How DV01 works

DV01 is the dollar change in price for a one basis point fall in yield:

$$\text{DV01} = \frac{D_{\text{Mod}} \times P}{10{,}000}$$

Modified duration is Macaulay duration divided by $1 + y/k$. On a 5-year 5 percent annual coupon bond at a 5 percent yield, the price is par, $1,000. Each coupon is $50. Macaulay duration is 4.55 years. Modified duration is $4.55 / 1.05 = 4.33$ years. DV01 is $4.33 \times 1000 / 10000 = 0.43$, so $0.43.

How bond duration works owns the wait and the percent slope. This page owns the money. The bond duration calculator on this page prints all three. Macaulay against modified duration is the two times. This page is why a hedge that needs dollars cannot stop at 4.33 years.

Face $1,000, 6 percent coupon, 5 percent yield, 10 years, two payments a year. Each half-year coupon is $30. The bond prices at $1,077.95. Macaulay duration 7.76 years, modified 7.57, DV01 $0.82.

Two things raised DV01 against the first sheet: a longer wait, and a larger price. $7.57 \times 1077.95 / 10000$ is $0.82. A premium coupon bond is more dollars at risk per basis point than a shorter par bond, even before you compare the waits.

Face $1,000, coupon 0, yield 5 percent, 5 years, annual. Price $783.53. Macaulay duration is 5.00 years, equal to maturity. Modified duration is 4.76 years, longer than the par bond's 4.33. DV01 is $0.37, less than the par bond's $0.43.

The slope in years is steeper. The price being shocked is smaller. DV01 multiplies them. Sorting two bonds by modified duration is not the same order as sorting them by DV01. The zero waits longer and moves fewer dollars, because there are fewer dollars to move.

It is not Macaulay duration. 4.55 years is a wait. $0.43 is money. A hedge that needs 'how far the price moves' and is built on 4.55 rather than $0.43 is using the wait as a cash amount.

It is not modified duration either. 4.33 years is a percent sensitivity. Multiply by price and divide by 10,000 before you have dollars.

It is not default risk. Duration and DV01 measure interest-rate sensitivity of a promised cash-flow schedule. A high-yield bond can have a small DV01 and a high chance of default at the same time.

The 10,000 in the denominator is how a basis point is written as a decimal of price. One percent would be modified duration times price over 100, a figure one hundred times $0.43, which is not DV01.

How bond pricing works is the $P$ in the numerator. Raise the yield and that $P$ falls, so DV01 on a later date is a different dollar amount on a different price. This page is one yield, one price, one DV01.

It is not convexity, not a hedge recipe, and not a default screen. The three sheets are a 5-year par bond (DV01 $0.43), a 10-year premium (DV01 $0.82), and a 5-year zero (DV01 $0.37). This is educational material, not financial advice.