Calculator Inputs
This model assumes a parallel shift in yields and standard fixed-coupon cash flows. It is useful for quick scenario analysis, not full yield-curve attribution.
Example Data Table
| Face Value | Coupon Rate | Current YTM | Shocked YTM | Years | Payments / Year | Quantity |
|---|---|---|---|---|---|---|
| 1,000 | 5.50% | 4.80% | 6.00% | 7 | 2 | 25 |
| 10,000 | 3.75% | 4.10% | 5.35% | 10 | 2 | 8 |
Formula Used
Bond Price: Price = Σ [ Cash Flowt / (1 + y / m)t ]
Macaulay Duration: DMac = Σ [ (t / m) × PV(Cash Flowt) ] / Price
Modified Duration: DMod = DMac / (1 + y / m)
Convexity: C = Σ [ CFt × t × (t + 1) / (1 + y / m)t + 2 ] / [ Price × m² ]
Approximate Price Change: ΔP / P ≈ -DMod × Δy + 0.5 × C × (Δy)²
DV01: DV01 ≈ DMod × Price × 0.0001
Here, y is annual yield, m is coupon frequency, and Δy is the change in annual yield in decimal form.
How to Use This Calculator
- Enter the bond’s face value and annual coupon rate.
- Input the current yield to maturity and the shocked yield scenario.
- Set years to maturity and coupon payments per year.
- Enter the number of bonds held in the portfolio.
- Click the calculate button to see price sensitivity above the form.
- Review exact repricing, duration approximation, convexity, DV01, and portfolio profit or loss.
- Use the graph to visualize how bond price changes across different yields.
- Export the results as CSV or PDF for reporting.
Frequently Asked Questions
1) What does interest rate risk measure?
It measures how much a bond or bond portfolio may gain or lose when market yields change. Longer maturities and lower coupons usually increase sensitivity.
2) Why does bond price fall when yield rises?
A higher yield means future coupon and principal cash flows are discounted more heavily. That lowers the present value, so the bond price drops.
3) What is modified duration?
Modified duration estimates the percentage price change for a small 1.00% change in yield. It is a first-order sensitivity measure used widely in fixed-income risk analysis.
4) What is convexity?
Convexity improves the duration estimate when yield changes are larger. It captures the curve in the price-yield relationship, making the approximation more accurate.
5) What does DV01 mean?
DV01 is the approximate dollar change in bond price for a one-basis-point move in yield. It helps compare rate exposure across different positions quickly.
6) Is the shocked price exact or estimated?
The shocked price is exact within this fixed-cash-flow model because the calculator fully reprices the bond at the shocked yield. The duration-convexity result is an approximation.
7) Can I use this for a portfolio?
Yes, for a portfolio of identical bonds. Enter the quantity held to scale market value, profit and loss, and overall exposure metrics.
8) What are the main limitations?
It assumes a parallel rate shift and fixed coupon cash flows. It does not model credit spread changes, embedded options, or complex curve reshaping.