La Bourse / Volume II / Nº II.05 / Quiz, reflection, essays

A man and a woman seated across a round table in a high office, the city pale behind the glass. — Plate II.05 · Quiz, reflection, essaysThe 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.

ASSESSMENT · Chapter II.05 — Complexity and Economic Networks

Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.

THE QUIZ — ten points

Four on recall.

1. Write the Molloy–Reed criterion and the random-removal threshold, and define every term.

A giant connected component exists while κ = ⟨k²⟩/⟨k⟩ > 2, where ⟨k⟩ is the mean degree and ⟨k²⟩ the mean of its square. The critical fraction of randomly removed nodes is f_c = 1 − 1/(κ − 1). One mark for the criterion, one for naming κ as a ratio of the second moment to the first — that is the term an average conceals.

2. State the four headline figures of the Vitali, Glattfelder and Battiston ownership study.

43,060 transnational corporations; an ownership network of 600,508 nodes and 1,006,987 ties; a strongly connected core of 1,347 nodes; and 147 holders accumulating forty percent of the control, with 737 accumulating eighty percent. Roughly 110 of the 147 are financial intermediaries.

3. What does Newman's assortativity coefficient measure, and what sign do measured interbank markets carry?

Whether high-degree nodes attach to high-degree nodes. Interbank markets are disassortative — negative r — with hubs attaching to leaves. The worked core-periphery example in the chapter returns r = −0.7813.

4. State May's stability criterion and rearrange it for the largest generically stable system.

Stable while a·√(nC) < 1, hence n_max = 1/(a²C), where a is typical interaction strength and C is connectance. At a = 0.10 and C = 0.30, n_max = 333.3 nodes.

Four on application.

5. A supervisor reports that the average institution in her market has fourteen counterparties and concludes the market is well connected and therefore sturdy. What has she not computed, and why does it decide the answer?

She has reported ⟨k⟩ and not ⟨k²⟩. Every threshold in the chapter is a function of κ, not of the mean. Two markets with identical mean degree can have κ of 7.000 and 121.483 respectively, and thresholds that differ by a factor of six between random and targeted removal. Full marks require naming the second moment and saying what it changes, not merely that the average is insufficient.

6. A colleague says: "The trade network survived losing 96 percent of its members in the model, so trade is essentially indestructible." Diagnose the claim.

The 96.44 percent figure is for random removal. Removing the same network's members in order of connectedness fragments it at 18.28 percent — a factor of 5.3. The claim silently assumes that damage arrives at random, and almost no economic damage does. Credit an answer noting that both figures come from the same divergent second moment and cannot be separated.

7. Your board proposes to integrate two business units so that each can draw on the other's liquidity, on the grounds that diversification reduces risk. What single estimate would you ask for before agreeing, and what would each possible answer imply?

The tail index α of the relevant loss distribution, with its confidence interval. Above α\ = 1.0780 the integration lowers expected defaults; below it, the integration raises them and a firebreak is strictly better. The stronger answer notes the asymmetry — the win is worth 0.66 percent at α = 3.00 and the loss is worth 12.49 percent at α = 0.80 — and that an interval straddling α\ means the decision is not determined by the data and must be made on other grounds, in writing.

8. Why does the chapter argue that removing the 147 holders would not change the concentration of corporate control?

Because the concentration is the fixed point of a rule, not of a membership. Control multiplies because the largest shareholder directs the firm and therefore the stakes the firm holds; that rule is ordinary company law and it operates on whoever occupies the position. Only changing the rule — how control is defined, how voting rights attach through chains, whether an intermediary may vote shares held for others — moves the number.

Two that require the arithmetic to be done.

9. A network has mean degree 6.00 and degrees follow a Poisson distribution. Compute κ and the random-removal threshold. Then a second network has κ = 29.124. Compute its threshold, and the ratio of the two thresholds.

Poisson: ⟨k²⟩ = ⟨k⟩² + ⟨k⟩ = 36 + 6 = 42.000, so κ = 42.000/6.00 = 7.000, and f_c = 1 − 1/6 = 83.33 %. Second network: f_c = 1 − 1/28.124 = 96.44 %. Ratio of thresholds 96.44/83.33 = 1.157. The point of the question is that the heavy-tailed network is the more robust one under random failure — which is the half of "robust-yet-fragile" people forget.

10. Twenty banks, each with an equity buffer of 1.00 unit. A shock of 20.50 units lands on one bank's external assets; the excess above its own equity passes to its interbank creditors. Compute the number of defaults under (a) the complete network, (b) two disconnected islands of ten. Then state the shock at which the complete network's answer changes, and by how much.

Shortfall s = 20.50 − 1.00 = 19.50 units. (a) Complete: creditors hold 19.00 units between them and 19.50 > 19.00, so all twenty default. (b) Islands: the shocked island's nine creditors hold 9.00 units, 19.50 > 9.00, so ten default — and the second island is untouched, whatever the size of the shock. The complete network's answer changes at a shock of 20.00 units, where it goes from one default to twenty: one extra unit of shock, twentyfold damage. Credit any working that identifies the creditors' aggregate buffer of 19.00 as the threshold term.

REFLECTION — eight questions, for one person and a pen

These are not for a room. Write the answers by hand if you can; the slowness is the point.

Draw, from memory, the ten relationships your work depends on most. Now draw the links between those ten. What did you learn in the second drawing that you did not know while doing the first?

Which single person, supplier, system or institution would, if it went dark tomorrow, disconnect the most of what you do? How long have you known that, and what has stopped you from second-sourcing it?

Where in your own life are you the hub — the node through which other people's paths run? What does that cost you that nobody sees, and what would it take to make one of those paths not need you?

Think of a time you were protected from something by being unconnected. What was the disconnection, and did you choose it or inherit it?

Recall a moment when everyone around you, all well-informed, was wrong in the same direction at the same time. What were you all reading? What would it have taken for one of you to be reading something else?

What would you have to give up to build a firebreak in your own working life — a part of it that deliberately cannot draw on the rest? Is the thing you would give up actually valuable, or is it convenience?

Where have you called something diversified when it was in fact many copies of one bet? Be specific about the bet.

What is a rule you personally set — for your team, your household, your own practice — that produces a concentration you have been blaming on the people inside it?

ESSAY PROMPTS — five

Each is arguable from more than one side. Each requires at least one source the chapter cites and at least one it does not.

1. Whether the 147 is a finding about power or about accounting. The chapter argues that the concentration measured by Vitali, Glattfelder and Battiston is the fixed point of an ownership-and-control rule rather than evidence of coordination, and that the political conclusions usually drawn from it do not follow. Argue for or against. Use Vitali et al. (2011) and Glattfelder and Battiston (2009), and at least one source on corporate governance, ownership concentration or index-fund voting that the chapter does not cite.

2. Is diversification a public good or a public bad? Take the α\ result seriously and argue whether financial regulation should encourage dense interconnection, discourage it, or — the harder position — require institutions to be different from one another* rather than individually prudent. Engage Acemoglu, Ozdaglar and Tahbaz-Salehi (2015) and Haldane and May (2011) directly, and one source on macroprudential policy or capital regulation that the chapter does not cite.

3. The boundary problem. Every network study must stop somewhere, and where it stops determines what it finds. Argue whether network measures of systemic importance can be made robust to boundary choice, or whether boundary sensitivity is a permanent limitation that should keep such measures out of binding regulation. Use Battiston et al. (2012) on DebtRank, and at least one methodological critique of network-based systemic risk measures that the chapter does not cite.

4. Ecology as a source of economic law. May (1972) was a result about randomly assembled ecosystems, and Haldane and May (2011) imported it into banking. Argue whether that import is legitimate — where the analogy holds, where it breaks, and what a financial system has that an ecosystem does not. Use May (1972) and one source from ecology or complexity science, written after 2000, that the chapter does not cite.

5. Measuring the graph changes the graph. Suppose supervisors published every institution's network position quarterly. Argue the case that this improves the system — comparability, discipline, price — and then the counter-case, that publishing a systemic-position score creates an incentive to restructure toward whatever the score does not see, and that the network would reorganise around the measure within two years. Use Soramäki et al. (2007) or Boss et al. (2004) for the measurement side, and one source on measurement effects, regulatory arbitrage or Goodhart's law that the chapter does not cite.