What a Number Is MeasuringMedium

Notional, exposure, market value and sensitivity are four different quantities, and three of them can be enormous while the fourth is nearly nothing. Almost every alarming figure in this subject is one of the four read as another.

5 min read · 948 words

One position, four numbers

• Notional — the reference amount a contract's payments are calculated from. It is an input to a formula. On most derivatives nobody ever pays it, receives it or owes it.
• Exposure — how much of the underlying the position behaves like. A future on 100 of an index behaves like 100 of the index, whatever was paid to enter it.
• Market value — what the position is worth right now: what it could be closed for. On the day a swap is struck this is approximately zero, by design.
• Sensitivity — how much the value changes when something moves. A basis point, a per cent, a volatility point: the quantity a risk seat actually manages.
• All four describe the same holding, and the gap between the largest and the smallest is routinely three orders of magnitude. Reading one as another is the single most common error of mechanism in this subject, and getting it right in writing names it first for that reason.

Where the confusion is manufactured

• An interest rate swap has a notional and nobody pays it. Two payment streams are computed from it and only the difference moves — the phase note on every swap diagram here says so. A firm with a very large swap book may have almost nothing at stake, or a great deal; the notional does not distinguish the two cases.
• A credit default swap's outstanding contracts can exceed the debt they reference, because nothing ties the number of contracts to the amount borrowed. Netting offsetting positions gives a far smaller figure, and that figure is the one that describes what would move — CDS against insurance follows this through.
• An option's notional is not its exposure either. A far out-of-the-money option on 1 000 shares behaves, today, like a handful of shares; near expiry and near the strike, it behaves like all 1 000 and then like none, within hours. One position, one notional, an exposure that moves on its own.
• A repo's numbers point in opposite directions. The cash lent is the exposure to the borrower; the securities held are the collateral against it; the market value of the trade is the small difference between them. Quoting the first as the risk ignores the second entirely.

The comparison

Which one is right for which question

• How much could this lose? Sensitivity, over a plausible move — and then the tail, because sensitivity is a local measure and the interesting moves are not local. Risk measures is the machinery.
• What is on the balance sheet? Market value, on the measurement basis the holder chose at recognition, which is a separate decision entirely — see amortised cost against fair value.
• What would have to be replaced if the counterparty failed? The market value where it is positive, plus what it could grow to before the position is closed out — which is why initial margin exists and why who has to still exist is a different question from what a position is worth.
• What is this position actually a bet on? Exposure. It is the only one of the four that answers it, and the only one that is not printed on any statement.
• How big is this market? None of them, honestly — which is why no figure of that kind appears anywhere on this site.

Where each one lies to you

• Notional overstates, spectacularly. It is the number that produces alarming headlines about derivative markets, and it is the number a firm's own risk report never uses on its own.
• Exposure understates a hedged book. Two offsetting positions net to nothing on exposure and to two separate counterparty exposures, two funding requirements and two sets of margin. LDI in 2022 is a hedge that was right on exposure and fatal on funding.
• Market value understates anything asymmetric. A sold option's value today is the premium; its liability is unbounded. A near-zero market value with a large tail is the shape of most positions that have surprised somebody.
• Sensitivity is a local truth and stops being one. It assumes small moves and stable relationships, and both of those assumptions fail in the same week. Everything in model risk applies here.

The habit worth forming

• Ask which of the four a figure is before doing anything with it. Most reported numbers in this subject do not say, and the answer changes the size of what is being described by a factor a reader would never guess.
• Never compare two figures that are different quantities, even when both have currency signs and one is plainly bigger.
• And treat "gross" and "net" as part of the number, not as adjectives. Gross notional, net exposure and market value after netting are three answers to three questions, and quoting one under another's name is how a correct figure becomes a false statement.