Serving the Quantitative Finance Community

 
User avatar
Fadai88
Topic Author
Posts: 2
Joined: February 23rd, 2015, 9:57 am

duration and modified duration

January 6th, 2018, 6:13 pm

By modelling duration and modified duration in Excel, I found that modified duration approximates bond price change well when there is a 1% increase in yield, while duration is a good approximation when there is a 1% decrease in yield. I checked this with about 10-15 couples of coupon rates and YTM, and it seems it works always. Is this true? If yes, what is the reason behind it? 
By duration I mean Macaulay duration; by modified duration I mean duration / (1+yield)
 
User avatar
ppauper
Posts: 11729
Joined: November 15th, 2001, 1:29 pm

Re: duration and modified duration

January 7th, 2018, 10:07 am

convexity.
the formula for modified duration is something like
modified duration = macaulay duration/(1+yield/(number of coupons a year))
so modified duration will be slightly less than macaulay

when you change the yield by an amount [$]\epsilon[$]
change in price = (something negative) x [$]\epsilon[$] + (something positive) x [$]\epsilon^2[$]+[$]\cdots[$]

for increases in yield, the quadratic term has the opposite sign to the linear term
for decreases in yield, the quadratic term has the same sign as the linear term