Effective Duration Calculator
Calculate the effective duration of a bond to measure its price sensitivity to interest rate changes. Effective duration accounts for embedded options and provides a more accurate measure of interest rate risk for complex bonds.
Bond Information
Duration Results
Effective Duration:
0.00 years
Price Change (1% Rate Change):
0.00%
Interest Rate Risk:
N/A
Risk Analysis
Duration Level:
N/A
Price Volatility:
N/A
Hedge Ratio:
0.00
Portfolio Impact
Value at Risk (1%):
$0.00
Duration Contribution:
0.00%
Immunization Status:
N/A
Understanding Effective Duration
Effective duration measures a bond's price sensitivity to changes in interest rates. Unlike modified duration, effective duration accounts for embedded options (like call or put features) and provides a more accurate measure of interest rate risk for complex bonds.
Effective Duration Formula
Basic Formula
- Effective Duration = (P- - P+) / (2 × P × ?y)
- P- = Price when rates decrease
- P+ = Price when rates increase
- P = Current price
- ?y = Change in yield (1% = 0.01)
Example Calculation
- Current Price: $950
- Price up 1%: $980
- Price down 1%: $920
- Duration: ($920 - $980) / (2 × $950 × 0.01) = 4.21 years
Duration vs Modified Duration
Key Differences
When to use each measure
Modified Duration
- Assumes no embedded options
- Based on coupon and maturity
- Good for bullet bonds
- Simpler calculation
Effective Duration
- Accounts for embedded options
- Based on actual price changes
- Accurate for callable/putable bonds
- More complex calculation
Duration Interpretation
| Duration Range | Risk Level | Characteristics | Examples |
|---|---|---|---|
| 0-3 years | Low Risk | Short-term, low sensitivity | Money market, short bonds |
| 3-7 years | Moderate Risk | Medium-term, moderate sensitivity | Corporate bonds, intermediate Treasuries |
| 7-12 years | High Risk | Long-term, high sensitivity | Long Treasuries, high yield bonds |
| 12+ years | Very High Risk | Very long-term, extreme sensitivity | Perpetual bonds, long mortgages |
Factors Affecting Duration
Bond Characteristics
- Time to maturity (longer = higher duration)
- Coupon rate (lower = higher duration)
- Embedded options (calls reduce duration)
- Yield level (lower yields = higher duration)
Market Conditions
- Interest rate environment
- Volatility levels
- Liquidity conditions
- Credit spreads
Duration Applications
Portfolio Management
- Risk assessment
- Hedging strategies
- Asset allocation
- Immunization
Risk Management
- Interest rate risk measurement
- Stress testing
- Value at risk calculations
- Scenario analysis
Duration and Convexity
Duration
- First derivative of price-yield curve
- Linear approximation
- Good for small rate changes
- Measures slope of curve
Convexity
- Second derivative of price-yield curve
- Curvature measure
- Adjusts duration approximation
- Important for large rate changes
Immunization Strategy
Duration Matching
- Match asset and liability durations
- Protect against interest rate risk
- Rebalancing required
- Assumes parallel yield curve shifts
Contingent Immunization
- Set minimum return threshold
- Active management if breached
- Combines passive and active strategies
- Higher potential returns
Limitations of Duration
Model Assumptions
- Parallel yield curve shifts
- Small interest rate changes
- No credit spread changes
- Constant cash flows
Practical Issues
- Large rate changes reduce accuracy
- Non-parallel yield curve shifts
- Changing volatility
- Transaction costs
Key Takeaways for Effective Duration Calculator
- Effective duration measures a bond's price sensitivity to interest rate changes, accounting for embedded options
- Calculated using actual bond price changes when yields move up and down by 1%
- Higher duration means greater price volatility and interest rate risk
- Effective duration is more accurate than modified duration for callable, putable, or complex bonds
- Duration is used for portfolio risk management, hedging, and immunization strategies
- The calculator helps assess interest rate risk and make informed investment decisions
- Duration should be used with convexity for more accurate risk assessments
- Use the calculator to compare interest rate risk across different bonds and portfolios