Reasoning behind dividing Swap BPV by 100

Dear all,

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?

For futures: Asset portfolio BPV + (Nf × Futures BPV) = Liability portfolio BPV

For swaps: Asset BPV+[NP×SwapBPV/ 100]=Liability BPV


I have no idea.

I’ll e-mail CFA Institute and ask.

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.

If so, it would certainly be nice for the curriculum to say so, for those candidates unfamiliar with (weird) market quoting conventions.

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.

I heard back from CFA Institute.

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.

Stay tuned.

Are you just emailing them with the generic ? I assumed the customer service people dont have a clue about these things.

I am.

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.

I have the same question. Any update from CFA institute Mr Magician ?


It appears that they dropped it.

Oh, well.

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.

you are right! thank you fino_abama

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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