# 2012 AM Exam - Q8 A ii

For the bond calculation, I get the same answer (63 bond futures) as CFAI but went about it differently than CFAI. Would I get full credit?

My process:

1. [(6.0 - 0.0) / 7.7] x (28mm / 103,000) x 1.0 = 211.8; This calculation both increases the allocation and gets to the desired duration in one step.

2. [(6.0 - 7.2) / 7.7] x (98mm / 103,000) x 1.0 = -148.3; This calculation decreases the portfolio duration to target on the original allocation.

CFAI first increases the allocation to the original duration and then adjusts that duration. We get to the same overall answer of 63 (or 64 possibly, given rounding) but the mechanics are just slightly different. Any thoughts on this?

Totally legit.

You can even do in one step via dollar duration:

N = (DD_new - DD_old) / DD_fut = (126,000,000*6*0.01 - 98,000,000*7.2*0.01) / (7.7*0.01*103,000) = 63.5

I’d do it the CFAI way tbh. Someone should use algebra to see if they are exactly the same.

Since the denominator is the same the numerators are additive and you can combine separate steps into one single step formula, or slice it the way you like into separate steps.