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%.). 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.
- 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. 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 price, 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:
- 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..
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
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. 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.
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. 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 Name||Price||Par Amount held (in million of USD)||Modified Duration|
The calculation is as follows:
- 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.
The following are some advantages of dollar duration.
- DV01 enables banks and other financial institutions to quickly assess the impact of change in yields on their portfolio in dollar terms. Thus they can be well prepared with different scenarios on the impact of yield movements on the Market Value of their Portfolio.
- It is relatively simple to calculate and easy to understand.
- DV01 is additive in nature, which means that one can calculate the same for each bond in the portfolio and aggregate them to derive the portfolio DV01.
- DV01 enables Bond Dealers and Portfolio managerPortfolio ManagerA Portfolio Manager is an executive responsible for making investment decisions & handle investment portfolios for fulfilling the client’s investment-related objectives. Also, he/she works towards maximizing the benefits & minimizing the potential risks for clients. to hedge their portfolio against adverse yield movements. By computing the DV01 separately for each Bond, Banks, and Financial Institutions can actually hedge their long positionLong PositionLong position denotes buying of a stock, currency or commodity in the hope that the future price will get higher from the present price. The security can be bought in the cash market or in the derivative market. The course of action suggests that the investor or the trader is expecting an upward movement of the stock from is prevailing levels. against a short position in a different bond with almost the same DV01.
Let us discuss some disadvantages of dollar duration.
- The biggest shortcoming of DV01 lies in its assumption of a parallel shift in the yield curveYield CurveThe Yield Curve Slope is used to estimate the interest rates and changes in economic activities. It is a plot of bond yields of a particular issuer on the vertical axis (Y-axis) against various tenors/maturities on the horizontal axis (X-axis)., which is more theoretical in nature than in the real world. The yield curve never shifts parallel. The impact of yield movement varies based on maturity and usually short maturity. Fixed Instruments yield change faster than long-maturity Fixed Instruments. By assuming a parallel shift, the impact suggested by DV01 on the value of Bond varies from the actual impact on the price of the Bond.
- Hedging undertaken using standard DV01-neutral hedge fails to provide a perfect hedge due to the imperfect one to one relationship caused by rising and fall of basis points across different instruments used for hedging.
- DV01 simple calculation assumes that Bonds pay fixed coupon payments at regular intervals; however, there are certain categories of Bonds such as Floating Rate Bonds, Zero Coupon BondsZero Coupon BondsIn contrast to a typical coupon-bearing bond, a zero-coupon bond (also known as a Pure Discount Bond or Accrual Bond) is a bond that is issued at a discount to its par value and does not pay periodic interest. In other words, the annual implied interest payment is included into the face value of the bond, which is paid at maturity. As a result, this bond has only one return: the payment of the nominal value at maturity., and Callable BondsCallable BondsA callable bond is a fixed-rate bond in which the issuing company has the right to repay the face value of the security at a pre-agreed-upon value prior to the bond's maturity. This right is exercised when the market interest rate falls. which requires the complex calculation to derive DV01.
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. 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 –