Effective Duration Calculator
Calculate bond interest rate sensitivity for bonds with embedded options
Calculate Effective Duration
Bond Information
Par value of the bond
Annual interest rate paid by the bond
How often coupons are paid per year
Time until bond matures
Yield Information
Current market yield of the bond
Rate change used for sensitivity analysis
Effective Duration Results
Formula: Effective Duration = (P₋ - P₊) ÷ (2 × P₀ × Δy)
Where: P₋ = Bond price when yield decreases, P₊ = Bond price when yield increases, P₀ = Current bond price, Δy = Yield change
Interpretation: A 1% change in interest rates will cause approximately a 7.28% change in bond price
Duration Analysis
Example Calculation
Bond Alpha Example
Face Value: $1,000
Coupon Rate: 5%
Frequency: Annual
Years to Maturity: 10 years
Yield to Maturity: 8%
Yield Differential: 1%
Calculation Steps
1. Current Price: $798.70
2. Price at 7% yield: $859.53
3. Price at 9% yield: $743.29
4. Duration = (859.53 - 743.29) ÷ (2 × 798.70 × 0.01)
Result: 7.277
Duration Types
Effective Duration
For bonds with embedded options
Most accurate for callable/putable bonds
Modified Duration
For straight bonds
Assumes fixed cash flows
Macaulay Duration
Weighted average time to receive cash flows
Time-based measure
Risk Interpretation
Duration < 3
Low interest rate risk, price stability
Duration 3-7
Moderate risk, balanced exposure
Duration 7-12
High risk, significant price volatility
Duration > 12
Very high risk, extreme sensitivity
Understanding Effective Duration
What is Effective Duration?
Effective duration measures the interest rate sensitivity of bonds with embedded options (callable or putable bonds). Unlike modified duration, it accounts for changing cash flows when interest rates change due to option features.
Why Use Effective Duration?
- •Accounts for embedded options in bonds
- •More accurate for complex bond structures
- •Essential for portfolio risk management
- •Helps in immunization strategies
Formula Explanation
ED = (P₋ - P₊) ÷ (2 × P₀ × Δy)
- ED: Effective Duration
- P₋: Bond price when yield decreases
- P₊: Bond price when yield increases
- P₀: Current bond price
- Δy: Yield differential (rate change)
Note: Effective duration provides a linear approximation of the price-yield relationship.
Embedded Options Impact
- ✓Callable Bonds: Duration shortens as rates fall (negative convexity)
- ✓Putable Bonds: Duration shortens as rates rise (positive convexity)
- ✓Straight Bonds: Duration changes predictably with rates
Investment Applications
- •Portfolio duration matching
- •Interest rate hedging strategies
- •Asset-liability management
- •Risk budgeting and allocation