[讨论]Duration and Modified duration

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are those to see the influence of yeild to change of bond pirce? what's the difference between the two.

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关键词：Duration Modified ration ratio ATION 讨论 Duration Duration Modified

Modified duration influnces bond price

change of price = Modified duration* change of r

Modified duration = duration/(1+r)

You can actually get the answer from any of the fixed income securities book. It's actually quite difficult to explain them in details, but i will try my best XD

Duration or more commonly known as the Macaulay Duration is usually used by investors as an indicator on the "Investment Pay Back Period" of a bond. Bonds that pay higher coupon will have a shorter duration while Zero-coupon bonds' duration is equals to their term to maturity.

And it's because of this reason, higher coupon bearing bonds are less sensitive to change in interest rate fluctuations as compared to zero coupon bonds.

The Macaulay duration is calculated by A/B, where,

A= sum of all (a) present value of each periodic cash, multiply by (b) time/period; and

B= the price of the security

The Modified duration is an extension of the Macaulay Duration, where it measures the sensitivity of the bond prices to changes in the market yield.

The formula for Modified Duration is = Macaulay Duration /(1+ Y/N), where

Y= market yield of yield to maturity of the bond

N= coupon payment frequency, for semi-annual coupon paying bonds, N=2

The theory of bond pricing does not stop here, you might want to have a look at the concept of "Convexity" in bond pricing, as the Modified duration represents the first derivative which is linear while the "Convexity" represents the second derivatives and helps us to measure more accurately the sensitivity of bonds in response to change of interest rate especially when the change is not a small one.

Cheers

[此贴子已经被作者于2008-5-27 20:00:18编辑过]

turandot 发表于 2008-5-27 19:58
You can actually get the answer from any of the fixed income securities book. It's actually quite difficult to explain them in details, but i will try my best XDDuration or more commonly known as the Macaulay Duration is usually used by investors as an indicator on the "Investment Pay Back Period" of a bond. Bonds that pay higher coupon will have a shorter duration while Zero-coupon bonds' duration is equals to their term to maturity.And it's because of this reason, higher coupon bearing bonds are less sensitive to change in interest rate fluctuations as compared to zero coupon bonds.The Macaulay duration is calculated by A/B, where,A= sum of all (a) present value of each periodic cash, multiply by (b) time/period; andB= the price of the securityThe Modified duration is an extension of the Macaulay Duration, where it measures the sensitivity of the bond prices to changes in the market yield.The formula for Modified Duration is = Macaulay Duration /(1+ Y/N), whereY= market yield of yield to maturity of the bondN= coupon payment frequency, for semi-annual coupon paying bonds, N=2The theory of bond pricing does not stop here, you might want to have a look at the concept of "Convexity" in bond pricing, as the Modified duration represents the first derivative which is linear while the "Convexity" represents the second derivatives and helps us to measure more accurately the sensitivity of bonds in response to change of interest rate especially when the change is not a small one.Cheers

[此贴子已经被作者于2008-5-27 20:00:18编辑过]

thanks for this explain. can u give us an example how to caculate the both?

I WAS DOUBT WHETHER IS THERE ANY  MATHMETIC TOOLS TO CACULATE  THESE QUESTIONS?

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