# Fixed income inquiry on duration formula

Does the duration formula (V subscript (-)ve minus V subscript (+)ve divided by 2V subscript 0 times delta y) always have to reflect price changes in response to “equal” increases and decreases in YTM? Why is it I cannot find price change due to 50 bp increase and 20 bp decreases?

Because you are doing the “secant approximation to the tangent” thing where you are getting the slope of the secant line and saying the secant is roughly parallel to the tangent. The situation in which yours is closer to parallel is a very unusual curve and you would have to know something more about the curve than you usually would to make such a statement.

I got this from the schewser notes. So do I understand right, this is not a must that basis points increases must equal the decrease in bp? Thanks

How weird do you want to look? Equal will be your best guess unless you have some really good reason to do it differently.

Gottu. Thanks Joey

The thing to remember here is that duration is an estimate or approximation of price sensitivity to a 100bps move in rates. If you want to estimate a 50bps move or 20bps then you simply divide your duration by either 2 or 5 respectively. Im sure there are ways to determine what a price move would be on either side, but for level I i wouldnt worry about that.

or reverse respectively or something…

on another note, this effect is described as double the bps. So when the formula holds 50 bps effect (50 up and 50 down) we describe it as 100 bps or the effect of 1%… right? because I noticed that implicitly in the notes… Thanks