The formulas for hedging liabilities with futures and swaps are almost similar, except Swap BPV to be divided by 100. Can anyone explain me the reasoning (logic) behind this difference?

Believe this simply relates to market quoting convention; the BPV of a swap is referenced per 100 units of notional, whereas the asset and liability BPVs are referenced per 1 unit of notional.

I certainly can’t argue with you on that one. I’ll be interested to hear how they respond to you on this - based on the OP’s question is definitely seems like the text would benefit from the addition of a simple explanatory paragraph.

They said that the one formula was for computing the number of (futures) contracts, while the other was for computing the notional value (of a swap).

I agreed, but stressed that that didn’t really explain the difference in divisors, as they’re both computing basis point values. I asked for clarification, and mentioned that the question had already been asked here.

They (presumably) pass this stuff along to the folks in the know.

I’ve always had success doing it this way. Well, success in the sense of it getting to people who can discuss it, but not necessarily success in the sense of them agreeing that I’m right.

If you refer to page 80 of Book 4, it is specified in the last paragraph that:

“The fixed rate on the swap is 4.16%. Its effective duration is +16.73, and its BPV is +0.1673 per USD 100 of notional principal. Exhibit 15 illustrates this swap.”

The notional was mentioned in the case, that’s why you have to convert the swap BPV to per $1 notional by dividing by 100.

Sorry for reviving an old discussion. I’d like to know in the real world do we need to divide the swap BPV by 100? I’m saying we are not taking the exam, but doing this for a real asset-liability job.

In real world, you would have picked an arbitrary notional for the swap (10, 100, 500, 1000, 10000), and compute the BPV based on that notional. And when you want to compute the BPV per $1 notional, just divide the computed BPV by the notional chosen