La Bourse / Volume II / Nº II.05 / Workbook — the executive

A man and a woman seated across a round table in a high office, the city pale behind the glass. — Plate II.05 · Workbook — the executiveThe Exchange, After Hours.The board is not the calls. The board is which calls are possible. Every economy has one, almost nobody has drawn it, and the drawing changes what you think you are looking at.

WORKBOOK — THE CORPORATE EXECUTIVE

Chapter II.05 · Complexity and Economic Networks

For the person with a P&L, a counterparty list, a supplier base and a risk committee. Everything here is executable from data your systems already hold, and none of it requires a new platform.

THE PREMISE, STATED COMMERCIALLY

Your enterprise risk register lists counterparties, suppliers and dependencies as a set of individually assessed items. Each is scored on its own characteristics: size, rating, tenure, financial strength.

That register cannot, in principle, tell you what you most need to know — because the thing that determines whether a disruption reaches you is not any counterparty's own properties but the shape of the connections between them. Two supplier bases containing exactly the same firms, with exactly the same financial strength, behave completely differently under stress depending on how those firms are wired to each other and to everyone else.

This is not a theoretical objection. It is arithmetic, and the chapter runs it: the same twenty banks, wired three different ways, produce one default or twenty from the same shock. Nothing about the institutions changed.

Three commercial consequences follow immediately.

You are probably over-provisioned against some exposures and under-provisioned against others, systematically, in a direction you can compute. Large peripheral counterparties are over-weighted; small central ones are under-weighted.
The cheapest risk reduction available to you is almost certainly second-sourcing one or two articulation points, and they are usually unglamorous — a transfer agent, a certifying body, a single logistics hub, a niche component maker three tiers down.
Integration decisions you are currently making on efficiency grounds have a risk sign that flips at a computable threshold. You can know which side of it you are on.

None of this needs board approval to begin. The first four numbers cost one analyst a fortnight.

PART ONE — DISCOVERY

Days 1–30: get the edge list

Exercise 1.1 — The five places the graph already exists (half a day)

You do not need to build a network. You need to assemble one from data your systems already hold. Look in five places, in this order.

Source	What it gives you
Accounts payable and receivable	Direct counterparty links, weighted by value
Procurement master data	Supplier links, and often tier-two declarations
Treasury counterparty limits	Financial counterparties and current exposures
The insurance schedule	Dependencies somebody already thought were material
Business continuity plans	Articulation points somebody already identified

The last two are the shortcut. Somebody in your organisation has already done part of this work under a different name, and has never been asked for it in this form.

Exercise 1.2 — State the boundary before you draw (one hour)

Write, in one sentence, where your graph stops. "All counterparties with more than £X of annual flow, plus their declared tier-one suppliers, as at quarter-end."

Then write, in a second sentence, what that excludes. This sentence goes on every page of every output for the rest of the programme. A network analysis without its boundary is a map with the edges torn off, and the most important node is very often just outside the frame.

Exercise 1.3 — Find the thing you already did right (one hour)

Before anything else, run the appreciative question through the operations team: when has a disruption somewhere in our network failed to reach us, and why? Somebody will name a second source that was set up years ago for a reason nobody remembers. Cost it. That is your first evidence, it is free, and it is a measurement rather than a forecast.

PART TWO — THE ARITHMETIC

Days 31–45: four numbers and a cascade

Exercise 2.1 — Compute the four numbers (three days)

From your edge list, compute and record:

Number	What it tells you	Where you are if…
κ = ⟨k²⟩/⟨k⟩	Which regime you are in	κ near ⟨k⟩: sturdy. κ an order of magnitude above: hub-dependent
`f_c` random	Tolerance for accidents	Almost always high; this is the reassuring one
`f_c` targeted	Tolerance for selection	On measured economic networks, four to six times lower
`r`	Core-periphery or not	Negative means hubs carry the paths; targeted removal is worse than degree suggests

For calibration: a random network with mean degree 6.00 gives κ = 7.000 and thresholds of 83.33 percent random against 55.43 percent targeted, a ratio of 1.50. A power-law network at exponent 2.6 — the measured world trade web — gives κ = 29.124, thresholds of 96.44 percent and 18.28 percent, a ratio of 5.3. Where your business sits between those two ratios is the single most informative sentence in the whole analysis.

Exercise 2.2 — Run the cascade on real buffers (three days)

Use your actual numbers. For counterparties: their equity or their liquidity headroom, whichever you can obtain. For suppliers: weeks of inventory buffer. For internal units: available cash.

Run three wirings — as-is, more connected, compartmented — across a range of shocks. Produce the table. The table is the deliverable; the commentary is not.

The chapter's worked case, for reference: twenty banks at 1.00 unit of buffer each, aggregate 20.00 units, creditors holding 19.00. The complete network gives one default at every shock up to 20.00 units and twenty defaults at 20.50 — one extra unit of shock, twentyfold damage. The two-island version caps at ten defaults and never exceeds it. Your business has a cliff too. Find where it is and write the number down.

Exercise 2.3 — Estimate α, and say what you do not know (two days)

Take your own loss history — credit losses, supply disruptions, operational events, whatever the domain is. Fit a tail index with a Hill estimator. Vary the threshold. Report the point estimate, the interval, and the sample size.

Then place it against α\* = 1.0780, the crossover at which dense connection stops lowering expected defaults and starts raising them.

α comfortably above. Integration is the better structure. Say so, and say by how little: at α = 3.00 the advantage is 0.66 percent.
α comfortably below. Compartmentalisation is better, and by a lot: at α = 0.80 the advantage is 12.49 percent.
The interval straddles it. Your structural decision is not determined by your data. Write that sentence down and take it to the committee, because it is a finding, and a committee that knows it is choosing rather than computing makes better choices.

Exercise 2.4 — The connectance conversation (one hour)

May's criterion gives n_max = 1/(a²C). At interaction strength 0.10, raising connectance from 0.10 to 0.50 cuts the largest generically stable system from 1,000.0 nodes to 200.0 — a factor of five.

Have the conversation with your own leadership in those terms, once. Every integration programme in the building is a connectance increase. That does not make them wrong. It makes them a trade with a second side that is currently unpriced.

PART THREE — DESIGN

Days 46–60: the instrument

Exercise 3.1 — Re-parameterise a framework you already have (five days)

You already run counterparty limits. Add one term.

  limit  =  base limit  ×  f(network position)

where f is published, monotone, and bounded — never worse than half the base, never better than the base. Bounded because an unbounded multiplier will be gamed, and because a limit nobody can predict is a limit nobody can plan around.

The position score is one number per counterparty, refreshed quarterly: its degree, its neighbours' degrees, and its contribution to expected losses in your own cascade.

Exercise 3.2 — Define the firebreak trigger before you need it (two days)

Write the pre-agreed action. When counterparty position score crosses X, the exposure moves to a ring-fenced vehicle with no cross-default to the parent.

The whole value is that it is written in a good week. A firebreak decided during an event is not a firebreak; it is a negotiation, and the counterparty knows it.

Exercise 3.3 — Price the second sources (three days)

List the articulation points — the nodes whose removal disconnects your graph. There will be fewer than you expect and they will be cheaper than you expect.

For each: the cost of qualifying a second source, and the expected loss avoided from your cascade at your estimated α. Rank by ratio. Fund the top three out of operational budget without going to the board, because three small qualification programmes are ordinary spend and a single board paper about network theory is not.

Exercise 3.4 — The balance-sheet treatment (two days, with your auditors)

Where you establish a ring-fenced vehicle, it is consolidated but separately capitalised, and the capital held against it is the expected loss from your cascade at your estimated tail index — not the regulatory minimum. Where the two differ, disclose both and say which you manage to.

Have this conversation early and frame it correctly: it is a provisioning methodology, and your auditors assess provisioning methodologies every year. They are comfortable with the genre.

PART FOUR — DESTINY AND DELIGHT

Days 61–90: make it hold

Exercise 4.1 — Get it into the pack (two days)

One page in the standing monthly pack: the four numbers, the cascade cliff, the articulation point list, the boundary sentence. Anything reviewed monthly persists. Anything reviewed by exception does not.

Exercise 4.2 — Automate the refresh (five days)

The edge list must rebuild itself from the source systems. Anything requiring a person to assemble it will be assembled late and then not at all. This is the single highest-return engineering task in the programme and it is small.

Exercise 4.3 — Offer the measure to a counterparty (one meeting)

Your largest counterparties have the same problem and mostly no measure of it. A shared measure between two institutions is worth more than a proprietary one inside either, and offering it costs nothing. This is also, quietly, a commercial move: the firm that sets the shared measure is the firm everyone calibrates against.

Exercise 4.4 — The wall (one afternoon)

Print the graph large and put it on a wall where the operating team works.

Watch what happens. Somebody will point at a node in the middle nobody has heard of, and somebody else will identify it, and in the following ten minutes the room will learn more about the business than the last strategy offsite produced. That is not a soft benefit. It is the fastest transfer of structural knowledge available to you and it costs the price of a plot.

WHERE THE FIRM'S OWN NUMBERS ALREADY SUPPORT THE MOVE

Four places, and in each of them the business case exists inside data you already report.

Business interruption premiums. Your insurer prices your concentration without telling you its model. The articulation-point list is the same object arrived at independently, and a second source that removes one is a negotiating position at the next renewal. Underwriters respond to structural change in a way they do not respond to policy documents.

Working capital tied to single-source risk. Safety stock held against a single supplier is capital on the balance sheet doing the job a second source would do more cheaply. Compute both, in the same units, on one page. The comparison is frequently decisive and it has never been made, because the inventory sits with operations and the supplier decision sits with procurement.

Counterparty limit utilisation. You are almost certainly holding unused limit against large peripheral counterparties and running close against small central ones. Re-parameterising by network position is capital-neutral in aggregate and risk-reducing in distribution — which makes it one of the rare proposals with no funding request attached.

Audit and certification dependencies. Certifying bodies, testing laboratories and transfer agents are the classic uncounted articulation points: low spend, high centrality, and invisible to a register that ranks by value. A graph ranks them correctly for the first time.

The pattern in all four is the same. The network view does not ask for new money. It re-allocates provisions you already hold to the exposures that actually carry the risk, and the arithmetic for doing so now exists on one page.

THE FAILURE MODES, NAMED

So you can see them coming

The graph is drawn once. Annual is decoration; quarterly is infrastructure.

The boundary is chosen for convenience. A tier-one-only map has all its important nodes outside the frame. State the boundary on every page.

α is quoted without its interval. A point estimate on forty loss events will be repeated as certainty within two meetings. Say the interval or do not say the number.

The model is mistaken for the market. The cascade assumes the network holds still while the shock travels. Real counterparties withdraw, hedge and refuse to roll, and the graph rewires during the event, usually for the worse. Present your cascade as a lower bound on damage, in writing, every time.

The score gets gamed. Publish f and bound it, and accept that within two years counterparties will restructure toward whatever the score does not see. Plan the second version before the first is deployed.

THE NINETY DAYS ON ONE PAGE

Day	Action	Artifact
1–15	Assemble the edge list from existing systems	Edge list, with boundary stated
16–30	Appreciative interviews: where did disruption fail to reach us?	Two costed existing defences
31–40	Compute κ, both thresholds, r	One page, four numbers
41–45	Run the cascade on real buffers, three wirings	The cascade table and the cliff
46–50	Estimate α with its interval	α, standard error, n
51–60	Draft the limit multiplier and the firebreak trigger	Framework memo
61–75	Price and fund the top three second sources	Purchase orders
76–90	Risk committee, one worked case	The decision paper

BOARD PAPER TEMPLATE

Title. Network position in our counterparty and supplier base: four measures and one proposal.

What is already working. The two existing defences found in Exercise 1.3, costed, with the disruption each prevented.

What we measured. The four numbers, the boundary sentence, the cascade table with the cliff identified.

What we do not know. The tail-index interval and its sample size. Stated plainly, before the recommendation.

The proposal. Three second sources funded from operational budget; one bounded limit multiplier; one pre-agreed firebreak trigger.

The number that decides it.

      expected loss avoided by the firebreak
   ----------------------------------------------   >   our hurdle rate
    annual cost of the separate vehicle + capital

What we are asking for. One decision, on one page. Not endorsement of a programme.

APPRECIATIVE QUESTIONS FOR YOUR LEADERSHIP TEAM

When has a disruption in our sector failed to reach us? What structure made that true, and did we design it or inherit it?
Who in this business already holds a map of who depends on whom — informally, in their head — and what do they see that the register does not?
If we published our network position to our largest counterparties and they published theirs, what could we do together that neither of us can do alone?
What is the smallest second-sourcing decision we could fund this quarter that would remove an articulation point, and who owns it?