The Right Word, the Wrong Reader

The structure

Three jurisdictions. Country A is an emerging market with a policy rate near 10%, capital controls, and tenor-dependent taxation of external borrowing. Country B is an advanced-economy financial centre with dollar funding near 0.25%, hosting a branch of the bank. Country C exports capital equipment.

Four parties. I, an importer-distributor resident in Country A. B, a bank headquartered in Country A, with branch B* in Country B and an issuing vehicle B° offshore. S, the equipment supplier in Country C. K, a third-party custodian.

Both advance rates are 77%, inside ordinary convention for secured lending against investment-grade paper. STYLIZED No individual haircut is anomalous, and this matters: a reviewer of any single leg sees nothing to report.

One further parameter carries most of what follows. The rate on the collateralized advance is 4%, and it is set centrally rather than priced by the lending branch.

Three arbitrages, superimposed

2.1 The rate wedge

Take Country A’s policy rate at 10% and a 200 bp corporate spread, so this borrower’s domestic cost is 12%; Country B’s dollar funding is 0.25%. The wedge is 1,175 bp, and the administered 4% divides it exactly:

I funds 800 bp below its domestic market. B* earns 375 bp over its own funding cost on an asset collateralized with money it advanced. COMPUTED

Neither party is compensated for bearing risk. Both are compensated by the existence of a border.

2.2 Collateral multiplication

A single cash pool supports a gross notional of

Each pledge is created downstream of the same funds. No external asset secures any leg. The chain resembles ordinary collateral re-use with one decisive difference: the re-pledged asset is issued by the secured party itself.

2.3 Circularity

Everything turns on the character of the securities subscribed at T₃.

If they are senior paper, this is an aggressive secured chain with acute wrong-way risk — the collateral impairs in precisely the state where it is called upon. Bad, and conventional.

If they are subordinated or perpetual instruments counted toward regulatory capital, the transaction is categorically different. The bank has raised capital using money it lent, secured on the capital it raised.

The result

In τ:

1. The instrument is written down to zero. I’s pledged asset is worthless.
2. I’s obligation to B remains L, now unsecured in substance.
3. Absent independent recourse capacity, B realises a credit loss of L.

The instrument absorbs nothing. Its write-down is exactly offset by the default that the write-down causes. The capital is capital in form and circular in substance.

The Basel framework prohibits the inclusion of own-funds instruments financed directly or indirectly by the issuing institution. CHECKED The prohibition is unambiguous and long standing. The difficulty addressed by this note is not the rule.

A diagnostic

Where the loan coupon r is set below the instrument coupon c, the subscriber’s net position is

This inverts the ordinary reading of a subsidised lending rate. The subscriber is not being financed on favourable terms. The subscriber is being paid to hold the issuer’s capital. COMPUTED

The diagnostic is offered as a screen, not a proof. A subscriber may hold cheap funding from an unrelated source; the test flags a case for the register join in §7 rather than settling it. OPEN

Why every leg passes review

The structure is not concealed from reviewers. It is decomposed among them.

• Advance rates are conventional. A credit committee reviewing T₂ alone sees a well-secured facility.
• Collateral is high-quality and independently custodied. Third-party custody satisfies the operational control test and creates a strong appearance of arm’s-length security.
• The trade has commercial substance. Goods exist, ship and are sold. There is no fictitious trade — the failure mode trade-finance controls are principally built to catch.
• Pricing is administered. Because the rate is set centrally, the lending branch has no pricing discretion and therefore no natural occasion to raise a risk-adjusted-return objection. The control that would ordinarily surface mispricing is removed by the instruction itself.
• No committee sees the circle close. The deposit, the advance, the subscription and the import undertaking are reviewed by different functions under different mandates.

Nomenclature as a routing failure

This is the finding the note exists to record.

Internally, structures of this kind are described as leverage — in the Portuguese-language institutional setting, alavancagem financeira. The description is accurate as to effect and misleading as to kind, and the difference decides who reads the file.

Leverage is a ratio question. Circularity is a numerator question. Calling the structure leverage routes it to reviewers least equipped to identify the defect — and those reviewers will correctly find the ratios satisfactory, because the ratios are satisfactory, conditional on a capital figure they did not compute and were not asked to test.

6.1 Two governance artifacts

An ethics finding without a compliance finding. Where an aggregate is recognised as objectionable, the recognition tends to be recorded in terms — not ethical, though legal — that create a record without triggering consequence. A compliance finding obliges notification, capital restatement and disclosure. An ethics finding obliges nothing. Its presence is evidence that the structure was seen, and that seeing it was insufficient.

Distributed approval. Collective authorisation is often advanced as evidence of soundness. It is a valid defence of every individual and no defence of the institution: distributed approval is the mechanism by which a structure no single officer would authorise alone becomes authorised by all of them. Committee review does not concentrate responsibility. It dilutes it until it is held nowhere.

Detection: the register join

No participant-level view reveals the structure. Detection requires the intersection of three registers ordinarily held apart:

1. The allocation list for the capital issuance — who subscribed, and in what size.
2. The consolidated exposure book, including offshore branch lending, matched to those subscribers.
3. The collateral register, identifying instruments pledged back to their own issuer.

Where a name appears in all three, in comparable size, within a short window, the circularity is visible immediately. Where the registers are not joined, it is invisible indefinitely.

This control is not known to be implemented in any supervisory regime. OPEN Establishing whether some jurisdiction already runs an equivalent join is the obvious next step and has not been done here.

What this note does not establish

Stated plainly, in keeping with the series’ practice of marking the limits of its own claims.

• No transaction is identified, and none is alleged. The structure is stylized and the parameters are chosen to make the arithmetic legible. Nothing here should be read as a finding about any institution, instrument or person.
• The Λ result is conditional on the instrument being own funds. Applied to senior paper the proposition does not hold, and the transaction reduces to a wrong-way-risk problem of ordinary kind.
• Λ = 0 assumes the subscriber has no independent recourse capacity for the exposure. A subscriber with substantial unencumbered assets changes the result quantitatively; whether it changes it materially depends on recovery assumptions this note does not model. OPEN
• The routing claim in §6 is argued from mechanism, not measured. It predicts that misrouting by classification is observable in supervisory records; it does not present such records.
• No claim is made about frequency. That structures of this shape have occurred says nothing about how often, and this note offers no estimate.

Verification

Per the standing rule that a published figure must be produced by a tool, every number on this page is computed by book6/wp95-verify.py, which prints the parameter table, the wedge split, the multiplier, π and Λ.

The script runs a known-answer self-test before reporting anything, and refuses to continue if the fixtures fail. Three fixtures: the circular case (L = F, expect Λ = 0); an over-financed case (L > F, expect Λ < 0); and an honest control — an independently funded subscriber (L = 0, expect Λ = F > 0). The control is the one that matters. A metric that cannot distinguish genuine capital from circular capital would report zero on everything and look authoritative doing it.

This follows the practice established for the axiom gate, the conclusion scan and duplicates.py: an instrument with no known-answer case is not known to work.

Parameters

References and continuity

1. Basel Committee on Banking Supervision. Basel III: A global regulatory framework for more resilient banks and banking systems (rev. June 2011), and the consolidated framework’s criteria for own-funds eligibility — source of the prohibition on instruments financed directly or indirectly by the issuing institution. CHECKED
2. Basel Committee on Banking Supervision. Credit risk mitigation: eligibility conditions excluding obligor- and issuer-related collateral. Source of the wrong-way-risk treatment in §2.3.
3. WP-80 · The Theorem and the Reader — establishes the general problem of a claim reaching a reader whose competence does not match it. This note is the same problem inside an institution rather than a literature.
4. WP-91 · A Theorem Twenty-Seven Characters Long — an instrument scoring a claim correctly against the wrong criterion. The registry badge and the balance-sheet committee fail in the same way.
5. WP-94 · One Hole, Five Words — five communities, five words, one object. This note is the converse case: one word, two objects, and the word selects the reviewer.