This effective duration calculator is used to compute the sensitivity of a bond’s price to changes in interest rates using Effective Duration = (P- – P+) / (2 * P0 * Δy) formula.
This calculator provides a more accurate measure of duration for bonds with embedded options, such as callable or putable bonds.
A 5-year corporate bond with a 4% coupon rate and a call option after 3 years. An Effective Duration Calculator would account for the possibility of early redemption, providing a more precise estimate of the bond’s price sensitivity compared to traditional duration measures.
Effective Duration Calculator
| Bond Type | Coupon Rate | Maturity | Price | Yield Change | Effective Duration |
|---|---|---|---|---|---|
| Treasury | 2.5% | 10 years | $980 | ±0.5% | 8.92 |
| Corporate | 4% | 5 years | $1020 | ±1% | 4.31 |
| Municipal | 3% | 15 years | $950 | ±0.75% | 11.58 |
| High-Yield | 6% | 7 years | $1,050 | ±1.25% | 5.67 |
| Convertible | 5% | 12 years | $1,100 | ±0.5% | 9.45 |
| Zero-Coupon | 0% | 20 years | $600 | ±1% | 18.34 |
| Callable | 4.5% | 8 years | $1,020 | ±0.75% | 6.22 |
| Putable | 3.8% | 10 years | $980 | ±1% | 7.15 |
| Agency | 3.25% | 15 years | $990 | ±0.5% | 10.01 |
| Foreign | 5.2% | 10 years | $1,050 | ±1% | 8.30 |
What is Effective Duration?
Effective duration is a sophisticated metric that quantifies the percentage change in a bond’s price for a given change in yield. It’s particularly useful for bonds with embedded options, as it considers how these options might impact the bond’s cash flows under different interest rate scenarios.
Effective Duration Formula
The formula for effective duration is:
Effective Duration = (P- - P+) / (2 * P0 * Δy)Where:
- P- = Bond price if yield decreases by Δy
- P+ = Bond price if yield increases by Δy
- P0 = Initial bond price
- Δy = Change in yield (usually 0.01 or 1%)
Let’s say a bond currently priced at $1000 (P0) has a price of $1020 (P-) if yields decrease by 1% and $980 (P+) if yields increase by 1%. The effective duration would be:
Effective Duration = (1020 - 980) / (2 * 1000 * 0.01) = 2This result indicates that for a 1% change in yield, the bond’s price would change by approximately 2%.
How to Calculate Effective Duration?
Calculating effective duration involves the following steps:
- Determine the initial bond price (P0)
- Calculate the bond price if yield decreases by Δy (P-)
- Calculate the bond price if yield increases by Δy (P+)
- Apply the effective duration formula
For a 10-year, 5% coupon bond priced at $1000, assuming a 1% yield change:
P0 = $1000
P- = $1080 (price if yield decreases by 1%)
P+ = $925 (price if yield increases by 1%)
Effective Duration = (1080 – 925) / (2 1000 0.01) = 7.75
What is the effective duration of a loan?
While typically associated with bonds, effective duration can also be applied to loans. For a loan, it represents the sensitivity of the loan’s value to interest rate changes, considering prepayment options.
A 30-year fixed-rate mortgage might have an effective duration of 7 years due to the likelihood of refinancing or selling the property before the full term.
Duration vs. Effective Duration
The key difference between duration and effective duration lies in their treatment of embedded options:
- Duration (Macaulay or Modified) assumes fixed cash flows.
- Effective Duration accounts for potential changes in cash flows due to embedded options.
A 10-year callable bond with a 5% coupon might have a modified duration of 8 years but an effective duration of only 6 years, reflecting the possibility of early redemption if interest rates fall.
Sources / Reference URLs
- CFA Institute – Fixed Income
- Investopedia – Effective Duration
- Federal Reserve Bank of St. Louis – Duration and Convexity
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