The Duration Coefficient Calculator shows how much a bond’s price changes when interest rates move. It measures a bond’s sensitivity to rate changes, helping you predict price drops or gains. The result, called the duration coefficient, tells you the percentage price change for a 1% rate shift. A higher number means bigger price swings.
This calculator helps with real-life decisions, like picking safe bonds, managing investments, or planning for rate changes. It’s reliable for important financial choices, like protecting your money. Want to know how it’s calculated? Let’s check out the formula next.
Formula for Duration Coefficient
The formula comes in three steps:
Step 1: Macaulay Duration
Macaulay Duration = Σ(t × PV(CFt)) / Price
Step 2: Modified Duration
Modified Duration = Macaulay Duration / (1 + y/m)
Step 3: Duration Coefficient
Duration Coefficient = -1 × Modified Duration
Where:
- Macaulay Duration = Average time to get cash flows (years)
- t = Time when each cash flow happens (years)
- PV(CFt) = Present value of cash flow at time t
- Price = Current bond price
- y = Yield to maturity (as a decimal, e.g., 5% = 0.05)
- m = Number of payments per year (e.g., 2 for semi-annual)
This formula comes from bond math. The negative sign shows prices drop when rates rise. Now, let’s make it easier with a table.
Quick Reference Table for Duration Coefficients
Why calculate every time? This table shows typical duration coefficients for common bonds. It’s a fast way to check without math.
| Bond Type | Years to Maturity | Coupon Rate | Yield | Duration Coefficient |
|---|---|---|---|---|
| 5-Year Treasury | 5 | 3% | 3% | -4.8 |
| 10-Year Corporate | 10 | 4% | 5% | -8.5 |
| 2-Year Zero-Coupon | 2 | 0% | 2% | -2.0 |
How to Use the Table
- Pick your bond type and terms.
- Check the duration coefficient.
- Use it to estimate price changes.
This table helps with searches like “duration for 10-year bond.” For exact results, use the formula. Next, let’s try an example.
Example of Duration Coefficient Calculator
Suppose you have a bond with:
- Price = $1,000
- Yield = 4% (0.04)
- Semi-annual payments (m = 2)
- Cash flows: $20 every 6 months for 2 years, plus $1,000 at the end
You want the duration coefficient. Here’s how to do it:
- Calculate Macaulay Duration:
- t1 = 0.5 yr, PV(CF1) = 20 / (1 + 0.04/2)¹ ≈ 19.61
- t2 = 1 yr, PV(CF2) = 20 / (1 + 0.02)² ≈ 19.23
- t3 = 1.5 yr, PV(CF3) = 20 / (1 + 0.02)³ ≈ 18.85
- t4 = 2 yr, PV(CF4) = 1,020 / (1 + 0.02)⁴ ≈ 942.32
- Σ(t × PV(CFt)) = (0.5 × 19.61) + (1 × 19.23) + (1.5 × 18.85) + (2 × 942.32) ≈ 1,943.07
- Macaulay Duration = 1,943.07 / 1,000 ≈ 1.94 years
- Calculate Modified Duration:
Modified Duration = 1.94 / (1 + 0.04/2) = 1.94 / 1.02 ≈ 1.90 - Find Duration Coefficient:
Duration Coefficient = -1 × 1.90 = -1.90
So, the duration coefficient is -1.90. If rates rise 1%, the price drops about 1.9%.
Most Common FAQs
It shows bond prices fall when rates go up—a key rule in bond investing.
Lower numbers (like -2 to -5) mean less risk—higher numbers mean bigger price swings.
Yes, as long as you have the cash flows, price, and yield, it works for any bond.