# How to Calculate DV01

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DV01, also known as basis point value, is a measurement of how bond prices will respond to changes in prevailing interest rates. Use the DV01 formula to estimate this quantity for a particular bond, which can be helpful in determining how much risk there is to the value of the bond based on shifts in interest rates. Keep in mind that it's often more accurate to estimate DV01 for a portfolio of bonds rather than one particular bond.

## Understanding the Bond Market

A bond is a type of security that can be bought and sold, similar in that way to stock. Unlike stock, which represents an ownership share in the issuing company, bonds represent a loan to a company, government agency or other entity that issued the bond. Typically, they pay interest over time according to a set schedule, ultimately paying back principal and interest to bondholders, but exactly what this schedule looks like varies significantly from bond to bond. Organizations often issue bonds for the same reason individuals often take out loans – to acquire money for some purpose, such as building a new facility, and pay it back over time.

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It's possible to buy bonds when they are issued and hold on to them until they are finished paying out, but since there is a secondary market for bonds, they are also often bought and sold between investors. Bond prices vary over time based on a variety of factors, including the overall health and credit score of the organization that issued them and prevailing interest rates. If an organization's credit rating decreases, meaning that it is thought to be more likely to fail to pay back its debt, its bonds will become cheap compared to others paying similar interest.

A bond's effective interest rate based on its current price is known as its yield. The bond's interest rate relative to its face value at issue is known as its coupon rate.

## Bond Prices and Interest Rates

Interest rates paid for new debt change over time due to a variety of factors, including economic conditions and actions taken by central banks like the Federal Reserve and the European Central Bank.

In general, when interest rates go down, bond prices go up. Conversely, when interest rates generally go up, bond prices go down. That's because investors will be drawn to bonds paying a good rate of interest when it's harder to get the same interest rate lending money elsewhere, and when there are good interest rates available through other investments, including bank products, those bonds become less attractive due to the competition.

## Understanding DV01 for Bonds

For investors making decisions about where to put their money, the rule of thumb that bonds generally become more valuable as interest rates go down isn't precise enough. They want to estimate how particular bonds they are considering investing in, or a particular set of bonds, will do under various possible interest rate conditions.

One measure of this is known as DV01, or basis point value. DV01 is a measure of how much in dollars a bond price will change given a one basis point change in interest rates. A basis point is one one-hundredth of a percent, 0r 0.0001, so an increase from 2 percent to 2.25 percent is a 25 basis point increase, and a decrease in interest rates from 2 percent to 1.6 percent is a 40 basis point decrease. A one percentage point change is, by definition, a 100 basis point change.

If a bond has a DV01 of 5, for instance, it means that a one basis point rise in rates will cause the price of the bond to fall \$5, while a one basis point decline will cause it to rise \$5. It's assumed that DV01 represents an increase when rates decrease and vice versa, since that's how bond values typically move in response to interest rate changes, so the effect on price is equal to -1 times DV01 times the interest rate change in basis points.

## Understanding DV01 Versus Duration

A related concept to DV01 is duration. This is typically used to mean the percentage change in a bond price for a 100 basis point, or 1 percentage point, change in interest rates.

So, for a bond with a DV01 of \$5, which would then see an approximate \$500 change in value for a 100 basis point shift in prices, the duration would be \$500 divided by the bond's price multiplied by 100 to convert to a percentage. If a bond was initially priced at \$250 and its price increased to \$500, the duration would be (\$500 - \$250) / \$250 = 1, or 100 percent.

The term dollar duration is sometimes used to refer to DV01 and sometimes used to refer to the change in dollar price per 100 basis points. Make sure you understand how these terms are being used in materials that you read.

## Calculating DV01 Formula for Bonds

To calculate DV01 for a bond, you will want to look at a short period where the bond's yield or another interest rate you want to compare the bond's price to changed, ideally by a relatively small amount.

Take the interest rate's change in basis points, meaning hundredths of a percentage point. For example, a change in interest rates from 2.05 percent to 2.07 percent would be a two basis point increase. Then, take the change in the bond's market price in dollars over that same period. For example, the bond's price may have changed from \$200 to \$210. Divide the price difference by the interest rate difference to get the DV01 value, such as (210 - 200) / (207 - 205) = 10 / 2 = 5.

Bonds with higher DV01 are more sensitive in dollar terms to shifts in interest rates. Note that bonds' sensitivity to interest rates may evolve over time so you will want to use a recently computed DV01 when possible rather than an older value when assessing or comparing investments.

## Limitations of DV01

Remember that as with many other calculations involving finance, DV01 is essentially an estimate, and you can't guarantee that a bond price will move in a precise way at a precise time, even if you can predict shifts in interest rates. Other factors, like corporate or government agency conditions, could have a bigger effect on a bond price than the change in interest rates. Exactly how the bond pays out interest, which can vary significantly from bond to bond, can also have a large effect.