Mod duration formula

[ziminli1228]

In the example of Mapping a two-bond portfolio, the spreadsheet used (1-(1+YTM)^-Maturity)*1/YTM, I might've seen this formula in p1 but cannot remember, is this an alternative of calculating mod duration?

 

[David Harper CFA FRM]

Hi @ziminli1228 Right, it is a convenient formula for modified duration but only for the special case of a bond that is priced at par. See below, Tuckman's 4.45; the "c=y" subscript indicates coupon rate equal to yield and, therefore, a bond that is priced at par. Tuckman's formula, as with his entire text, presumes semi-annual compound frequency. My XLS mimcs Jorion, who is always assuming annual compound frequency, so my version is the annual-equivalent version of 4.45 below, where the only difference is that 1/[(1+y/2)^(2T)] is replaced with 1/(1+y)^T) = (1+y)^-T, just as it would be in pricing. Thanks!