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I'm a bit confused about the definition of contract notional value for a futures contract. It is not defined in John Hull's Options, Futures, and Other Derivatives. I find two definitions online. Both have a lot of sources:

Some even use one definition in the formula or definition, but use the other definition as a numerical example:

Similarly, in CFA Level 3 curriculum (May 2022),

  • In Reading 9 about Swaps, forwards, and futures strategies, Section 8.1, the first definition is used. It writes

Once the notional values to be traded are known, Rossi determines how many futures contracts should be purchased or sold to achieve the desired asset allocation. The FTSE MIB Index futures contract has a price of 23,100 and a multiplier of €5, for a value of €115,500. The DAX index futures contract has a price of 13,000 and a multiplier of €25, for a value of €325,000.

  • In Reading 11 about fixed-income portfolio management, Section 7.2.1 about using futures for leveraging fixed income portfolio, the second definition is used. It writes

A futures contract’s notional value equals the current value of the underlying asset multiplied by the multiplier, or the quantity of the underlying asset controlled by the contract.

So I'm shocked by the divergence of opinions. Personally, I think the first one makes more sense since its daily changes is used for mark to market and it is also used to calculate the hedge ratio, e.g. in cross-hedging. I don't know why the second definition pops out.

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  • $\begingroup$ I am surprised that the CFA Reading 11 endorsed the second definition, since it seems to me the first definition is more correct, and it is supported by the CME which I think would know the proper terminology for futures. $\endgroup$
    – nbbo2
    Commented May 12, 2022 at 13:43
  • $\begingroup$ Of all the sources you cite I think the CFA program and the CME are the most reliable, the others are either low accuracy (eg. investopedia) or vague (one is about "derivatives" rather than specifically "futures"; others mention "price" but not specifically "spot price", etc.) $\endgroup$
    – nbbo2
    Commented May 12, 2022 at 14:07
  • $\begingroup$ Thank you. I agree. $\endgroup$
    – L. Francis Cong
    Commented May 15, 2022 at 2:25

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The definitions of 'notional' sizes for futures are pretty arbitrary and are not comparable. Comparing between futures types (eg, interest rate futures and index futures) is especially meaningless.

What determines a futures contract 'size' is the contract terms. In many cases there is a number in those terms that may seem appealing to use as a comparative size. For example, different oil futures contract terms may specify the number of (standard size) barrels at delivery. That's comparable (even if they aren't fungible), but that doesn't mean anything when related to a S&P index future.

When looking for a standard sense of relative size, you might also consider delta. But again this isn't as comparable as we might want, as it implicitly is bound to the underlying's price semantics. For example, we might look at the deltas of a position in S&P index futures, vs a position of FTSE 100 Index futures. The deltas (PnL / point ratio) might be equal, but the points of each index are not equal, so your positions' PnL responses to market repricings of risk (the real delta) isn't equal either.

Similarly, multiplying a contract 'size' by the price is also pointless, because price semantics can be so different across contracts.

Issues like this are why comparing (or aggregating) financial risk of securities positions is a non-trivial exercise.

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