What is DV01 (Dollar Duration)?

  • In other words, where Duration is basically the ratio of the percentage change in the price of a security to a change in yield in percent, DV01 helps to interpret the same in Dollar terms, thereby enabling relevant stakeholders to understand the price impact of change in yields.For instance, suppose a Bond has a Modified Duration of 5 and the Market Value of the Bond as on date is $1.0 million, the DV01 is calculated as Modified DurationCalculated As Modified DurationModified Duration tells the investor how much the price of the bond will change given the change in its yield. To calculate it, the investor needs to calculate Macauley duration which is based on the timing of the cash flow.read more multiplied by Market Value of the Bond multiplied by 0.0001 i.e., 5 * $1 million* 0.0001= $500. Thus the bond will change by $500 for a one-point change in basis point in yield.Dollar Duration or DV01 can also be calculated if one is aware of the Bonds Duration, current yieldCurrent YieldThe current yield formula essentially calculates the yield on a bond based on the market price instead of face value. The current yield of bond= Annual coupon payment/current market priceread more, and change in yield.

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:

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Where,

  • ΔBV = change in Bond valueΔy = change in yield

Hereby Bond Value means the Market Value of the Bond, and Yield means Yield to MaturityYield Means Yield To MaturityThe yield 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 returns are scheduled after making all the payments on time throughout the life of a bond. Unlike current yield, which measures the present value of the bond, the yield to maturity measures the value of the bond at the end of the term 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

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:

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:

The calculation is as follows:

  • Dollar Value of One Basis Point = Dollar Duration * $10000000.0001= $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 relationshipLinear RelationshipA linear relationship describes the relation between two distinct variables - x and y - in the form of a straight line on a graph. When presenting a linear relationship through an equation, the value of y is derived through the value of x, reflecting their correlation.read more 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).

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 –

  • Macaulay Duration FormulaWhat is the Formula of Convexity?Calculate Macaulay DurationCalculate Convexity of a Bond