# Effective Duration.

Effective duration is a measure of a bond's price sensitivity to changes in interest rates. It is used to estimate the price change of a bond in response to a interest rate change. The higher the effective duration, the more sensitive the bond's price is to changes in interest rates.

The effective duration of a bond can be calculated using the following formula:

D = -∆P / ∆r

where:

D = effective duration
∆P = change in bond price
∆r = change in interest rates

The effective duration of a bond is affected by a number of factors, including the bond's maturity, coupon rate, and yield to maturity.

For example, a bond with a longer maturity will have a higher effective duration than a bond with a shorter maturity. This is because a longer-term bond is more sensitive to changes in interest rates than a shorter-term bond.

A bond with a higher coupon rate will also have a higher effective duration than a bond with a lower coupon rate. This is because a bond with a higher coupon rate will have a greater price sensitivity to changes in interest rates than a bond with a lower coupon rate.

Finally, a bond with a higher yield to maturity will have a higher effective duration than a bond with a lower yield to maturity. This is because a bond with a higher yield to maturity is more sensitive to changes in interest rates than a bond with a lower yield to maturity.

### What does DV01 mean?

DV01 is a financial ratio that measures the sensitivity of a bond's price to changes in interest rates. It is calculated by taking the change in the bond's price divided by the change in interest rates. For example, if a bond has a DV01 of \$100 and interest rates increase by 1%, the bond's price will decline by \$100. How many types of duration are there? There are four types of duration:
-Macaulay duration
-Modified duration
-Effective duration
-Key rate duration

Macaulay duration is the weighted average maturity of a bond's cash flows, where the weights are the present value of the bond's cash flows.
Modified duration is the percentage change in a bond's price for a 1% change in interest rates.
Effective duration is the percentage change in a bond's price for a 1% change in interest rates, assuming that the change in interest rates will not cause a change in the bond's cash flows.
Key rate duration is the percentage change in a bond's price for a 1% change in interest rates at a specific point on the yield curve.

##### What is the difference between duration and maturity finance?

Duration is a measure of a security's price sensitivity to changes in interest rates. It is used by investors to determine how much a change in interest rates will impact the price of the security. Maturity is the length of time until a security's principal is repaid.

#### What is the relationship between duration and yield to maturity?

The relationship between duration and yield to maturity is inversely proportional, meaning that as duration increases, yield to maturity decreases. The reason for this is that when a bond's duration is longer, it is more sensitive to changes in interest rates. Therefore, when interest rates rise, the price of the bond will fall more than a bond with a shorter duration, and vice versa.

### Is effective duration same as modified duration?

No, effective duration is not the same as modified duration. Effective duration is a measure of a bond's price sensitivity to changes in interest rates, taking into account the embedded options in the bond. Modified duration is a measure of a bond's price sensitivity to changes in interest rates, ignoring the embedded options in the bond.