Bond Duration Calculator

Frequently Asked Questions

What is modified duration?

An estimate of price sensitivity to a 1% change in yield. A duration of 7 means the bond price falls roughly 7% if yields rise 1%, and rises 7% if yields fall 1%. It is the best single risk metric for bonds.

How does duration differ from maturity?

Maturity is when principal is repaid. Duration weights all cash flows by present value, so a 30-year bond with high coupons has a much lower duration than a zero-coupon 30-year bond. Zero-coupons have duration equal to maturity.

What are typical durations for common bond funds?

Short-term Treasury funds: 2-3 years. Intermediate (AGG/BND): about 6 years. Long Treasury (TLT): 16-17 years. The longer the duration, the wilder the swings; TLT lost over 30% in 2022.

What is convexity?

A second-order correction to duration. Bonds gain more when yields fall than they lose when yields rise by an equal amount. Convexity matters most for long-duration and callable bonds; for plain-vanilla bonds duration is a good first approximation.

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Investment Disclaimer: Estimates only. Not investment advice.

This calculator provides estimates for educational purposes only and is not investment advice. Past performance does not guarantee future results. Consult with a qualified financial advisor before making investment decisions. All investments carry risk, including potential loss of principal.

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How This Calculator Works

You enter a bond's face value, annual coupon rate, yield to maturity (YTM), years to maturity, and how many coupons it pays per year. The calculator first discounts every cash flow - each periodic coupon plus the face value returned at maturity - back to today using the per-period yield, summing them to the bond's price. It then computes Macaulay duration, the present-value-weighted average time until you receive each cash flow, and converts that to modified duration, which estimates the percentage price move for a 1% shift in yield. Finally it adds convexity, the second-order term that corrects duration's straight-line approximation, and uses both to project the price change if rates move ±1%. A sensitivity label (low, moderate, or high) flags how exposed the bond is to rate risk.

Formula and Method

Periodic coupon = (Face × CouponRate) ÷ m, where m is payments per year, and the per-period yield y = YTM ÷ m over n = years × m periods. Price = Σ CF_t ÷ (1 + y)^t. Macaulay (in periods) = Σ t×PV(CF_t) ÷ Price, then divided by m to express in years. Modified duration = Macaulay ÷ (1 + y). Convexity = Σ t(t+1)×PV(CF_t) ÷ (Price × (1+y)²), rescaled by m². The estimated price change for a yield move Δy is −ModDur×Δy + ½×Convexity×Δy².

Worked Example

A $1,000 bond with a 5% coupon paid semiannually, 4.5% YTM, and 10 years to maturity pays $25 every six months over 20 periods at a 2.25% per-period yield. Because the coupon exceeds the yield, it trades at a small premium - roughly $1,040. Its Macaulay duration is about 8.0 years and modified duration about 7.8 years, so a 1% rise in rates is estimated to cut the price by roughly 7.8% (slightly less after the convexity correction), while a 1% fall lifts it slightly more - the asymmetry convexity captures.

Common Mistakes

Confusing duration with maturity - a 10-year coupon bond typically has a Macaulay duration of only 7–8 years because coupons return capital early. Only a zero-coupon bond has duration equal to maturity.

Forgetting the payment frequency - semiannual is the U.S. default and changes both price and the per-period yield.

Using duration alone for large rate moves; without convexity it overstates losses when rates rise and understates gains when they fall.

Assuming higher coupons mean higher risk - higher coupons actually lower duration because more cash arrives sooner.

Tips & FAQ

Rules of thumb: longer maturity raises duration, while higher coupons and higher yields lower it. Pension funds and insurers use duration matching to immunize liabilities, and bond-fund fact sheets publish weighted-average duration so you can budget portfolio rate risk. Duration is a first-order estimate around the current yield; for big moves or callable bonds it loses accuracy, and option-adjusted measures become more appropriate. This is educational and ignores taxes, credit risk, and accrued interest - not investment advice.

Frequently Asked Questions

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