Calculator Inputs
Use the controls below to model several bond positions in one portfolio. The page keeps a single-column structure, while each bond entry uses a responsive 3, 2, and 1 column grid.
Example Data Table
These sample holdings show how different maturities and yields affect weighted portfolio duration.
| Bond Name | Face Value | Coupon Rate | YTM | Years | Payments/Year | Quantity | Market Price |
|---|---|---|---|---|---|---|---|
| Treasury Note 2Y | 1000 | 4.20% | 4.05% | 2 | 2 | 12 | Auto |
| Corporate Bond 5Y | 1000 | 5.60% | 5.85% | 5 | 2 | 8 | Auto |
| Municipal Bond 10Y | 1000 | 4.80% | 4.50% | 10 | 2 | 6 | Auto |
Formula Used
1) Bond Price
Each bond can be priced from its coupon stream and principal repayment using the entered yield and payment frequency.
Price = Σ [Cash Flow at time t / (1 + y / m)^t]
Where y is annual yield to maturity and m is payments per year.
2) Macaulay Duration
Macaulay duration measures the weighted average time required to receive the bond’s discounted cash flows.
Macaulay Duration = Σ [(t / m) × PV(Cash Flow)] / Bond Price
3) Modified Duration
Modified duration estimates price sensitivity for a small yield change.
Modified Duration = Macaulay Duration / (1 + y / m)
4) Portfolio Duration
The portfolio result is a market-value weighted average of individual bond durations.
Portfolio Duration = Σ [Weight of Bond × Bond Duration]
Weight is based on each holding’s market value divided by total portfolio market value.
5) Convexity and Scenario Estimate
The scenario estimate combines modified duration and convexity for a more refined price-change approximation.
ΔP / P ≈ -Modified Duration × Δy + 0.5 × Convexity × (Δy)^2
Here, Δy is the rate shock converted from basis points to decimal form.
How to Use This Calculator
- Enter the interest rate shock in basis points for scenario testing.
- Add one or more bond holdings using the bond input cards.
- Provide face value, coupon, yield, maturity, payment frequency, and quantity.
- Optionally enter a market price if you want market-value weighting based on a known price.
- Click Calculate Portfolio Duration to show results above the form.
- Review the summary cards, holding table, and chart for sensitivity insight.
- Use the CSV or PDF buttons to save your portfolio analysis.
FAQs
1) What does portfolio duration tell me?
Portfolio duration estimates how sensitive your bond portfolio is to interest rate changes. A higher duration usually means larger price movement when yields rise or fall.
2) Why show both Macaulay and modified duration?
Macaulay duration is a weighted time measure. Modified duration turns that time measure into a practical sensitivity estimate for price change from a small yield shift.
3) What happens if I leave market price blank?
The calculator prices the bond from coupon cash flows, yield, maturity, and payment frequency. That auto-price is then used for weighting and result display.
4) What is DV01 in this calculator?
DV01 estimates the dollar value change for a 1 basis point move in yield. It helps compare rate sensitivity across bonds and across full portfolios.
5) Why include convexity?
Convexity improves the rate shock estimate when yield moves are larger. Duration alone is linear, while convexity adds curvature and usually gives a better approximation.
6) Can I analyze different payment frequencies?
Yes. The form supports annual, semiannual, quarterly, and monthly payment schedules. Frequency affects pricing, duration, and convexity because discount timing changes.
7) Is this only for government bonds?
No. You can use it for Treasury, corporate, municipal, and other fixed-coupon bonds, provided the basic cash-flow pattern fits the entered assumptions.
8) Should I rely on duration alone for investment decisions?
No. Duration is useful, but investment decisions should also consider credit risk, liquidity, call features, taxes, reinvestment assumptions, and your overall objectives.