# The modified duration of a bond is the price sensitivity of a bond. It measures the percentage change in price with respect to yield. As such, it gives us a (first order) approximation for the change in price of a bond, as the yield changes. When continuously compounded, the modified duration is equal to the Macaulay duration. To account for the fact that bond prices are negative This was

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Annualized Modification Duration. Annualized Yield to Maturity.

For a small change in yield, ,
Modified Duration to Worst as of Apr 08, 2021 -0.46 3.16. Effective Duration as of Apr 08, 2021 -0.00 yrs 3.63 yrs. Weighted Avg Maturity as of Apr 08,
Modified duration quantifies the sensitivity by specifying the percentage change in bond price for every 100-bps change in the interest rates. Limitations Although highly used and one of the prominent risk measures for fixed income securities, The duration is restricted for wider use because of underlying assumptions of interest rates movement. Modified duration to worst is the approximate percentage change in a bond’s price for a 100 basis points change in yield. A bond’s duration is computed using the bond’s nearest call date or maturity, whichever comes first. concept of ‘modified duration’ was developed, which offered a more precise calculation of the change in bond prices given varying coupon payment schedules.

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3 Macaulay and Modified Duration The definition of Macaulay duration is mac (1 ) (1 ) ( ) . (1 ) kk k tt k k k k k N k N t k kN t a i t a i Di ai Pi ¦¦ ¦ (3 .1 ) The definition of modified duration is 1 mod (1 ) ( ) . ( ) ( ) t k kk kN t a i Pi Di P i P i c (3 ¦.2 ) Macaulay duration is the weighted average of the times of the cash flows The modified duration of a bond is the price sensitivity of a bond.

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In the mid-1980s, as interest rates began to drop, several investment banks developed the concept of ‘option-adjusted duration’ (or ‘effective duration’), The definition of modified duration is 1 mod (1 ) ( ) . ( ) ( ) t k kk kN t a i Pi Di P i P i c (3 ¦.2 ) Macaulay duration is the weighted average of the times of the cash flows, where the weights are the present values of the cash flows. Modified duration is the negative derivative of the present- Macaulay duration, modified duration and effective duration are three types of duration calculations. Investors will more than likely run across effective duration numbers.

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### Macaulay duration, modified duration and effective duration are three types of duration calculations. Investors will more than likely run across effective duration numbers. It is calculated by taking into account how fast a bond’s initial purchase price will be repaid based on its cash flow – this may be a weighted average if looking at a bond portfolio such as in an ETF or mutual fund.

Modified duration is an extension of the Macaulay duration Modified Duration to Worst—Yield change calculated to the priced to worst date; generally used to reflect the behavioral characteristics of a bond as of a specific price/yield and date; consistent with industry calculations, always calculated to the priced to worst date, including all call features. purpose, because neither one reflects the the Modified Duration), jumping from fact that a bond’s cash flows can change 0.94 out to 5.61. Of course, neither in response to a change in interest rates.