Calculator Input
Enter your bond terms and compare the original market yield with a new yield scenario.
Example Data Table
These sample scenarios show how bond prices respond when market yields change.
| Face Value | Coupon Rate | Years | Frequency | Original Yield | New Yield | Initial Price | New Price | % Change |
|---|---|---|---|---|---|---|---|---|
| 1,000 | 5.00% | 10.00 | Semiannual | 4.00% | 4.75% | 1,081.7572 | 1,019.7185 | -5.7350% |
| 1,000 | 3.50% | 7.00 | Semiannual | 5.20% | 4.60% | 901.3121 | 934.8002 | 3.7155% |
| 1,000 | 6.00% | 15.00 | Annual | 5.00% | 6.25% | 1,103.7966 | 976.1111 | -11.5678% |
Formula Used
Exact bond price:
Price = Σ [Cash Flowt / (1 + y / m)t]
Percentage change in price:
Percentage Change = ((New Price − Initial Price) / Initial Price) × 100
Duration estimate:
%ΔP ≈ −Modified Duration × ΔYield
Duration plus convexity estimate:
%ΔP ≈ −Modified Duration × ΔYield + 0.5 × Convexity × (ΔYield)2
This calculator computes exact repricing from discounted cash flows, then compares that result with duration and convexity estimates for better risk analysis.
How to Use This Calculator
- Enter the bond face value.
- Type the annual coupon rate.
- Enter years remaining to maturity.
- Select how many coupon payments occur yearly.
- Enter the original market yield.
- Enter the new market yield scenario.
- Add the number of bonds you hold.
- Click the calculate button.
- Review exact repricing, estimated sensitivity, and chart output.
- Download the results as CSV or PDF if needed.
FAQs
1. What does percentage change in bond price mean?
It shows how much a bond’s market price moves after yield changes. The calculator compares the original bond price with the repriced bond value and expresses the difference as a percentage. Positive values mean price gains. Negative values mean price declines.
2. Why do bond prices usually fall when yields rise?
Existing coupon payments become less attractive when new bonds offer higher yields. Investors then pay less for older bonds to match current market returns. That inverse relationship drives most bond pricing behavior and explains why yield changes matter.
3. What is the difference between exact pricing and duration estimates?
Exact pricing discounts every cash flow at the chosen yield. Duration estimates summarize sensitivity with one measure. Duration works well for small yield moves, while convexity improves the estimate when changes become larger or bonds are longer dated.
4. What does convexity add to the analysis?
Convexity captures the curve in the price-yield relationship. Bonds do not move in a perfectly straight line when yields change. Adding convexity improves the estimate and usually reduces error for larger rate shifts or long-maturity bonds.
5. Can this calculator handle zero-coupon bonds?
Yes. Set the coupon rate to zero. The calculator will then value the bond only from the discounted face value at maturity. Duration and convexity still work, and the price change result will reflect pure discounting effects.
6. Does payment frequency matter?
Yes. Payment frequency changes cash flow timing and discounting periods. Semiannual, quarterly, and monthly coupon structures can produce different prices, durations, and convexity values even when face value, coupon rate, and yield stay similar.
7. Is the total value change useful for portfolios?
Yes. Per-bond price changes help with security analysis, but total value change shows how the yield move affects your full position. That makes it helpful for portfolio monitoring, scenario testing, and practical investment decisions.
8. Can I use this for interest rate scenario planning?
Yes. Enter different new yield values to test potential market outcomes. You can compare exact repricing, duration-only estimates, and duration-plus-convexity estimates to understand how sensitive a bond or position may be under changing rates.