Fixed Income - # of futures contracts to modify duration

CFA Level III Fixed Income
#1

Regarding the # of futures contracts you need to modify PF duration to a new level…

Does anyone know why Reading 22 CFAI EOC #26 uses division in the denominator of the equation?

I have only seen the equation as (new desired duration - current duration) * PF value / Futures duration * futures price

The textbook answer divides futures duration by price, don’t think I’ve seen the equation like this anywhere else…does anyone know when (if at all) you’re supposed to divide the futures duration instead of multiply?

Thanks

#2

Total Bond Duration Current = 6.2

Required Bond Duration = 5.6

Futures Contract Priced at 100,000, Duration = 8.2, Conversion Factor = 1.1

So # of Futures Contracts = (5.6 - 6.2) * 3,062,000,000 / (100,000 * 8.2) * Conversion Factor 1.1 = -2240.82 * 1.1 = -2465 Contracts

Sell 2465 Contracts

Answer C

#3

Got it thanks. I guess the answer key just has a mistake in it!