DV01 (Dollar Duration)

What is DV01 (Dollar Duration)?

DV01 or Dollar Value of 1 basis point, measures the interest rate risk of bond or portfolio of bonds by estimating the price change in dollar terms in response to change in yield by a single basis point ( One percent comprise of 100 basis pointsBasis PointsBasis points or BPS is the smallest unit of bonds, notes and other financial instruments. BPS determines the slightest change in interest rate, to be precise. One basis point equals 1/100th part of 1%.read more). DV01 is also known as Dollar Duration of a Bond and is the foundation of all Fixed Income instruments risk analysis and is used in abundance by Risk Managers and Bond Dealers.

Formula of DV01

The calculation of the Dollar Value of one basis point, aka DV01 is very simple, and there are multiple ways to calculate it. One of the most common formulas used to calculate DV01 is as follows:

DV01 Formula = – (ΔBV/10000 * Δy)
DV01

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For eg:
Source: DV01 (Dollar Duration) (wallstreetmojo.com)

Where,

  • ΔBV = change in Bond value
  • Δy = change in yield

Hereby Bond Value means the Market Value of the Bond, and Yield means Yield to MaturityYield Means Yield To MaturityYield to Maturity refers to the expected returns an investor anticipates after keeping the bond intact till the maturity date. In other words, a bond's expected returns after making all the payments on time throughout the life of a bond.read more.

It is important to note here that we are dividing by 10000 because DV01 is based on linear approximation but is one basis point, which is 0.01%. So by dividing it by 10000, we are rescaling from 100% to 0.01%, which is equivalent to one basis point.

Examples of DV01 / Dollar duration

Let’s understand the same with the help of a simple numerical example

You can download this DV01 Excel Template here – DV01 Excel Template

Example #1

Ryan is holding a US Bond with a yield of 5.05% and is currently priced at $23.50. The yield on the Bond declines to 5.03%, and the price of the BondPrice Of The BondThe bond pricing formula calculates the present value of the probable future cash flows, which include coupon payments and the par value, which is the redemption amount at maturity. The yield to maturity (YTM) refers to the rate of interest used to discount future cash flows.read more increases to $24.00. Based on the information, let’s calculate DV01 using the formula stated above:

Dv01 Example 1-1

The calculation of DV01 is as follows:

  • DV01 formula = – ($24.00-$23.50)/10,000 * (-0.0002)
  • = $0.25

Thus the value of the Bond will change by $0.25 for every single basis point change in the yield of the Bond.

Example #2

Let’s understand the same with the help of a more complex practical example:

ABC Bank has the following portfolio of Bonds in its Trading BookTrading BookTrading book is the type of book maintained by the bank, financial institution or a stockbroker banks for recording the transactions of the clients who have given them an opportunity to act as the broker or middle person for dealing in securities. read more and intends to quickly understand the impact on its Market value due to change in Interest Rates. The Par Value of each Bond is $100. Based on the details furnished below to let’s try to calculate the value of the Portfolio’s DV01 and understand the resultant impact:

Bond NamePricePar Amount held (in million of USD)Modified Duration
A101.4332.36
B84.8954.13
C121.8786.27

The calculation is as follows:

Example 2-1
  • Dollar Value of One Basis Point = Dollar Duration * $1000000*0.0001
  • = $85.84* $1000000*0.0001
  • = $8,584

Thus it implies that for each single basis movement in yield, the portfolio will get impacted by $8584.

Advantages

The following are some advantages of dollar duration.

Disadvantages

Let us discuss some disadvantages of dollar duration.

Conclusion

The Dollar Value of a Basis Point (DV01) is the dollar exposure of a Bond Price for a change in yield of a single basis point. It is also the duration times the market value of the Bond and is additive across the entire portfolio and is an important tool used by Portfolio managers and Bond Dealers to measure the linear relationship between Bond Prices and Bond yield impact.

It enables them to understand and assess the riskiness of a bond to the changes in yield rates and the likely impact on the Bond Price. An important point worth noting about DV01 is that it is almost the same as DurationDurationDuration is a risk measure used by market participants to measure the interest rate sensitivity of a debt instrument, e.g. a Bond. It tells how sensitive is a bond with respect to the change in interest rates. This measure can be used for comparing the sensitivities of bonds with different maturities. There are three different ways to arrive duration measures, viz. Macaulay Duration, Modified Duration, and Effective Duration.read more except that the units are changed and includes a Price Inflection. Stated otherwise, one can easily calculate DV01 if one has already calculated the Modified Duration by just simple multiplying the same with the Price of Bond and dividing the result by 10000 (DV01 = duration * Price/10,000).

Recommended Articles

This has been a guide to DV01 (Duration Duration). Here we discuss the formula to calculate Dollar Duration along with examples, advantages, and disadvantages. You can learn more about Fixed Income from the following articles –

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