As yields rise, modified duration decreases. A higher modified duration implies that a security is more interest rate sensitive. Conversely, a lower modified duration implies that a security is less sensitive. Modified duration assumes no convexity, but for small changes in yield it’s an effective measure of interest rate sensitivity that can be used to manage interest rate risk.
Calculating the modified duration of a bond or note can be a rather complicated procedure. Assuming that you already know what the modified duration of a bond or note is, you can use it to derive the security’s DV01.
For example, if the modified duration of a Treasury security is 6.23 years, the DV01 of the instrument is:
[ (0.01 x Modified Duration) x Price ] x 0.01 = DV01
[ (0.01 x 6.23) x $108,593.75 ] x 0.01 = $67.65
If you break down the formula, you find three components:
(0.01 x Modified Duration): The slope of the price-yield curve at the current price.
Price: The current price from which the DV01 will be calculated.
0.01: Single basis point move.
By using this formula, we see that the DV01 is based upon its sensitivity (slope), position on the price-yield curve (price), and magnitude of the rate change (one basis point).
A Word of Caution: These calculations are used to monitor small changes in interest rates. Since modified duration assumes no convexity (when in fact there is), the greater the rate change, the greater the error due to this assumption.
Calculating the DV01 of a U.S. Treasury Futures Contract
The price of a Treasury futures contract typically derives from the price of the most economical Treasury security to deliver into the contract. Under most market circumstances, the price of a Treasury futures contract tracks the price of the CTD Treasury security. Since a Treasury futures contract derives its DV01 from the Treasury securities in the contract’s delivery basket, it is important to know what security is being tracked. Once you have identified the CTD security and determined its DV01, you can then calculate the Treasury futures contract’s DV01.
Every cash note or bond that is eligible for delivery has a conversion factor. For any delivery month, each deliverable issue has a specific conversion factor that reflects its coupon and remaining time to maturity as of that delivery month. A conversion factor is the approximate decimal price at which $1 par of a security would trade if it had a 6% yield-to-maturity.