# Duration: When to use which formula? : URGENT

there are two formulae of duration. When to use which?

use the one that incorporates the most elements provided in the question…

There are two formuale for modified duration (one starting with Macaulay duration, the other using up price and down price). If they ask for modified duration, they’ll give you enough information for you to be able to use only one of them.

There’s only one formula for effective duration (the same formula as for modified duration with up price and down price), and there’s only one formula for Macaulay duration. Those’ll be easy.

effective and modified duration give the same results for option free bonds so u can use any… they prolly wont give duration,valuation etc of option embedded bonds(i guess they are in level 2)

Could you list those formulae plz??

one of the formula is -D(del y)+ 0.5* C (del y squared)

del = delta.

I’ve also read that in one of the formula you need not use 0.5 So, where to use which?

My mistake: you’re talking about the two formulae for computing the duration/convexity effect.

One is in the reading on credit analysis (the one where you include the ½), and one (without the ½) is everywhere else. Use the ½ only for a question about credit analysis.

It’s stupid that they have a disagreement on these formulae. You just have to make the best of it. (If it’s any consolation, I’d be surprised if they included as a wrong answer choice the one you’d get if you used the wrong formula; that would be cruel.)

what is the formula of macaulay duration?

Multiply the present value of each future cash flow on a bond by the amount of time until you receive that cash flow. Add all of those together and divide the total by today’s price for the bond:

{Σ [PV(CF_i_) × (time to receipt of CF_i_)]} / price