Where you are. Two lessons of netting have collapsed a day of traffic. Lesson 13 offset each pair’s obligations down to a single difference; lesson 14 put a hub in the middle and collapsed the whole day to one net position per bank. Both kept score on one axis: cash moved. But you have been warned twice that the axis is not alone. Module 2’s batch rail ended on a web of promises standing until the batch lands, and promised that this module would weigh cash moved against risk concentrated. Lesson 10 then showed what a standing promise becomes on the day a counterparty dies: a Herstatt-style loss of the full amount owed. This lesson keeps module 2’s promise. It runs one tape through all three settlement modes and measures both axes at once.
The treasurer and the risk officer
Friday afternoon at Cedar, one of the four dealer banks whose dollar legs you have been netting for two lessons. The treasurer loves the hub: tonight the day’s twenty obligations will settle as a handful of net payments, and Cedar funds a fraction of what it owes gross. Down the corridor, the risk officer reads the same tape and asks a different question. It is three in the afternoon, the cutoff is hours away, nothing has settled yet: who owes Cedar the most, right now, and what happens if that name does not open on Monday? The treasurer’s number is about tonight. The risk officer’s number is about now. This module has spent fourteen lessons quietly building the tension between them: the nostro float parked money to save hops, the batch rail queued promises to save reserves, and netting cancels traffic precisely by letting obligations stand open. Nothing was free. Every saving in cash showed up somewhere else as risk, and today the two numbers meet on one chart.
The idea in one paragraph
Take the exact tape lessons 13 and 14 settled - twenty seeded dollar obligations among four dealer banks, one day of FX-trade dollar legs, stylised units throughout - and run it through all three plumbings: gross, where every obligation settles in full the moment it arises; bilateral, where each pair’s day stands open and settles as one difference at the cutoff; multilateral, where every obligation is rewritten against the hub at birth and each bank settles one net position. For each mode, measure two numbers. Cash moved you know. The new one is peak exposure: the largest amount owed to any single participant at any moment of the day, which by lesson 10 is exactly the most anyone stands to lose if one name fails at the worst time. Plot the three modes as three points, cash on one axis and exposure on the other, and no point beats another on both. That is the lesson: gross versus net is not a ranking but a trade-off, and every settlement system in this course is one chosen point on it.
The second axis
To measure exposure you need the day as a stream, not a summary. Two verbs are enough. An obligation arises: the payer owes the payee. An obligation is discharged: the payer pays. Replay the day event by event, keep a running book of who owes whom, and after every event ask, for each participant: what does each counterparty still owe it, net of what it owes back, floored at zero, summed across counterparties? That figure is the participant’s exposure at that instant - the money it loses if all its debtors fail right now. Track the largest figure anyone carries at any moment and you have peak exposure, one honest number for the whole day. It is a fold over a log, and you will write it as one in the exercise.
Three plumbings, one tape
Under gross settlement the two events are adjacent: each obligation arises and is paid in the same breath. Nothing ever stands open, so the largest exposure anyone carries is one obligation, for one instant - on this tape, 500, the biggest single trade. The price is the one module 2 lesson 4 itemised: every payment needs its full value available at its own moment, so the day moves its entire gross value, 5,370, through funded accounts. Expensive traffic, negligible standing risk, and no hub anywhere.
Bilateral netting lets each pair’s obligations stand open all day, offsetting in both directions, and settles six differences at the cutoff, moving 2,790. But the offsets arrive in tape order, not in anyone’s favour. Mid-afternoon, Cedar is owed 1,910 net across its counterparties - nearly four times the biggest single trade on the tape - and it stays owed until the cutoff settles. Half the cash, and a standing pile.
Multilateral netting rewrites each obligation the moment it is born: the payer owes the hub, and the hub owes the payee. At the cutoff each bank settles one signed position against the hub - four payments, 2,240, the least cash of the three. But watch the hub’s own line in the running book. Mid-day it is owed 2,910: more than the cash the entire day will end up moving. The cutoff nets are an end-of-day fact; exposure is an intraday fact, and it peaks before the offsets finish arriving.
| mode | payments | cash moved | peak exposure |
|---|---|---|---|
| gross | 20 | 5,370 | 500 |
| bilateral net | 6 | 2,790 | 1,910 |
| multilateral net | 4 | 2,240 | 2,910 |
n = 20 trials · one seeded day of FX dollar legs, four dealer banks, stylised units
Read the two right-hand columns together: each is monotone, and they run in opposite directions. Every step of netting carries the same day in fewer payments and less cash, and every step lets obligations stand longer and pile higher on fewer names. The exercise states both orderings as asserts, so the claim is not prose.
The figure plots the three modes on the two axes at once. Gross sits far right and low: maximum cash, minimum concentration. Multilateral sits far left and high: minimum cash, maximum concentration. Bilateral sits between on both. The corner everyone wants - little cash, little exposure - is empty, and the whole design space of settlement lives along the line the three points trace.
Check yourself
1. On any tape whatsoever, gross settlement’s peak exposure equals the largest single obligation. Why must it, and what does gross pay for that guarantee?
Settle-on-arrival means each obligation arises and is discharged before the next event; at no instant does more than one obligation stand open, so the worst moment is the biggest trade, alone. The exercise pins this with an assert. The price is full funding: every payment moves its whole value at its own moment, so cash moved equals the tape’s gross value - module 2 lesson 4’s liquidity bill, paid in exchange for carrying almost no standing risk.
2. The hub’s cutoff payments total 2,240, yet the tracker catches it owed 2,910 mid-day. Where does the extra 670 come from?
From time. A net position is the residue after every offsetting obligation has arrived, and offsets arrive all day in tape order. Mid-stream, banks have piled obligations onto the hub that later flows would have offset but have not yet. The cutoff report is the day at its most flattering moment; exposure is measured at its least. The exercise asserts the peak exceeds the cash precisely so you cannot confuse the two.
3. A colleague computes 1 - 2,240/5,370 and announces that multilateral netting cut risk by more than half. What did they actually measure, and what happened to the risk?
They measured cash moved, the treasurer’s number. The same twenty obligations are discharged in full either way; what changed is who is owed, how much at once, and for how long. Standing exposure rose from 500 to 2,910 and moved from many pairwise instants onto one name. Netting is a genuine saving in liquidity and a genuine concentration of counterparty risk, and quoting the first as if it were the second is how hubs get built too small.
4. A bank fails at three in the afternoon, before any cutoff. Who takes the hit under each of the three modes?
Under gross, almost no one: everything before the failure settled on arrival, so at most one obligation is mid-flight, bounded by the largest single trade. Under bilateral, the failed bank’s pair counterparties each stand exposed up to their open pairwise net. Under multilateral, formally the hub alone - every claim runs against it - but the hub’s promises to the payees were to be funded by the failed bank’s paying-in, so in substance everyone is exposed through the hub. Whether a hub can honour the dead bank’s obligations anyway is exactly what module 5’s clearing houses exist to answer, with collateral and rules, not hope.
Do this
Twenty minutes, from module-03-across-borders. Open code/gross_vs_net.py. The tape is lessons 13 and 14’s, replayed byte for byte, and the three event builders are written: each settlement mode told as one time-ordered stream of owe and pay events. Your work is peak_exposure, the tracker. Keep a running book keyed by the ordered debtor-creditor pair: an owe event adds its amount to that channel, a pay event removes it. After every event, compute each participant’s exposure - the sum over counterparties of max(0, what that counterparty owes it minus what it owes back) - and remember the largest figure anyone carried at any point. Do not special-case the hub: it enters the book like any other name, which is exactly how the concentration becomes visible.
python3 code/gross_vs_net.pyGreen is this scoreboard, ending with the final line verbatim:
mode payments cash moved peak exposure
gross 20 5370 500
bilateral net 6 2790 1910
multilateral net 4 2240 2910
cash falls, concentration rises: netting buys cheap settlement by letting exposures stand and pointing them at one hubIf gross’s peak prints 5,370 instead of 500, your pay events are not clearing the book: everything accrued and nothing was discharged, so check the sign on the pay branch. If the multilateral peak prints 2,240, you measured exposure once, after the last event, instead of after every event - the peak lives mid-stream, and the assert comparing it to the cash moved will say so. And if the hub never shows up as the peak holder, you filtered it out of the participants: the hub is a counterparty like any other, and excluding it hides the exact concentration this lesson exists to measure. The completed version is solutions/gross_vs_net.py; compare after you are green.
What you can now do. You can take any settlement design - the ones this course has built and the ones it has not met yet - and place it as a point on a two-axis chart: the cash it moves against the exposure it lets stand. You can say why the cheap corner concentrates, why the safe corner pays, and why the corner with neither cost is empty. And you can hear a netting ratio and ask the risk officer’s follow-up: where did the exposure go, who holds it now, and what happens if that name fails before the cutoff. Next lesson is the module’s project: the border crossing, where the chain simulator, the Herstatt replay, the PvP repair, this netting report and the remittance cost stack assemble into one run.