How this number is made
This is a bond that pays the coupon once a year and the face value at the end. Macaulay duration is the weighted average time until those cash flows, in years. Modified duration turns that into a percent price change for a one-point move in yield. DV01 is the dollar change for a one-basis-point move, using modified duration, so it is a small-move estimate. Convexity is why a large move is not exactly that line. Semi-annual coupons, a call, and a spread over a curve are not in the price.
- A par bond has a coupon equal to the yield. The price should be the face value.
- Years are whole coupons. Ten and a half years is treated as ten or eleven, whichever you round to by typing the whole number.
Formula
Price discounts each coupon and the face. Macaulay = Σ t × present value ÷ price. Modified = Macaulay ÷ (1 + yield). DV01 = modified duration × price × 0.0001.
Worked example
With the figures already in the form, modified duration, years is 7.72.
Questions
Why is duration shorter than maturity?
Because some of the cash arrives as coupons before maturity. A zero-coupon bond’s duration is its maturity. This page always has a coupon if you type one.
Will the price really move by the DV01?
For one basis point, close. For a large yield move, convexity adds a difference this linear estimate misses. The convexity row is there so you can see the size of that term.