help with this question

I think you need to know the convexity and modified duration, but maybe not

it's an interview question. I'm not sure if there is too little information

actually, this question can't be solved without knowing the convexity because;

delta (p) = 0.5 * cv * (change in yield)

Problem: find approx % change in bond price given that bond is a 2 yr zero coupon bond and change in yield is -20 bps

Solution:

let s = change in yield = -20 bps = -0.002

let PV(i) = (1+i)^-2 -> PV'(i) = -2(1+i)^-3 -> PV'(i) / PV(i) = -2(1+i)^-1

[ PV(i+s) - PV(i) ] / s ~= PV'(i) (for small s)

[ PV(i+s) - PV(i) ] / PV(i) ~= sPV'(i)/PV(i) = -2s(1+i)^-1 ~= -2s (for small i)

Thus since s = -0.002, the bond price should go up by 40 bps (approx).

To summarize the above:

Duration = 2, since it's a zero coupon

Modified Duration = 2 / (1+i) ~= 2 for small i

So % change in price ~= +2 * 20bp = 40 bp

To get more technical, you'd have to know what i is - are we talking govt's or junk bonds? And you could factor in convexity, which will be positive since it's (presumably) a vanilla-type bond, i.e. 40 bp is underestimating the actual change. In an interview you may mention any/all of these points, but there's no need to calculate anything beyond saying approx. 40 bp increase in price.

waterlooquant, I am also a waterloo BMath. I did the above for jokes :P

BMath as well or an engineer?