Modified duration

[jsshuai158]

this may sound like a stupid question. but can someone please explain in simple common sense terms what modified duration means? i know that mathematically, it is maucauly duration divided by (1+YTM). but why discount the Mauculay duration by 1+YTM? what is the practical use of this measure?
thanks.

 

[ABAL]

I shall attempt to explain inutitively and hope that may make sense:
A small edit Mod Dur= Mac. dur/(1+ PERIODIC Yield)
The Yield-Price curve is essentially a comvex one and the Duration is the LINEAR approximation of unit change in price to unit change in yield. Hence, it is also the tangent to the Bond Price-Yield curve at any given point.
Now, Mac. Considered a YTM which is a single disc. Rate assuming the investor holds onto the sec. Till maturity and the sec. Is option free. It is a fine measure.
However the yield changes every time and so does the price of the sec. Try visualing the P-Y curve with constant change in curvature , this would necessisate to find the Dur. At each such point change which could be infinitesemally small, the yield thus changes and thus now be called PERIODIC yield.
Think the periodic yield as spot rate. To find Duration at every point as that would be theoritically appropriate the eqn. is Mod Dur= Mac. dur/(1+ PERIODIC yield).
Hope this suffice.

 

[S2000magician]

ABAL wrote:… the Duration is the LINEAR approximation of unit change in price to unit change in yield. Hence, it is also the tangent to the Bond Price-Yield curve at any given point.

This is a common mistake that finance people and finance texts make.
Duration is not an approximation to the unit change in the bond’s price; it’s an approximation to the percentage change in the bond’s price. So it’s not tangent to the price/yield curve.
(It’s actually tangent to the ln(price)/yield curve, but let’s not go there.)

 

[ABAL]

Agree…Magician, my bad. Duration is an approximation to % change. I should have incorporated the same in my explanation.
Thanks Magician.

 

[ink]

I found Magician’s explanation from lvl 1 a very good refresher for different types of duration, so I highly, highly recommend reading it: http://financialexamhelp123.com/macaulay-duration-modified-duration-and-...

 

[S2000magician]

ABAL wrote:Agree…Magician, my bad. Duration is an approximation to % change. I should have incorporated the same in my explanation.
Thanks Magician.

My pleasure.