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Category Finance & Calculations

Face Value ($)

Annual Coupon Rate (%)

Yield to Maturity (%)

Years to Maturity

Coupon Frequency

Period Elapsed (0–1) Fraction of current coupon period elapsed (for accrued interest). 0 = on coupon date.

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About

Mispricing a bond by even 10 basis points on a $10M portfolio translates to a $10,000 error per year of duration. This calculator computes the theoretical clean price P by discounting each coupon cash flow C and the face value F at the yield to maturity y, then derives Macaulay duration D_mac, modified duration D_mod, and convexity CV. It assumes a flat yield curve and reinvestment of coupons at the stated yield. Results diverge from market quotes when credit spreads shift or embedded options exist. For callable or putable bonds, option-adjusted spread models are required instead.

The tool supports annual, semi-annual, quarterly, and monthly coupon frequencies with 30/360 and Actual/Actual day count conventions. Accrued interest is approximated using a linear fraction of the coupon period from the last coupon date to the assumed settlement. Pro tip: compare the calculated clean price against broker quotes to detect potential data-entry errors in yield or coupon rate before executing a trade.

Formulas

The clean price of a fixed-coupon bond is the sum of the present values of all future cash flows discounted at the yield to maturity:

P = n∑t=1 C(1 + r)^t + F(1 + r)ⁿ

This simplifies via the annuity formula to:

P = C × 1 − (1 + r)⁻ⁿr + F(1 + r)ⁿ

Macaulay Duration measures weighted-average time to receipt of cash flows:

D_mac = n∑t=1 t × CF_t(1 + r)^tP

Modified Duration adjusts for compounding:

D_mod = D_mac1 + r

Convexity captures the curvature of the price-yield relationship:

CV = n∑t=1 t(t + 1) × CF_t(1 + r)^t+2P

Where: P = bond clean price, F = face (par) value, C = periodic coupon payment (F × annual coupon rate ÷ frequency), r = periodic yield (annual YTM ÷ frequency), n = total number of coupon periods (years × frequency), t = period index, CF_t = cash flow at period t (coupon C for t < n, coupon + face value for t = n).

Reference Data

Bond Type	Typical Coupon	Frequency	Day Count	Duration Range	Notes
US Treasury Note	2% - 5%	Semi-Annual	Actual/Actual	1 - 9 yr	Benchmark risk-free rate
US Treasury Bond	3% - 6%	Semi-Annual	Actual/Actual	10 - 25 yr	Long-duration exposure
Corporate IG (AAA-BBB)	3% - 7%	Semi-Annual	30/360	2 - 12 yr	Spread over Treasuries
Corporate HY (BB and below)	5% - 12%	Semi-Annual	30/360	2 - 8 yr	Higher default risk premium
German Bund	0% - 3%	Annual	Actual/Actual	5 - 28 yr	Euro-area benchmark
UK Gilt	1% - 5%	Semi-Annual	Actual/Actual	3 - 30 yr	Quoted clean in London
Japanese JGB	0.1% - 2%	Semi-Annual	Actual/365	2 - 35 yr	Ultra-low yield environment
Municipal Bond (US)	2% - 5%	Semi-Annual	30/360	5 - 20 yr	Tax-exempt; compare after-tax yield
Eurobond	1% - 6%	Annual	30/360	3 - 15 yr	Bearer instrument, offshore
Zero-Coupon Bond	0%	N/A	Varies	= Maturity	Duration equals maturity exactly
Floating Rate Note	SOFR + spread	Quarterly	Actual/360	≈ 0.25 yr	Near-zero duration at reset
Inflation-Linked (TIPS)	0.1% - 2%	Semi-Annual	Actual/Actual	3 - 28 yr	Real yield; principal adjusts with CPI
Convertible Bond	1% - 4%	Semi-Annual	30/360	2 - 7 yr	Embedded equity option; OAS needed
Emerging Market Sovereign	4% - 10%	Semi-Annual	30/360	3 - 15 yr	Currency and political risk
Perpetual Bond	4% - 8%	Varies	Varies	≈ 1÷y	No maturity; P = C ÷ y

Frequently Asked Questions

Market quotes are typically clean prices (excluding accrued interest), while the actual settlement amount is the dirty price (clean + accrued). Additionally, this calculator assumes a flat yield curve and no credit spread changes. Market prices embed liquidity premiums, credit risk adjustments, and supply-demand dynamics that a theoretical present-value model cannot capture. For callable bonds, the embedded option value further distorts the comparison.

Higher coupon frequency (e.g., quarterly vs. annual) means cash flows arrive sooner, reducing Macaulay duration. At the same annual yield, a semi-annual bond prices slightly higher than an annual bond because coupons are discounted over shorter intervals. The periodic yield r = annual YTM ÷ frequency, and total periods n = years × frequency. Mismatching frequency in your calculation leads to systematic pricing errors.

As yield r approaches 0, the discount factors approach 1, and duration converges toward the simple weighted-average maturity of cash flows. Convexity increases significantly because the price-yield curve becomes steeper and more curved near zero rates. For zero-coupon bonds, Macaulay duration exactly equals maturity regardless of yield level. Modified duration diverges from Macaulay duration only by the factor 1 ÷ (1 + r), which is negligible near zero.

Accrued interest equals the coupon payment multiplied by the fraction of the coupon period elapsed since the last coupon date. Under the 30/360 convention, each month has 30 days and each year has 360, so accrued = C × (days since last coupon ÷ 360 ÷ frequency). Under Actual/Actual, actual calendar days are used. This calculator uses a simplified elapsed-fraction input (0 to 1) representing how far into the current coupon period the settlement falls. For exact settlement pricing, use the actual settlement and last coupon dates.

Duration provides a linear approximation of price change for small yield shifts. For large moves (e.g., 100 basis points), the linear estimate systematically underestimates the price increase when yields fall and overestimates the price decrease when yields rise. Convexity corrects this by adding the second-order term: ΔP ≈ −D_mod × Δy + 0.5 × CV × (Δy)². Portfolios with higher convexity outperform in volatile rate environments, all else equal.

Yes. Set the coupon rate to 0%. The price reduces to P = F ÷ (1 + r)ⁿ. Macaulay duration equals maturity in years, modified duration equals maturity ÷ (1 + r), and there is no accrued interest. Current yield will display 0% since there are no periodic payments.