Rounding Error (more than 0.15 away).

Question 9

Is the Hedge Ratio Calculator free to use?

Accepted Answer

Yes. The Hedge Ratio Calculator Pro on StockToolHub is completely free with no registration, account, or subscription required. All five tabs — Beta Hedge, Min-Variance, Options, Portfolio, and Scenarios — are fully accessible with no limitations and no sign-up required.

Hedge Ratio Calculator Pro

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Beta Hedge

Min-Variance

Options

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