Finance

# Dollar Duration (DV01)

Dollar Duration (DV01)

What is DV01 (Dollar Duration)?

A bond analysis method that helps an investor ascertain the sensitivity of the bond price to interest rate changes is called Dollar Duration(DV01). It is formally referred to as DV01 (i.e., dollar value per 01) It measures the change in bond price for every 100 basis points of change in interest rates. Bond fund managers use DV01 as a way of approximating the portfolio’s interest rate risk in nominal or dollar amount terms. It is used to calculate risk for many fixed income products such as forwards, zero-coupon bonds, par rates, etc.

Explain the formula

The formula for calculating dollar duration is:

Dollar Duration = DUR x (∆ I /1+ I) x P

Where,

Dur= bonds straight duration

∆ I = Change in interest rate

I = current interest rate

P = bond price

The formula for dollar duration if the value of bond and yield are known:

DV01 = – (ΔBV/10000 * Δ y)

Where,

ΔBV = Change in bond value

Δ y = Change in yield

Example of DV01:

1. Sean is holding a US Bond with a yield of 4.05% and is currently priced at \$22.50. The yield on the Bond declines to 4.03%, and the price of the bond increases to \$23.00. Calculate the DV01

DV01 = – (ΔBV/10000 * Δ y)

= – (23-22.5)/10000 * (4.03%-4.05%)

= – (0.5)/ 10000 * (-0.0002)

= – (0.5) / -2

= 0.25

The bond value will change by \$0.25 for every single basis point.

1. Alex holds a US Bond for 4.7 years having an interest rate of 5%. The interest rate declines to 4.5% and the bond are priced at \$25. Calculate the dollar duration.

Dollar Duration = DUR x (∆ I /1+ I) x P

= 5 * (4.5%-4.7%)/ (1+ 4.7%) * 25

= 5 * (-0.0002) / (1+0.047) * 25

= 5 * (-0.0002) / (1.047) * 25

= 5 * (0.00019) * 25

= 0.024

The bond value will change by \$0.024 for every single basis point.

Conclusion

Dollar Duration is used in assessing the relationship between the duration of a financial relationship with the price or value of the investment. Investors can get a better understanding of the yield of given instruments thus determining the worthiness of the security. Calculating this duration from time to time helps the investor to determine if the investment is remaining on track, and the desired return that is obtained once the security reaches maturity is still possible.

Author: Urvi Surti