Bond Price, Duration and DV01 Calculator

A bond's price and its yield move in opposite directions, and how much the price moves for a change in yield depends on the bond's coupon and maturity. This calculator prices a plain fixed coupon bond from its yield to maturity, then measures its interest rate sensitivity with Macaulay duration, modified duration and DV01, the dollar change in price for a one basis point change in yield. It assumes the bond is valued on a coupon date, so there is no accrued interest.

Calculator#

How it works#

Price = Σ (Coupon / (1 + y)^t) + Face / (1 + y)^n
Macaulay duration = Σ (t × PV of cash flow t) / Price, in years
Modified duration = Macaulay duration / (1 + y)
DV01 = Modified duration × Price × 0.0001

Here y is the yield per period (annual yield divided by coupons per year), t counts periods and n is the total number of periods. See Yield to Maturity and Duration.

Premium, par and discount#

Try changing the yield to 5% in the calculator to see the price move to par.

What drives duration#

Using DV01 in practice#

Traders use DV01 to size and hedge rate positions. A portfolio of bonds with a total DV01 of $5,000 gains or loses about $5,000 for each basis point move in yields. To hedge, sell futures or swaps with an offsetting DV01. See Bond Trading and Yield Curve Trades: Steepeners, Flatteners and Butterflies.

Limitations#

1. No accrued interest: between coupon dates, quoted (clean) prices exclude accrued interest.
2. Plain bonds only: callable bonds, floating rate notes and inflation linked bonds need other models.
3. Flat yield: all cash flows are discounted at one yield rather than a full yield curve. See Yield Curves.
4. Linear approximation: duration understates gains and overstates losses for large moves; convexity corrects this.
5. Credit risk: the yield already includes it; the calculator does not model default. See Credit Spreads.

Trying scenarios#

Change one input at a time to build intuition. Raise the yield from 4% to 6% and watch the price fall below par. Shorten the maturity from 10 years to 2 and watch duration and DV01 shrink. Cut the coupon to zero and see duration equal maturity. These experiments show why long dated, low coupon bonds are the most sensitive to interest rate changes.

Frequently asked questions#

Why do bond prices fall when yields rise?#

Because a bond's fixed cash flows are worth less when discounted at a higher rate, so its price must fall to offer the new market yield.

What is DV01?#

The dollar value of a one basis point change in yield: how much the bond's price changes when its yield moves by 0.01 percentage points.

What does modified duration mean?#

The approximate percentage change in a bond's price for a one percentage point change in yield.

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