Hedge Ratio Calculator
Calculate optimal hedge ratios for portfolio risk management. Determine the right amount of hedging instruments to minimize portfolio volatility.
Hedge Ratio Results
Hedging Analysis
Hedging Strategies
Perfect Hedge: 100% correlation
Cross Hedge: Imperfect correlation
Over Hedge: More than needed
Under Hedge: Less than optimal
Note: Balance cost vs. risk reduction
Understanding Hedge Ratios
A hedge ratio determines the optimal amount of hedging instruments needed to minimize portfolio risk. It represents the proportion of a portfolio that should be hedged to achieve desired risk reduction.
Hedge Ratio Formula
The basic hedge ratio is calculated as:
Hedge Ratio = (ß_p × ?) / ß_h
Where: ß_p = portfolio beta, ? = correlation, ß_h = hedge instrument beta
Types of Hedging
- Perfect Hedge: Completely eliminates risk (correlation = ±1)
- Cross Hedge: Uses related but not identical assets
- Dynamic Hedge: Adjusts hedge ratio over time
- Minimum Variance Hedge: Minimizes portfolio variance
Beta and Correlation
Beta measures systematic risk relative to the market. Correlation measures how closely two assets move together.
- Beta > 1: More volatile than market
- Beta = 1: Same volatility as market
- Beta < 1: Less volatile than market
- Correlation = 1: Perfect positive correlation
- Correlation = -1: Perfect negative correlation
- Correlation = 0: No correlation
Hedging Instruments
| Instrument | Typical Beta | Use Case | Cost |
|---|---|---|---|
| S&P 500 Futures | 1.0 | Stock portfolio hedge | Low |
| Inverse ETF (SH) | -1.0 | Market downturn protection | Medium |
| Put Options | Varies | Downside protection | High |
| Gold Futures | 0.1-0.2 | Inflation hedge | Medium |
Hedging Effectiveness
Hedging effectiveness measures how well a hedge reduces portfolio risk. It's calculated as the reduction in portfolio variance.
Hedging Effectiveness Formula:
Effectiveness = 1 - (s_h² / s_u²)
Where: s_h² = hedged portfolio variance, s_u² = unhedged portfolio variance
Over-hedging vs. Under-hedging
- Over-hedging: Reduces risk more than intended, may miss upside
- Under-hedging: Leaves residual risk exposure
- Optimal Hedging: Balances risk reduction with cost and opportunity
- Dynamic Hedging: Adjusts hedge ratio as market conditions change
Cost of Hedging
Hedging involves costs that reduce the effectiveness of the strategy. These include transaction costs, bid-ask spreads, and opportunity costs.
- Transaction Costs: Commissions and fees
- Basis Risk: Imperfect correlation between hedge and portfolio
- Opportunity Cost: Forgone returns from hedging
- Maintenance Costs: Ongoing adjustment costs
When to Hedge
- Market Downturns: Protect against significant losses
- High Volatility: Reduce portfolio swings
- Event Risk: Protect against specific events
- Target Risk Level: Maintain desired risk profile
- Short-term Goals: Protect near-term objectives
Hedging Strategies
- Portfolio Insurance: Buy puts to protect downside
- Collar Strategy: Buy puts, sell calls to limit risk
- Constant Mix: Maintain target allocation
- Stop-Loss Orders: Automatic selling at price levels
- Diversification: Spread risk across assets
Tip: Hedging can protect portfolios from downside risk but involves costs and may limit upside potential. Use this calculator to determine optimal hedge ratios based on your risk tolerance and market conditions. Remember that perfect hedges are rare, and basis risk is common.