i What this calculator does
Quick answer: A bond’s yield to maturity is the discount rate that makes its future coupons and redemption equal today’s price; modified duration is the approximate percentage price change for a one percentage point move in yields. With the default inputs the calculator returns yield to maturity: 5.662%.
A fixed-coupon bond pays a known stream of coupons and returns its face value at maturity, so its price and yield are two ways of saying the same thing. Pay less than face value and the yield is higher than the coupon; pay more and it is lower. This calculator solves either way: enter the market price to find the yield to maturity, or a yield to find the price. It then measures interest rate risk with Macaulay duration, modified duration, convexity and DV01, the change in value for a one basis point move, and shows the exact price change for rate shocks from minus to plus 200 basis points.
It works for government, corporate and inflation-unlinked bonds anywhere, quoted per 100 of face value. The way bonds trade on exchanges and as CFDs is covered in how bond CFDs work.
This calculator is for educational purposes only. Results are estimates and may vary depending on market conditions, spreads, commissions, platform settings, and exchange rates. It should not be considered financial advice.
Common results
What the calculator returns as the market price per 100 changes, with every other input at its default (face value held 1000, coupon rate 5, years to maturity 10, coupons a year Semi-annual (2), solve for Yield, from a price, yield 5.5, years to first call 0, call price 100).
| Market price per 100 | Yield to maturity | Modified duration | Value of one basis point |
|---|---|---|---|
| 90 | 6.367% | 7.617 | 0.6855 |
| 95 | 5.662% | 7.709 | 0.7324 |
| 98 | 5.260% | 7.761 | 0.7606 |
| 100 | 5.000% | 7.795 | 0.7795 |
| 102 | 4.746% | 7.827 | 0.7984 |
| 105 | 4.377% | 7.874 | 0.8268 |
Duration: the number that measures rate risk
Macaulay duration is the weighted average time until you receive the bond’s cash flows, in years. Modified duration converts it into price sensitivity: a modified duration of 7.7 means a 1 percentage point rise in yields cuts the price by about 7.7%. Longer maturities and lower coupons mean higher duration, which is why long-dated and zero-coupon bonds swing the most when central banks move rates. DV01 puts the same idea in money: the change in your holding for a 0.01% move.
Convexity: why the estimate is not exact
The price-yield relationship is curved, not straight. Duration alone overstates the fall when yields rise and understates the gain when they fall; convexity corrects for the curve. The table compares the exact repriced value with the duration-plus-convexity estimate so you can see how close the approximation is for small and large moves. Positive convexity is a benefit to the holder: gains from falling yields are larger than losses from rising yields of the same size.
Yield to call and what yield does not tell you
A callable bond can be redeemed early by the issuer, usually when rates have fallen, so the yield to call is often the more realistic figure for bonds trading above the call price. Yield to maturity also assumes coupons are reinvested at the same yield and the bond is held to maturity without default. Credit risk, liquidity and taxes all sit outside the calculation; the link between bond yields and currencies is one example of what moves yields in practice.
Spotted an outdated figure? If a rate, limit or formula in this calculator no longer matches its source, email us the page and the source. A material correction is dated on the Updates Log.
Frequently asked questions
What is yield to maturity?
The annual return you earn if you buy the bond at today’s price, hold it to maturity, receive every coupon and the face value, and reinvest coupons at the same yield.
Why do bond prices fall when yields rise?
Because the coupons are fixed. When new bonds offer higher yields, an existing bond is only worth buying at a lower price that lifts its yield to match.
What is the difference between Macaulay and modified duration?
Macaulay duration is a weighted average time to the cash flows, in years. Modified duration divides it by one plus the yield per period and measures the percentage price change for a change in yield.
What is a good duration?
It depends on your view of rates. Short duration, under three, limits the damage from rising yields; long duration, over ten, gains most when yields fall.
What is DV01?
The change in a bond’s value for a one basis point (0.01%) change in yield. Traders use it to compare and hedge interest rate risk across bonds.
What is current yield?
The annual coupon divided by the price. It ignores the gain or loss as the price moves to face value at maturity, which yield to maturity includes.
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