Calculator Inputs
Example Data Table
| Face Value | Coupon Rate | Yield | Maturity | Frequency | Shock |
|---|---|---|---|---|---|
| 1,000 | 6.50% | 5.20% | 8 Years | 2 | 50 bp |
| 5,000 | 4.00% | 4.75% | 12 Years | 2 | 100 bp |
| 10,000 | 3.25% | 2.90% | 5 Years | 4 | 25 bp |
Formula Used
Bond Price: Price = Σ [Cash Flowt / (1 + y / m)t]
Macaulay Duration: D = Σ [t × PV(Cash Flowt)] / Price
Modified Duration: Dmod = D / (1 + y / m)
DV01: DV01 = Modified Duration × Price × 0.0001
Convexity: C = Σ [PV(Cash Flowt) × t × (t + 1)] / [Price × m² × (1 + y / m)²]
Estimated Price Change: ΔP / P ≈ -DmodΔy + 0.5 × C × Δy²
This calculator discounts each coupon and principal payment by the periodic yield. It then weighs each present value by time to estimate duration and convexity. That combination helps you measure first-order and second-order sensitivity to interest-rate changes.
How to Use This Calculator
- Enter the bond face value, annual coupon rate, and current yield to maturity.
- Choose years remaining and the coupon payment frequency.
- Optionally enter a market price if you want risk metrics based on an observed price.
- Set a yield shock in basis points for scenario testing.
- Click Calculate Bond Risk to display results above the form.
- Use the CSV or PDF buttons to export the result summary.
Why Duration Risk Matters
Duration risk shows how sharply a bond price can move when yields change. Higher duration means greater sensitivity, especially for lower-coupon and longer-maturity bonds. Modified duration estimates the linear move, while convexity improves accuracy for larger rate shocks.
Portfolio managers often compare DV01 across holdings because it converts rate sensitivity into a dollar amount. That makes hedging, risk limits, and scenario analysis easier to manage across different bond prices and maturities.
FAQs
1. What does Macaulay duration measure?
Macaulay duration measures the weighted average time needed to receive a bond’s discounted cash flows. It helps show how long your invested capital is effectively tied up.
2. Why is modified duration more useful for risk?
Modified duration directly estimates the percentage price change for a small change in yield. Investors often use it because it links interest-rate movements to bond price sensitivity.
3. What is DV01?
DV01 is the approximate dollar change in a bond’s price for a one-basis-point move in yield. It is useful for comparing rate exposure across positions.
4. Why does convexity matter?
Convexity improves price estimates when yield changes are larger. Duration alone assumes a straight-line relationship, but real bond prices curve as yields move.
5. Should I enter market price or leave it blank?
Leave market price blank to use the model’s theoretical value. Enter a market price when you want risk measures tied to an observed trading price instead.
6. Does payment frequency affect duration?
Yes. More frequent coupon payments return cash earlier, which usually lowers duration and slightly reduces interest-rate sensitivity compared with otherwise similar bonds.
7. Can this calculator handle zero-coupon bonds?
Yes. Set the coupon rate to zero. The model will discount only the final principal payment, which typically produces a duration close to maturity.
8. Is the estimated price change exact?
No. It is an approximation based on duration and convexity. It is generally reliable for moderate yield moves, but actual prices may differ.