The Global-Dollar & Digital-Money Frontier

Finance-Plus Ring · Branch MS (Money & Monetary Systems) · Node MS1.04 · CROWN · ~20 focused hours · Mastery gate ≥ 90%

This Ring is additive institutional/CFA breadth, it presents the toolkit and the plumbing alongside, not in place of, the program's process-over-P&L, concentration-over-diversification philosophy.

Roughly nine and a half trillion dollars of foreign exchange changed hands on an average day in April 2025, and the US dollar was on one side of 89% of it (BIS, Triennial Central Bank Survey, September 2025). Almost none of that dollar activity happened inside the United States, almost none of it was created by an American bank, and a very large share of it was not a trade at all but a loan wearing a trade's clothing. Meanwhile more than fourteen trillion dollars of gross settlement obligations came due each day, about ten percent of them settled with no protection whatsoever against the possibility that the other side takes your currency and never delivers theirs (BIS, Quarterly Review, June 2026).

This is the plumbing, where the money system actually is, as distinct from where the news says it is. It is the crown of the money track for a reason that becomes the module's spine: every one of these arrangements is a balance sheet, and you understand it exactly when you can say who owes what to whom, whose balance sheet expands, and what happens at the moment of settlement. A eurodollar is not "a dollar held overseas"; it is a dollar-denominated deposit liability of a bank outside the United States. An FX swap is not "a currency trade"; it is a collateralised loan whose repayment obligation is legally a forward contract and therefore appears in no debt statistic on earth. A CBDC is not "digital money", deposits have been digital since the 1970s, it is a central-bank liability held directly by someone previously not allowed to hold one. A stablecoin is not a dollar; it is an unsecured claim on a private issuer, collateralised by assets you cannot attach, redeemable on terms the issuer sets. Get the balance sheet right and the headlines become readable. Get it wrong and you will be fluent, confident and useless.

The whole module in one sentence: money is a hierarchy of promises, and every question in global finance (who funds whom, who fails first, what a settlement system is for, what a digital currency changes) is a question about which promise sits above which, and what happens at the moment one is exchanged for another.

A standing warning, stated once and meant. This region is the corpus's highest AI-over-trust risk, and it is worse here than in any pricing module. In FI1.04 a wrong option-adjusted spread is at least a number, and a reader can demand the tree that produced it. Here the wrong answers are sentences, fluent, plausible, superficially expert sentences about how the eurodollar market works, what CLS does, why the basis is negative, whether a stablecoin is "fully backed", with no arithmetic on the page to check. An AI will tell you, confidently, that the Fed can supply eurodollars directly, that a CCP eliminates risk, that an FX swap and a cross-currency swap are the same instrument, that a 100%-reserved stablecoin cannot break the buck, and that a wholesale CBDC is a new kind of money. Every one is wrong, every one is a common professional error, and every one reads beautifully. Read §5.11 before you let a model near any of this.

Learning objectives

By the end you can:

1. Define the eurodollar/offshore-dollar system as a balance-sheet fact (a dollar deposit liability of a bank outside the United States) and trace, T-account by T-account, how an offshore bank creates dollar credit without any US bank's balance sheet growing and without a reserve moving at the Federal Reserve. Compute the offshore credit multiplier and say what constrains it now that US reserve requirements are zero.
2. Decompose an FX swap into its two legs and re-read it as a collateralised loan, who lends, who posts collateral, whose balance sheet expands, and why the repayment obligation is invisible to every published debt statistic. Size the market from the BIS's own numbers.
3. Work covered interest parity forward and backward with correct day counts, price a forward from two money-market rates, invert a market forward into an implied funding rate, compute the cross-currency basis in basis points, sign it correctly, convert it into dollars of cost, and explain from balance-sheet costs why the arbitrage that "should" close it does not.
4. Explain the global dollar backstop (swap lines and the FIMA repo facility) as balance-sheet operations: who takes FX risk, who takes credit risk, which balance sheets expand, and why the facility exists given that the Fed cannot lend eurodollars directly.
5. Size Herstatt (principal) settlement risk against replacement-cost risk, explain the time-zone mechanism that creates it, describe how payment-versus-payment kills it, read the BIS's 2025 settlement measures, compute netting compression, and say why the rupee's absence from CLS forces a domestic answer.
6. Explain novation, multilateral netting and the CCP default waterfall, compute the compression a CCP achieves over bilateral netting, walk a default down the waterfall to the last rupee, and state the honest trade, a CCP does not remove risk, it concentrates and mutualises it.
7. Compute the settlement-cycle arithmetic of T+1: why margin scales with the square root of the horizon, what a one-day cycle releases, what it costs in FX funding and pre-funding, and situate the US (Rule 15c6-1, 28 May 2024) and Indian (SEBI T+1 from 27 January 2023; optional T+0) timelines.
8. Distinguish retail from wholesale CBDC on the only axis that matters (who may hold the central bank's liability) read the two-tier distribution model, and compute the disintermediation and liquidity-coverage consequences of a retail conversion, including the design levers that bound it.
9. Read a stablecoin as a balance sheet and stress it: reserve composition, attestation versus audit versus a fund's holdings disclosure, the redemption-liquidity tests a US government money market fund must pass and a "fully reserved" token need not, who earns the reserve income, and how to price an observed depeg into known impairment plus run premium.
10. Situate monetary regimes (the trilemma, the "dilemma," the de facto taxonomy, managed floats, intervention and sterilisation arithmetic) and place every digital innovation correctly on that map: new rails do not change the regime unless they change who issues the unit of account.
11. (Productivity objective: R10 duality.) Use AI and code to pull, normalise and reconcile plumbing data while running the verification that makes the output admissible, and know why unverified AI output about mechanisms is more dangerous here than unverified output about numbers anywhere else.

The duality, stated once (R10). Items 1–10 are the understanding objective the gate rewards; you earn the crown by drawing the balance sheets and doing the arithmetic yourself. Item 11 is the productivity payoff. The duality is sharper here than anywhere else in the program: elsewhere a wrong AI output is a wrong number, and a number can be recomputed; here it is a wrong story about how a system works, and a story can only be checked against a primary source that describes the mechanism. Verification in this module is bibliographic as much as arithmetic: name the document, cite the paragraph, then compute.

Prerequisites & connections

Builds on. This is the crown of the MS branch and assumes the branch entire. MS1.01 gave you the hierarchy of money, the aggregates, and the fact that bank lending creates deposits, every balance sheet here is that fact applied offshore. MS1.02 gave you the payment rails (RTGS/Fedwire, ACH/NACH, UPI, cards, correspondent banking with nostro and vostro accounts); you must be able to trace a payment before you can be told what settlement risk is. MS1.03 gave you central-bank operations, reserves and IORB, repo and the collateral complex, and money market funds, the stablecoin section is a direct application of the MMF material, the swap-line section of the reserve-supply material. From the core: M7.01 (endogenous money), M7.02 (central-bank toolkit), M7.03 (the curve), M7.06 (the FX/eurodollar macro view this node turns into plumbing), M5.01/M5.02 (how banks and NBFCs fund themselves). From this Ring: FI1.03 (bootstrapping, and the discipline that a curve must reprice its own instruments), DV1.01 (forward pricing, of which CIP is the FX case), AL1.03 (digital assets as an asset class).

Deliberate non-overlaps (R1). We do not re-teach the hierarchy of money or money creation (MS1.01), the domestic payment rails or correspondent-banking mechanics (MS1.02), central-bank balance-sheet reading, repo mechanics, haircuts or MMF structure (MS1.03), the macro narrative of dollar cycles (M7.06), bank capital regulation (M5.01), forward pricing from first principles (DV1.01), or crypto-assets as a portfolio holding, correlation, sizing, the asset-class case, the Indian VDA tax regime (AL1.03 owns all of that; the seam is exact: whose balance sheet and how does it clear is this node, what does holding it do to a portfolio is AL1.03). New here and owned nowhere else: the offshore-dollar balance sheet, FX-swap funding and the basis, PvP and settlement risk, CCP mechanics, settlement-cycle compression, CBDC design, the stablecoin-versus-MMF comparison, and the regime map that situates them all.

Feeds forward. FI1.01–FI1.04 price bonds off curves whose short end is set in the funding markets described here. DV1.01's FX forward pricing is §5.3 in one equation. AA1.01–AA1.03 inherit currency-hedging cost as a computable drag on an international allocation, the basis is the part of that drag no return forecast contains. PW1.03 and AL1.02 meet cross-border settlement whenever an asset is bought in another currency. ES1.02 owns the regulatory map in general; this node's regulatory content is its payments-and-settlement instance. And every module quoting a "market" number about the dollar system inherits this node's rule: name the BIS table, or do not quote the number.

Case Lab context. The MS branch's two live Case Labs sit upstream. Follow the Payment: a Cross-Border Remittance (MS1.02) and A Repo Run in 72 Hours (MS1.03). Run both first; this node assumes you can trace a payment leg and read a repo book unprompted.

The one-sentence version. Offshore, the dollar is created by banks that no US authority licenses and no US backstop directly reaches; it is funded overwhelmingly through FX swaps, whose price deviates from covered interest parity by a basis measuring how scarce dollars are and how expensive balance sheet is; the resulting obligations settle through systems built to eliminate the possibility that one side pays and the other does not. PvP for currencies, central counterparties for cleared trades, ever-shorter cycles for securities; and the digital innovations of the last decade are all attempts to change the rails on which those promises move, which changes the regime only where it changes who issues the unit of account.

Core teaching content

5.0 The one-page map: five questions any monetary arrangement must answer

Every arrangement in this module (a eurodollar deposit, an FX swap, a CLS settlement, a CCP trade, a CBDC wallet, a stablecoin) can be interrogated with the same five questions, and if you cannot answer all five you do not understand it.

1. Whose liability is it? Central bank, commercial bank, private non-bank issuer, or nobody's. This sorts the entire hierarchy of money and is the question non-specialists never ask.
2. What is it a promise to deliver, and on what terms? At par? On demand? Subject to a gate, a minimum size, a business-day calendar, a discretionary fee?
3. Whose balance sheet expands when it is created? Somebody's must, an asset and a liability appear together, always. Name them.
4. What settles it, and when is that settlement final? Finality is a legal state, not a technical one: the point after which the transfer cannot be reversed even by a participant's insolvency. Between execution and finality, someone bears principal risk.
5. Who is the backstop, and can they reach this instrument? A central bank can create its own liability without limit. It cannot create another central bank's liability at all. That asymmetry is the source of half the crises in this module.

Run those over a bank deposit and you get the familiar answer: a commercial bank's liability, payable in central-bank money on demand at par, created when the bank lends, settled finally across the central bank's books, backstopped by deposit insurance and the discount window. Every arrangement below is a deviation from that answer, and the deviation is where the risk lives.

5.10 Monetary regimes situated: the trilemma, the dilemma, and where the new rails actually sit

The trilemma (the impossible trinity). From Mundell–Fleming: a country may choose at most two of (a) a fixed exchange rate, (b) free capital mobility, (c) an independent monetary policy. The mechanism: if capital moves freely and you fix the rate, any attempt to set a domestic rate different from the world rate invites arbitrage flows that force you to buy or sell foreign currency without limit, changing your monetary base until your rate is dragged back. You may abandon the peg (float, keep independence), abandon capital mobility (controls, keep peg and independence), or abandon independence (currency board, dollarisation, monetary union).

The dilemma. Hélène Rey's refinement (Jackson Hole, 2013) argues that under genuinely free capital mobility a floating rate does not deliver full monetary independence, because the global financial cycle (driven substantially by US monetary policy and global risk appetite) transmits into domestic credit conditions regardless of regime. On that reading the choice collapses to a dilemma: free capital mobility or monetary independence. This is not settled; knowing that it is live is itself part of the competence.

The regime taxonomy. The IMF's Annual Report on Exchange Arrangements and Exchange Restrictions classifies regimes by de facto behaviour rather than announcement, the correct discipline. Ascending flexibility: no separate legal tender (dollarisation, monetary union), currency board, conventional peg, stabilised arrangement, crawling peg / crawl-like, pegged within bands, other managed arrangement, free floating. India's stated framework is a market-determined rate with RBI intervention to contain excessive volatility, without a target level, which de facto methodologies have generally classified in the managed/stabilised region rather than as a free float, and the discrepancy between stated and classified regime is exactly what an analyst should notice.

Intervention and sterilisation, in arithmetic. A managed float is not free. Suppose the RBI buys $5 billion to lean against appreciation at 86.40. It pays with newly created rupees: ₹43,200 crore of reserve money enters the system as a by-product of an exchange-rate operation. Left alone, at a 4% cash reserve ratio that base could support up to ₹10,80,000 crore of deposits if fully lent, a monetary expansion nobody chose. So the central bank sterilises, draining the rupees through open-market sales, reverse repo or a dedicated instrument. Sterilisation carries a cost: the bank now holds dollar assets yielding, say, 4.30% while paying, say, 6.40% on the rupee liabilities issued to drain the liquidity, a negative carry of ₹907 crore per year on this one operation. That is the price of the trilemma, paid annually, and why "just intervene" is never free. (MS1.03 owns the domestic liquidity-operation mechanics; this is the FX-side application.) Reserves themselves are the buffer: at $700 billion against $60 billion of monthly imports, 11.67 months of import cover, read the current level from RBI's Weekly Statistical Supplement, never a headline.

Now place the digital innovations on this map. A retail CBDC changes who may hold the central bank's liability. A wholesale CBDC changes the format in which institutions settle. A tokenised unified ledger changes what can settle atomically against what. A CCP changes who your counterparty is. T+1 changes when finality arrives. None changes the trilemma, because none changes who issues the unit of account or how freely capital may cross the border. They are changes to the rails.

There is exactly one case where the rails change the regime, and it is the one worth watching: when a foreign-currency instrument becomes a convenient domestic medium of exchange. A dollar stablecoin that residents of a high-inflation economy can hold and spend on a phone is not a new payment rail; it is digital dollarisation, and dollarisation is a regime change, the country gives up seigniorage, lender-of-last-resort capacity in the circulating currency, and the monetary-independence corner of the trilemma, without any authority deciding to. That is the substantive concern behind much official-sector caution about foreign-currency stablecoins in emerging markets; it is coherent, testable, and entirely different from, and far more serious than, the retail-payments arguments that dominate the coverage.

5.11 R10: why this region is the corpus's highest AI-over-trust risk

In a pricing module an AI's error is a number, and numbers are falsifiable: a wrong option-adjusted spread is caught by demanding the tree, a wrong IRR by re-running the cash flows. Here the AI's error is a mechanism (a sentence about how a system works) and a wrong mechanism is not falsifiable by arithmetic. It is falsifiable only by a document, and a model will happily produce a plausible mechanism with a plausible citation attached.

The specific inventory of confidently-wrong sentences this region produces. Every one is common, every one reads well, every one is false:

1. "The Fed can supply eurodollars directly." No, a eurodollar is another bank's liability; the Fed can only supply reserves to institutions with Fed accounts, which is why swap lines and FIMA exist (§5.1, §5.4).
2. "An FX swap is a currency trade, not borrowing." It is a collateralised loan whose repayment obligation is recorded as a near-zero-value derivative and appears in no debt statistic (§5.2).
3. "An FX swap and a cross-currency swap are the same thing." Different tenors, cash-flow structures and markets (§5.2).
4. "A CCP eliminates counterparty risk." It transforms it into concentrated, mutualised, margined exposure to the CCP, with a waterfall that reaches surviving members (§5.6).
5. "A negative basis means the euro is weak." The basis is a funding price, not a directional view; it can be deeply negative with the euro rising (§5.3).
6. "CLS eliminates FX settlement risk." Only for the trades it settles in the currencies it supports, per the BIS's April 2025 measures, 40% of CLS-eligible-pair obligations, leaving $1.4 trillion a day settling with no mitigation (§5.5).
7. "A CBDC expands the central bank's balance sheet." Issuing retail CBDC against reserves changes the composition of central-bank liabilities, not the total (§5.8).
8. "A wholesale CBDC gives banks access to central-bank money." Banks already have it; it is called reserves. The novelty is the tokenised format and atomic settlement (§5.8).
9. "A 100%-reserved stablecoin cannot break the buck." Full reserving is a solvency claim; runs are a liquidity event, and a fully reserved token can fail both of Rule 2a-7's liquidity tests (§5.9).
10. "An attestation means the reserves were audited." An attestation is a point-in-time report on management's assertion; an audit is an opinion on financial statements over a period (§5.9).
11. "T+1 reduced risk with no downside." It transferred operational and funding risk to cross-border investors, compressing the CLS window from 26 hours to 2 (§5.7).
12. "India has a free-floating rupee." The stated framework is intervention against volatility without a level target, and de facto classifications have generally placed it in the managed region (§5.10).

The rule is procedural, not attitudinal: in this region, no mechanical claim enters your work until you have opened the primary document that states it. BIS statistical releases and Quarterly Review articles for eurodollars and the basis; CLS's and CCIL's own published descriptions and the BIS CPMI reports for settlement; the SEC rule and the SEBI circular for settlement cycles; the central bank's concept note and FAQ for CBDC; the statute and the issuer's own attestation for stablecoins. The Primary-Source Guardrail's five checks (Trace, Match, Recompute, Date-check, Cite) apply as elsewhere, with one addition specific to plumbing: Match includes matching the jurisdiction and the vintage of the design, a 2021 pilot's rules are not a 2026 system's rules, and a US rule is not an Indian rule.

Common mistakes & how experts think differently

1. Treating "eurodollar" as a location rather than a balance sheet. The novice says "dollars held abroad." The expert says "a dollar-denominated deposit liability of a non-US bank office" and immediately derives the consequences: no Fed access, no FDIC insurance, no reserve requirement, credit created by loans-create-deposits, and a backstop gap that swap lines exist to fill. The definition does all the work.

1. Missing that an FX swap is debt. Because the far leg is booked as a derivative at fair value (about zero at inception) an enormous, short-dated, rollover-dependent dollar obligation appears in no debt statistic. The BIS's estimate is $26 trillion for non-US non-banks alone, twice their on-balance-sheet dollar debt. The expert's habitual question when reading any leverage analysis of a non-US financial institution: what is the off-balance-sheet FX-swap obligation, and where would I even find it?

1. Conflating FX swap, currency forward and cross-currency swap. Three instruments, priced differently, used differently, reported differently. Assume any source that uses them interchangeably has not checked anything else either.

1. Reading the cross-currency basis as a currency view. It is a funding price (the premium for dollars obtained synthetically rather than borrowed directly) driven by dollar scarcity and by the cost of the balance sheet needed to arbitrage it, which is why it spikes over quarter- and year-ends for reporting reasons and snaps back. The expert reads a widening negative basis as "dollar funding is getting expensive," checks for a turn-of-period artefact, and never as "the euro is going down."

1. Confusing settlement risk with market risk. Replacement-cost risk is a percentage of notional; principal (Herstatt) risk is the whole notional: 66.7 to 1 in Worked Example 4. The entire architecture of PvP, DvP and CCPs exists to convert the second into the first.

1. Believing a CCP removes risk. It concentrates and mutualises it: a surviving member with no exposure to the defaulter still takes a pro-rata hit: ₹162.50 crore in Worked Example 5. The sophisticated questions are how deep the prefunded waterfall is relative to the largest members' positions, whether the CCP meets "cover 2," how procyclical the margin model is, and what the assessment rights are.

1. Confusing solvency with liquidity in stablecoin analysis, the oldest error in banking. "Fully backed" is a solvency statement; a run is a liquidity event. A 100%-reserved token can fail both of Rule 2a-7's liquidity floors, and its liabilities trade 24/7 while its assets settle on a banking-day calendar. Every bank that ever failed while solvent failed for this reason.

1. Confusing an attestation with an audit, and a snapshot with an average. A 100%-reserved snapshot is fully consistent with 95% average coverage across the quarter if the balance is dressed for the reporting date. The expert reads the as-of date and the engagement scope before the numbers.

1. Calling any digital thing "new money." Reserves and deposits are digital. What is new about a retail CBDC is who may hold a central-bank liability; about wholesale CBDC, the settlement format. Reach for the balance sheet and the holder class, not the technology stack.

1. Assuming the rails change the regime. New settlement technology does not touch the trilemma. The single exception, a foreign-currency stablecoin becoming a convenient domestic medium of exchange, i.e. digital dollarisation, is a regime change, and it happens by adoption rather than by decision.

1. Quoting a market aggregate without naming the table. The BIS publishes several overlapping measures: daily turnover from the Triennial, outstandings from the semiannual OTC statistics, settlement obligations from the settlement survey, credit from the global liquidity indicators. April 2025 turnover was $9.6 trillion a day and settlement obligations more than $14 trillion a day, and both are correct, because a trade generates obligations in two currencies and the surveys have different scopes. The expert never quotes one as the other and always names the release.

The thread through all eleven: the expert reasons from the balance sheet and the legal claim, and treats the label as a hint rather than a fact.

Worked examples

Worked example 1: A eurodollar is created, and no American balance sheet grows (US $)

Grupo Andino S.A. (synthetic) holds a $500 million demand deposit at a New York bank. Seeking a better rate it moves the money to London Merchant Bank plc (synthetic), a non-US bank with no Federal Reserve account, as a 90-day dollar time deposit. LMB then lends $400 million to Nihon Shosha K.K. (synthetic), keeping 20% of its dollar deposits as correspondent balances.

Solution. Step 1, the deposit moves. The New York bank debits Grupo Andino and credits LMB's correspondent (vostro) account. The New York bank's balance sheet is unchanged in total, same $500m of deposit liability, different owner, and no Fed reserves move, because both parties bank at the same institution.

Step 2: LMB's balance sheet expands. LMB books an asset of +$500m (its nostro claim on the New York bank) and a liability of +$500m (the time deposit). Its balance sheet grew by $500m out of nothing but the willingness of two parties to deal. A dollar deposit now exists that did not exist before, issued outside US jurisdiction. That is a eurodollar, and it is the entire definition.

Step 3, the loan creates a second deposit. LMB lends $400m to Nihon Shosha by crediting its account: asset +$400m (loan), liability +$400m (deposit), taking LMB to $900m a side. When Nihon Shosha draws the money, LMB instructs the New York bank to transfer $400m to the supplier's bank: LMB's nostro falls to $100m and the deposit liability to zero, leaving $500m ($100m nostro + $400m loan) against $500m. The 20% retained is exactly the $100m correspondent balance.

Step 4: system-wide. If every offshore bank behaves this way, 500 + 400 + 320 + 256 + 204.8 + … converges to 500 ÷ 0.20 = $2,500 million of offshore dollar deposits, of which $2,000 million is credit. At a 10% ratio: $5,000m and $4,500m; at 5%: $10,000m and $9,500m.

Read it. (a) Total US bank deposits never changed; Fed reserves never changed; dollar credit grew by $2,000m, any story about "the money supply" that looks only at domestic aggregates is blind to this. (b) The ratio r is not a legal reserve requirement: US requirements on Eurocurrency liabilities went to zero on 27 December 1990 and all US ratios went to zero effective 26 March 2020 (Federal Reserve Board, Reserve Requirements). What binds is prudence, capital, liquidity rules and rollover capacity. (c) Ask question 5: if Grupo Andino wants its $500m back before the loan matures, LMB must find $400m of dollars it cannot print, from a lender it must persuade, in a currency whose central bank does not bank it. That is every dollar-funding crisis of the last fifty years in one sentence.

Worked example 2: Covered interest parity and the cross-currency basis, to the basis point (US $ / EUR)

Take spot S = 1.0850 USD per EUR; 91 days; 3-month USD OIS 4.30% and EUR OIS 2.05% (both ACT/360); market 3-month outright forward F_mkt = 1.0917.

Solution. Step 1: day count. τ = 91/360 = 0.2527778 for both legs.

Step 2, the CIP forward. 1 + r_USD·τ = 1.0108694; 1 + r_EUR·τ = 1.0051819. So F_CIP = 1.0850 × 1.0108694 / 1.0051819 = 1.091139, i.e. 61.39 pips of premium on the euro. Sanity-check: dollar rates are higher, so the dollar trades at a forward discount, more dollars per euro forward than spot. It does.

Step 3: prove no-arbitrage at F_CIP. Start with €1. Route A: invest euros to €1.0051819, sell forward at 1.091139 → $1.0967933. Route B: convert to $1.0850, invest → $1.0967933. Identical to ten decimals. That identity is CIP; rebuild it and you never need to memorise the formula.

Step 4, the basis. The market forward at 1.0917 is 67.00 pips, 5.61 pips richer than CIP. Solve F_mkt · (1 + (r_EUR + x)·τ) = S · (1 + r_USD·τ): x = [S·(1 + r_USD·τ)/F_mkt − 1]/τ − r_EUR = −0.002043 = −20.43 basis points.

Step 5, the same fact as a funding rate. r_USD_implied = [(F_mkt/S)·(1 + r_EUR·τ) − 1]/τ = 4.5056% against a 4.30% dollar OIS, a 20.56 bp premium for obtaining dollars synthetically. (The 20.43 and 20.56 differ only by the (1 + r_EUR·τ) scaling between conventions; both are correct, and quoting one while labelling it the other is a standard desk error.)

Step 6: money. On $1 billion for 91 days the 20.56 bp premium costs $519,614; the pure basis component is $516,425.

Read it. The negative basis says dollars are scarce relative to euros in the swap market, a price, observable in real time, of a condition no macro narrative pins down as precisely. The arbitrage that should kill it: borrow $1bn unsecured at 4.30%, buy euros, invest at 2.05%, sell forward at 1.0917, receive $1,011,389,059, owe $1,010,869,444, a riskless $519,614. It persists because the trade consumes gross balance sheet the leverage ratio charges capital against, because CVA/FVA price the counterparty and funding legs, and because at quarter-end balance sheet is not available at any price (Du, Tepper and Verdelhan, 2018).

Worked example 3: The rupee forward premium and the onshore–offshore wedge (India ₹)

Take S = 86.40 INR per USD; 91 days; onshore 3-month forward points 42 paise; USD rate 4.30% (ACT/360); offshore NDF 86.95.

Solution. Step 1: day counts, carefully. USD is ACT/360: τ_USD = 0.2527778. INR is ACT/365: τ_INR = 0.2493151. Using 360 for the rupee leg is a common error worth about 1.4% of the rupee rate.

Step 2, the outright and the implied rupee rate. F = 86.40 + 0.42 = 86.82. Invert CIP: r_INR = [(F/S)·(1 + r_USD·τ_USD) − 1] / τ_INR = [(86.82/86.40)(1.0108694) − 1]/0.2493151 = 6.3307%.

Step 3, the annualised premium, and why it is not the differential. Market convention: (F − S)/S × 365/d = (0.42/86.40) × (365/91) = 1.9498% p.a. But the implied differential is 6.3307% − 4.30% = 2.0307 percentage points. These are not the same number, and the ~8 bp gap is real: the premium is a ratio of a price difference to spot, the differential compares two rates on different day-count bases with a compounding term between them.

Step 4, the offshore wedge. An NDF at 86.95 implies r_INR_offshore = 6.9408%, a 61.01 bp wedge, equivalent to 0.13 rupees of forward points. On $100 million that is ₹1.30 crore of raw pickup.

Read it. In a fully open market that 61 bp would be arbitraged away in minutes. It survives because the rupee is not fully convertible on the capital account: the onshore forward requires an underlying exposure and a domestic banking relationship, while the NDF is a cash-settled offshore contract in which no rupee is delivered. The two pools price the same risk under different access rules, and the wedge measures the price of the boundary, narrowing when the boundary is made more permeable (as when the RBI permitted banks with IFSC Banking Units into the NDF market from 1 June 2020) and widening in stress, which is why it is among the most-watched indicators of pressure on the rupee. All levels here are stated inputs; the market levels of the day must be read from FBIL/CCIL publications, never assumed.

Worked example 4: Herstatt risk sized, then killed by PvP (US $ / JPY)

A dealer sells $100 million against yen at 150.00, so the yen leg is ¥15,000,000,000. The yen leg settles across BOJ-NET, final at 15:00 Japan Standard Time; the dollar leg across Fedwire, final at 18:00 New York time the same calendar day.

Solution. Step 1, the time-zone gap. JST is UTC+9, so 15:00 JST is 06:00 UTC; New York summer time is UTC−4, so 18:00 ET is 22:00 UTC. The yen payer has paid and not been paid for 16 hours.

Step 2, size the two risks side by side. Failure before settlement costs replacement value: at a 1.5% adverse move, $1,500,000. Failure inside the window costs the entire principal delivered: $100,000,000: 66.7× larger. This is why Herstatt risk is categorically different, and why the 1974 failure. Bankhaus Herstatt's licence withdrawn at 15:30 CET, 10:30 in New York, with dollar legs unsettled, reshaped the settlement architecture (BIS CPSS, Settlement risk in foreign exchange transactions, 1996).

Step 3, PvP removes the window, not the trade. Under payment-versus-payment the yen leg is final if and only if the dollar leg is final. The 16 hours become zero: not shorter, but structurally absent.

Step 4, netting, the second reason PvP utilities exist. Suppose the day's book with one counterparty is USD +250m, −180m, +95m, −220m; JPY −37,500m, +21,000m; EUR +140m, −165m. Gross pay-and-receive, valued in dollars at 150.00 and 1.0850, is $1,465.93 million. Netting per currency gives USD −55m, JPY −16,500m ($110.00m) and EUR −25m ($27.12m): total $192.12 million, an 86.89% compression. Extend that multilaterally across seventy-plus members and eighteen currencies and you get CLS's published claim that it shrinks funding requirements by over 96%: on over $8.0 trillion settled daily, pay-ins are under $320 billion.

Read it. One machine delivers two separate goods, and you should never conflate them: PvP kills principal risk; netting kills funding need. The residual matters, per the BIS's April 2025 measures, of more than $14 trillion of daily obligations, $5.157tn (36%) settled PvP, $4.950tn (35%) intragroup, $2.167tn (15%) compressed by pre-settlement netting to just $337bn (an 84.45% compression, 6.43-to-1), $496bn (3%) with timing controls, and $1.416tn (10%) gross bilaterally with no mitigation at all. Only 40% of CLS-eligible-pair obligations actually used PvP. Herstatt risk is reduced, not solved.

Worked example 5: Multilateral netting and a default waterfall, to the last rupee (India ₹)

Five clearing members (Arka, Bharati, Chandra, Dweep and Eshan (all synthetic)) end the day with fifteen bilateral obligations (₹ crore): Arka owes Bharati 1,200, Chandra 800, Dweep 450; Bharati owes Arka 950, Dweep 600, Eshan 1,100; Chandra owes Arka 700, Bharati 380, Eshan 520; Dweep owes Chandra 640, Eshan 910, Arka 300; Eshan owes Bharati 870, Chandra 410, Dweep 760. Then Dweep defaults, leaving a close-out loss of ₹1,850 crore.

Solution. Step 1: gross. Sum the fifteen legs: ₹10,590 crore must move if everything settles gross.

Step 2: bilateral netting. Offset each pair: Arka–Bharati 250, Arka–Chandra 100, Arka–Dweep 150, Bharati–Dweep 600, Bharati–Eshan 230, Chandra–Bharati 380, Chandra–Eshan 110, Dweep–Chandra 640, Dweep–Eshan 150. Total ₹2,610 crore, a 75.35% compression.

Step 3: multilateral netting through a CCP. Each member's net position against the CCP: Arka −500, Bharati −200, Chandra +250, Dweep −40, Eshan +490. (They sum to zero, the arithmetic check you must always run; if they do not, your matrix is wrong.) Only the debits need funding: 500 + 200 + 40 = ₹740 crore: 93.01% compression against gross, and a further 71.65% reduction against bilateral netting.

Step 4, the default waterfall.

Step 5: allocate the mutualised loss. Utilisation is 650/4,200 = 15.4762%. Pro rata on contributions: Arka (₹1,050 cr) → ₹162.50 cr; Bharati (₹1,260 cr) → ₹195.00 cr; Chandra (₹840 cr) → ₹130.00 cr; Eshan (₹1,050 cr) → ₹162.50 cr, summing to ₹650.00 crore.

Read it. (a) Dweep's own resources covered (900 + 180)/1,850 = 58.38% of the loss it caused: initial margin alone 48.65%, which is what "margin sized to a close-out estimate" means when the estimate is exceeded. (b) Total prefunded resources of ₹5,400 crore were 2.92× the realised loss: the system is designed with wide cover, and that cover is what members pay for. (c) Chandra had a positive net position and no relationship with Dweep, and still lost ₹130 crore, that is mutualisation, and anyone who says "a CCP eliminates counterparty risk" has never done this arithmetic. (d) The CCP's skin-in-the-game sits ahead of members deliberately, so the entity setting the margin model has its own capital at stake first. India's CCIL operates as a Qualified Central Counterparty under RBI regulation and publishes PFMI disclosures against CPMI-IOSCO's Principles for Financial Market Infrastructures (2012), whose Principle 4 sets the "cover 2" standard.

Worked example 6: T+1: the margin released, and the FX window destroyed (US $ / India ₹)

A clearing house holds a $500 million gross position against a member. Daily volatility is 1.10%; margin is set at 99% one-tailed (z = 2.326) over the close-out horizon.

Solution. Step 1: margin at each horizon. Potential move = z · σ · √h. Two days: 2.326 × 0.0110 × √2 = 3.6184%. One day: 2.5586%. The ratio is 1/√2, so the reduction is 29.29%, depending on nothing but the square-root-of-time rule, which is why it recurs in every settlement-cycle impact study.

Step 2: money. $500,000,000 × 3.6184% = $18,092,034 at T+2; $12,793,000 at T+1; $5,299,034 of collateral released.

Step 3, the cost, on the FX side. CLS's submission deadline is 00:00 CET on value date; CET is six hours ahead of US Eastern winter time, so that is 18:00 ET on the previous calendar day. A European fund executing a US equity purchase at 16:00 ET on trade date T:

A 92.3% compression of the operational window for a trade otherwise unchanged. The three responses are all costly: execute the FX earlier (losing the ability to match the exact executed quantity, creating a residual); settle the FX bilaterally outside PvP (reintroducing Worked Example 4's Herstatt exposure); or pre-fund.

Step 4: price the pre-funding. One extra day on a $50 million ticket at 4.30% ACT/360 is $5,972.22. On a $2 billion fund turning over 80% annually: $1.6 billion of purchases, the annual cost is $191,111, or 0.956 basis points of AUM, every year. A $40 million fail for three days at 4.30% is $14,333 of pure funding.

Read it. The regimes: the SEC amended Rule 15c6-1 from T+2 to T+1 with a compliance date of 28 May 2024, alongside Rule 15c6-2 (same-day allocation, confirmation, affirmation) and a Rule 204-2 recordkeeping amendment. India got there first: SEBI phased T+1 from 25 February 2022, complete by 27 January 2023, and introduced an optional T+0 beta cycle from 28 March 2024. Note the further arithmetic in the T+0 direction: moving from T+1 to an intraday (quarter-day) horizon scales margin by √0.25 = 0.50 (a further 50% reduction) while compressing the FX window to essentially zero, which is why same-day settlement is optional and why its first application is in a market with a domestic-currency investor base. The compression is genuinely good and the transfer of risk to cross-border participants is genuinely real; state both.

Worked example 7: A stablecoin reserve, stressed: attestation versus a 2a-7 fund (US $)

Anchor Dollar (ANCD) (synthetic) has $40,000 million of tokens outstanding against reserves of $32,000m Treasury bills (45-day weighted-average maturity), $5,600m overnight tri-party repo collateralised by Treasuries, and $2,400m of uninsured demand deposits across three banks.

Solution. Step 1, the headline everybody quotes. Reserves of $40,000m against $40,000m of tokens: 100.0000% reserved. Composition: 80.00% bills, 14.00% repo, 6.00% deposits. Every marketing statement stops here.

Step 2, apply Rule 2a-7's tests, which a regulated fund holding the same assets must pass. Daily liquid assets (cash, direct Treasury obligations maturing within one business day, same-day receivables) = repo + deposits = $8,000m / $40,000m = 20.00% against a 25% floor: fail, short $2,000m. Weekly liquid assets = the above plus government securities maturing within five business days; assume $2,000m of bills qualify, giving 25.00% against a 50% floor: fail, short $10,000m. WAM = 45 × 0.80 + 1 × 0.14 = 36.1 days, inside the 60-day limit: pass. So: fully reserved, short-duration, and not permitted to operate as a US government money market fund, because of liquidity, not credit or duration.

Step 3, a bank fails. One of the three banks holding $1,600m goes into receivership. Reserves fall to $38,400m; the arithmetically correct NAV is 38,400/40,000 = $0.9600, a 4.00% impairment.

Step 4, read the market price. The token trades at $0.8780, implying reserves of $35,120m, the market priced $3,280m of loss beyond the disclosure, 8.54% of the surviving reserve. Decompose: known impairment 4.00%, run premium 8.54% of what is left, total implied loss 12.20%. The run premium is the price of not knowing which remaining bank is next, whether redemptions will be honoured on Monday, and at what minimum size. This is the shape of the real reference episode: Circle disclosed on 10–11 March 2023 that $3.3 billion of USDC reserves remained at Silicon Valley Bank; USDC traded to roughly $0.87–0.88 and recovered when the deposits were made whole (Circle pressroom, March 2023; BIS Working Paper No 1164).

Step 5, the redemption stress, and the counter-intuitive result. A 25% redemption is $10,000m in a day. Same-day assets are repo $5,600m plus surviving deposits $800m = $6,400m, leaving a $3,600m shortfall to be met by selling bills. At a 15 bp yield concession on 45-day paper the price hit is 0.0015 × 45/360 = 0.0001875 = 0.018750%, a loss of $675,000: 0.17 basis points of tokens outstanding. The mark-to-market cost of the fire sale is negligible. The problem is entirely timing: the bills settle on a banking-day calendar and the tokens trade continuously on a chain that does not close for weekends. A stablecoin does not break because its assets fell in value; it breaks because its liabilities can run when its assets cannot be sold.

Step 6: snapshot versus average. The reserve report is an attestation: an accountant's report on management's assertion, as of one date. If $2,000m of the bill portfolio were financed only across the reporting date, the attested ratio would still read 100.00% while the ex-snapshot ratio was 95.00%. Nothing in the attestation is false; it certifies a moment. A 2a-7 fund files position-level holdings monthly on Form N-MFP and posts holdings and NAV to its website, a different quantum of transparency entirely.

Step 7: follow the income. Reserves of $40,000m at 4.30% earn $1,720.0 million a year, $0.0430 per token per year, and under the GENIUS Act's prohibition on paying yield the holder gets none of it. A government MMF passing 4.05% net would pay shareholders $1,620.0 million: 94.2% of the gross carry. For an individual holding $10,000 for ten years: $14,873.76 in the fund; $10,000.00 in the token. Forgone interest: $4,873.76.

Read it. The instrument is a narrow bank without a backstop whose economics transfer float income from holder to issuer, and whose failure mode is a liquidity–calendar mismatch that "100% reserved" says nothing about. None of that makes it useless, it settles fast, globally, at low cost, a genuine service. It does mean "fully backed" is a solvency claim answering a question nobody's run was ever about.

Worked example 8: Retail CBDC, three balance sheets and a liquidity ratio (India ₹)

Sahyadri Bank (synthetic) has ₹4,20,000 crore of deposits, of which ₹1,68,000 crore is retail CASA; ₹78,000 crore of high-quality liquid assets; and ₹60,000 crore of modelled 30-day net cash outflows. A retail CBDC launches with no holding cap and no remuneration, and 5% of CASA converts within a month.

Solution. Step 1, the starting ratio. LCR = 78,000 / 60,000 = 130.00%.

Step 2, the three balance sheets, which are the actual content. 5% of ₹1,68,000 crore is ₹8,400 crore, just 2.00% of total deposits.

• The household: −₹8,400 cr of bank deposit, +₹8,400 cr of e₹. Total unchanged; it has swapped a commercial-bank claim for a central-bank claim, moving up the hierarchy of money.
• Sahyadri Bank: −₹8,400 cr of deposit liability, settled by surrendering reserves: −₹8,400 cr of its current account at the RBI. Both sides shrink. It has lost cheap funding and HQLA in one movement, which is why the liquidity effect is worse than a naive reading suggests.
• The Reserve Bank of India: −₹8,400 cr of reserve liability to the bank, +₹8,400 cr of e₹-in-circulation liability to the public. The RBI's balance-sheet total is unchanged; only the composition of its liabilities changes. This is the single most-missed fact about CBDC and the cleanest test of whether someone has thought about it.

Step 3, the liquidity ratio. HQLA falls to ₹69,600 crore. Modelled outflows fall only by the run-off factor on the departed stable retail deposits, at 5%, 60,000 − 0.05 × 8,400 = ₹59,580 crore. New LCR = 69,600/59,580 = 116.82%: a 13.18 percentage-point fall from a 2% deposit movement, because the numerator takes the full hit and the denominator a twentieth of it.

Step 4: find the breaking point. Solve (78,000 − C)/(60,000 − 0.05C) = 1.00 → 18,000 = 0.95C → C = ₹18,947.37 crore, verified to give an LCR of exactly 100.000000%. That is 11.28% of CASA and 4.51% of total deposits. An 11% shift out of retail current and savings accounts exhausts this bank's entire regulatory liquidity buffer.

Step 5, the design levers that stop it. The RBI's e₹ is deliberately unremunerated: "given the cash-like features of e₹, there is no interest payable on the wallet balances." An unremunerated instrument competes with cash, not with a savings account, and cash has not emptied the banking system. Add a per-wallet holding cap and the bound becomes mechanical: at a ₹2,00,000 cap, reaching the ₹18,947 crore breaking point at this one bank would require roughly 947,000 fully-loaded wallets. Tiered remuneration achieves the same more precisely. The two-tier distribution model is itself a control point, since banks manage the conversion boundary.

Read it. The disintermediation debate is not ideological; it is this arithmetic run across a banking system with a distribution of starting LCRs. (a) The problem is worst for banks most dependent on retail CASA, precisely the funding profile regulators otherwise consider safest, an awkward interaction. (b) Note what did not happen: no money was destroyed and no credit extinguished at the moment of conversion. The system-level effect works through the price and availability of bank funding, not through a mechanical contraction of the money stock, and confusing those two is the most common error in the entire CBDC literature. India's pilots, e₹-W from 1 November 2022 and e₹-R from 1 December 2022, per the RBI's Concept Note of 7 October 2022, are deliberately capped, unremunerated and intermediated for exactly the reasons this example computes.

Practice set

Work each problem fully before reading its solution. A calculator is assumed; answers are within ±2%. All entities are synthetic unless traced to a named source; all rate levels are stated inputs, not market quotations.

P1 (guided). Define a eurodollar, mechanically. State what a eurodollar is in one sentence, then name the three consequences that follow.

Solution. A eurodollar is a US-dollar-denominated deposit liability of a bank office located outside the United States. Consequences: (1) it is created by an institution with no Federal Reserve account, so the Fed cannot supply it directly and reaches it only through swap lines or FIMA repo; (2) it carries no US deposit insurance and, since 27 December 1990 for Eurocurrency liabilities and universally since 26 March 2020, no US reserve requirement; (3) it is created by the ordinary loans-create-deposits mechanism, so offshore dollar credit can grow with no change in US bank deposits or Federal Reserve reserves.

P2 (guided). The offshore multiplier. An offshore system holds a base of $250 million and maintains a prudential balance ratio of 12.5%. Compute supportable deposits and credit. What actually binds this ratio today?

Solution. Deposits = 250 / 0.125 = $2,000.0 million; credit = 2,000 − 250 = $1,750.0 million. Nothing legal binds it: US reserve requirement ratios have been zero since 26 March 2020, and Eurocurrency liabilities have carried a zero requirement since 27 December 1990. What binds is prudential, correspondent balances for payments, capital, the LCR, internal limits, and the ability to roll dollar funding the bank cannot print.

P3 (guided). Price a forward from two rates (India ₹). Spot USD/INR 86.40; 182 days; INR 6.40% (ACT/365); USD 4.30% (ACT/360). Compute the outright forward, the points and the annualised premium.

Solution. F = 86.40 × (1 + 0.0640 × 182/365) / (1 + 0.0430 × 182/360) = 87.2603. Points = 0.8603 rupees = 86.03 paise. Annualised premium = (0.8603/86.40) × (365/182) = 1.9969% p.a. Direction check: the higher-rate currency (INR) trades at a forward discount, so more rupees per dollar forward than spot. It does.

P4. Invert a forward into a basis (US $). Spot EUR/USD 1.1000; 91 days; USD 4.50%, EUR 2.20%, both ACT/360; market forward 1.1075. Compute the CIP forward and the basis in basis points, and say what the sign means.

Solution. τ = 0.2527778. F_CIP = 1.1000 × 1.0113750/1.0055611 = 1.1063599 (63.60 pips of premium). The market forward of 1.1075 is 11.40 pips richer, so the basis is negative: x = [1.1000 × 1.0113750/1.1075 − 1]/0.2527778 − 0.0220 = −0.004095 = −40.95 bp. Read the same fact as a funding rate: r_USD_implied = [(1.1075/1.1000)(1.0055611) − 1]/0.2527778 = 4.9123%, a 41.23 bp premium over the 4.50% dollar rate. A negative basis means dollars obtained synthetically through the swap market cost more than the dollar money-market rate: dollars are scarce. It is a funding price, not a view on the euro.

P5. Which funding route? A non-US bank can issue unsecured USD paper at SOFR + 60 bp, or raise domestic currency at OIS + 10 bp and swap it. The basis is −45 bp. Which is cheaper, and at what basis do they cross?

Solution. Swap all-in = SOFR + 10 bp − (−45 bp) = SOFR + 55 bp; unsecured = SOFR + 60 bp. The swap route is cheaper by 5 bp. They cross where 10 − x = 60, i.e. at −50 bp: any basis more negative makes unsecured cheaper. Note the trap's direction, a widening (more negative) basis pushes the bank toward unsecured markets exactly when its unsecured spread is also widening.

P6. Herstatt, sized. A dealer settles a $250 million USD/CHF trade. The franc leg is final at 16:00 CET (UTC+1), the dollar leg at 18:00 New York winter time (UTC−5). Compute the exposure window and compare principal with replacement-cost risk at a 1.2% move.

Solution. 16:00 CET = 15:00 UTC; 18:00 ET = 23:00 UTC; the franc payer is exposed 8 hours. Replacement cost = 250,000,000 × 0.012 = $3,000,000; principal risk = $250,000,000: 83.3× larger. PvP does not shorten the 8 hours; it makes each leg conditional on the other so the window does not exist.

P7. Walk a waterfall. A CCP faces a ₹2,400 crore close-out loss. The defaulter posted ₹1,100 crore of initial margin and ₹150 crore to the default fund; the CCP's skin-in-the-game is ₹200 crore; survivors' contributions total ₹3,000 crore, of which Member X contributed ₹450 crore. How much does X lose, and what fraction did the defaulter's own resources cover?

Solution. 2,400 − 1,100 = 1,300; − 150 = 1,150; − 200 = ₹950 crore hits the mutualised pool. Utilisation = 950/3,000 = 31.667%; X loses 950 × 450/3,000 = ₹142.50 crore. The defaulter's own resources covered (1,100 + 150)/2,400 = 52.08%; initial margin alone 45.83%. X had no exposure to the defaulter and still paid, that is mutualisation.

P8. Margin and the horizon. A clearing house margins at 99% one-tailed (z = 2.326) with daily σ = 0.85% on a ₹8,000 crore position. Compute margin at T+2, T+1 and an intraday quarter-day horizon, with the percentage reductions.

Solution. T+2: 2.326 × 0.0085 × √2 = 2.7960% → ₹223.68 crore. T+1: 1.9771% → ₹158.17 crore (29.29% lower). Quarter-day: × √0.25 = 0.9886% → ₹79.08 crore (50.00% below T+1, 64.64% below T+2). Every percentage follows from √h alone, independent of σ and position size, which is why the same numbers appear in every settlement-cycle study.

P9. The T+1 FX window. CLS's submission deadline is 00:00 CET on value date = 18:00 ET on the previous calendar day. A fund executes a US equity trade at 15:30 ET on trade date. Compute the window under T+2 and T+1, and list the three responses if it is missed.

Solution. Under T+2, the deadline is 18:00 ET on T+1: (24 − 15.5) + 18 = 26.5 hours. Under T+1, the deadline is 18:00 ET on T: 2.5 hours. The three responses: (1) execute FX earlier, before the fill is known, leaving a residual to true up; (2) settle bilaterally, outside PvP, reintroducing Herstatt principal risk; (3) pre-fund, at a computable cost. There is no fourth option, and each has a price.

P10. Read a stablecoin balance sheet. A token has $25,000 million outstanding against $25,000 million of reserves. Compute NAV after losses of $50m, $125m and $250m, and the loss that puts NAV at exactly $0.9950.

Solution. NAV = (25,000 − L)/25,000. At $50m: $0.998000 (20.0 bp below par). At $125m: $0.995000 (50.0 bp). At $250m: $0.990000 (100.0 bp). The loss producing exactly $0.9950 is 25,000 × 0.005 = $125.0 million, i.e. 0.50% of reserves. Note how small: a 100% reserve gives zero buffer above par, so any impairment breaks the peg arithmetically.

P11. Liquidity, not solvency. A fully reserved token holds 88% Treasury bills (50-day WAM), 8% overnight repo, 4% bank deposits. Compute daily liquid assets, weekly liquid assets (assume 3% of the total qualifies from bills) and WAM, and test each against Rule 2a-7's government-fund standards.

Solution. Daily liquid assets = 8% + 4% = 12.0% against a 25% floor: fail by 13 points. Weekly = 12% + 3% = 15.0% against 50%: fail by 35 points. WAM = 50 × 0.88 + 1 × 0.08 = 44.1 days against 60: pass. Verdict: fully reserved, short-duration, and radically less liquid than a regulated fund holding materially the same assets.

P12. Decompose a depeg. A token with $18,000m outstanding and $18,000m of reserves discloses that $900m sits at a failed bank. It trades at $0.9250. Split the implied loss into known impairment and run premium.

Solution. Known impairment = 900/18,000 = 5.00%, so the justified NAV is $0.9500. A market price of $0.9250 implies total loss 7.50%, i.e. reserves valued at $16,650m against $17,100m surviving, an extra $450m, 2.63% of the surviving reserve. Known impairment 5.00%; run premium 2.50 percentage points of price, 2.63% of the surviving reserve. The run premium prices redemption uncertainty, not asset value.

P13. Who earns the float? An issuer holds $60,000 million of reserves at 4.10% and pays holders nothing. Compute annual reserve income, income per dollar of token, and the ten-year forgone compounding on $25,000 versus a fund passing 3.85% net.

Solution. Income = 60,000 × 0.0410 = $2,460.0 million a year, or $0.0410 per token per year. A fund passing 3.85% would pay 60,000 × 0.0385 = $2,310.0 million: 93.9% of the gross carry. On $25,000 for ten years: 25,000 × 1.0385^10 = $36,475.82 versus $25,000.00: $11,475.82 forgone. The GENIUS Act's prohibition on paying yield is the legal source of this transfer, and it is the issuer's business model.

P14. Intervention and sterilisation. The RBI buys $8 billion at 86.00. Compute the reserve money created, the deposits it could support at a 4% CRR if fully lent, and the annual sterilisation carry if the dollar assets yield 4.20% and the rupee liabilities cost 6.50%.

Solution. Rupees created = 8,000,000,000 × 86.00 = ₹68,800 crore of reserve money. At a 4% CRR, 68,800/0.04 = ₹17,20,000 crore of deposits if fully lent, a monetary expansion nobody chose, which is why sterilisation happens. Carry cost = 68,800 × (0.0650 − 0.0420) = ₹1,582.4 crore per year, the price of holding two corners of the trilemma, paid annually.

P15. Regimes, placed. For each of (a) a retail CBDC, (b) a wholesale CBDC, (c) a domestically popular foreign-currency stablecoin, say whether it changes the rails or the regime, and why.

Solution. (a) Rails: it changes who may hold the central bank's liability; the unit of account and capital-account rules are unchanged, so the trilemma is untouched. (b) Rails, it changes the settlement format for institutions that already hold central-bank money as reserves. (c) Regime, this is digital dollarisation: the country loses seigniorage, lender-of-last-resort capacity in the circulating currency, and the monetary-independence corner of the trilemma, by adoption rather than by decision. That is the case an emerging-market analyst should actually watch for.

P16. Reconcile two BIS numbers. April 2025 FX turnover was $9.6 trillion per day, while daily gross FX settlement obligations were more than $14 trillion. A colleague says one must be wrong. Rebut.

Solution. Both are correct because they measure different things. Turnover (Triennial Survey) counts the value of trades on a single-currency basis, adjusted for local and cross-border inter-dealer double counting. Settlement obligations (settlement questionnaire) count the payment legs (every FX trade generates an obligation in each of two currencies) over a reporting population and scope defined for that survey. A dollar of turnover can generate roughly two dollars of gross obligations before netting. The professional habit is to name the release and the table for any market aggregate; the two BIS measures are not substitutes and never were.

Applied mini-project

Build the Global-Dollar & Digital-Money Plumbing Dossier.

Produce one dossier that does for real data what this module did for stylised inputs: trace the dollar system's price, its settlement and its digital frontier, each to a named primary source, with every derived number recomputed by you. Nothing here requires paid data.

Part 1, The offshore dollar, measured. From the BIS Data Portal, pull the global liquidity indicators. Record, with the exact table and release date: US dollar credit to non-bank borrowers outside the United States, latest and four quarters prior; the same for emerging market and developing economies; and the year-on-year growth rate computed by you from the exchange-rate-adjusted change series, not from the difference of stocks. Then say, in balance-sheet terms, whose liability that credit is and why the Federal Reserve cannot supply it directly.

Part 2, The basis, computed (US $). Choose a pair and tenor. From named primary sources obtain a spot rate, an outright forward (or points), and two money-market/OIS rates on their correct day counts. Compute the CIP forward, the deviation in pips, the cross-currency basis in basis points, and the implied synthetic dollar funding rate, showing the day-count fractions explicitly, then the cost of funding $500 million for the tenor through the swap market rather than at the dollar benchmark. Flag your observation date if it falls within five business days of a quarter- or year-end.

Part 3, The rupee wedge (India ₹). Repeat Part 2 for USD/INR using onshore forward points from a named Indian source (FBIL or CCIL), with the rupee leg on ACT/365 and the dollar leg on ACT/360. Compute the implied rupee rate, the annualised forward premium, and the difference between those two numbers, explaining why they are not the same. If you can obtain an offshore NDF quote, compute the wedge in basis points and its value on $50 million; if you cannot, say so and explain what that difficulty tells you about the market's structure.

Part 4: Settlement, read from the source. From the BIS's settlement-risk publication and CLS's own description, record total daily gross settlement obligations; the amount and share settled PvP; the amount settled gross bilaterally with no mitigation; and the pre-settlement netting gross and net figures. Recompute the netting compression yourself, as a percentage and a ratio. Then answer in three sentences: for a USD/INR trade, what provides PvP protection, and which document says so?

Part 5, One digital instrument, dissected. Choose either a retail CBDC or a fiat-reserve stablecoin and produce: (a) the five answers from §5.0; (b) T-accounts for every party at issuance; (c) if a stablecoin, the daily-liquid-assets, weekly-liquid-assets and WAM tests from its latest reserve report, with your own arithmetic and the report's as-of date and engagement type quoted verbatim; if a CBDC, the LCR impact on a bank of your construction at a 5% CASA conversion, with the breaking-point conversion solved algebraically.

Part 6, The regime verdict. In no more than 300 words, place your instrument on the regime map of §5.10 and say whether it changes the rails or the regime. If you conclude "rails," name the one condition that would flip your answer.

Deliverable and self-check. One dossier, six parts, every figure carrying a named source with release date and table reference, every derived number shown with its inputs, and a closing verification log listing each number, its source and the check you ran. Score yourself, 2 points each: (a) both jurisdictions present (₹ and $) with correctly day-counted arithmetic; (b) every market figure traced to a named primary source with a date, no aggregators, no unnamed "market data"; (c) basis and netting compression recomputed by you, with fractions and ratios shown, not quoted; (d) all balance sheets correct in Part 5, including the central bank's total being unchanged if you chose a CBDC; (e) the regime verdict argued from the trilemma, with the flip condition named. Pass at 8/10 with no zero on any item. A zero on (b) means redo the whole dossier: in this region an untraced number is not a weak answer, it is a wrong one.

Reading & resources

Everything below is an anchor to verify against. The BIS and the central banks are primary; everything else is commentary, however good.

The primary statistical sources (learn to navigate these, not to quote summaries of them):

• BIS Triennial Central Bank Survey: the definitive measurement of FX and OTC derivatives turnover; the September 2025 round is the source for the $9.6 trillion daily figure, the instrument split and the currency shares. [Free] [Intermediate]
• BIS Data Portal: locational and consolidated banking statistics, global liquidity indicators, OTC derivatives statistics; bulk CSV and a public SDMX API. This is where the offshore dollar is actually measured. [Free] [Intermediate–Advanced]
• BIS Quarterly Review: the standing source for plumbing analysis. Essential: Dollar debt in FX swaps and forwards: huge, missing and growing (December 2022); Uncovering FX settlement risk: new measures from the 2025 BIS Triennial Survey (June 2026); FX settlement risk: an unsettled issue (December 2022). [Free] [Intermediate–Advanced]
• RBI Weekly Statistical Supplement and Annual Report, the primary source for India's reserves, reserve money and the e₹ pilots. Never take an Indian macro number from a newspaper when the WSS exists. [Free] [Beginner–Intermediate]
• Federal Reserve H.4.1 ("Factors Affecting Reserve Balances"), the weekly source for central bank liquidity swaps outstanding and every other Fed balance-sheet line. [Free] [Intermediate]

Framework and founding documents (read these once, properly):

• BIS CPSS, Settlement risk in foreign exchange transactions (the Allsopp Report, 1996), defined FX settlement risk and led to CLS. [Free] [Intermediate]
• CPMI-IOSCO, Principles for Financial Market Infrastructures (2012), the standard for CCPs, payment systems and CSDs; Principle 4 is "cover 2." [Free] [Advanced]
• BIS, Annual Economic Report 2025, Chapter III, the singleness/elasticity/integrity tests and the tokenised unified ledger; Chapter III of the 2026 report continues the argument. [Free] [Intermediate–Advanced]
• BIS Innovation Hub, Project Agorá: tokenised cross-border settlement with eight central banks and 40+ private firms; see the project page and the May 2026 press release announcing real-value testing. [Free] [Intermediate]

Rules, statutes and official designs (the documents that decide the answers):

• SEC, Shortening the Securities Transaction Settlement Cycle, the T+1 adopting release, the small-entity compliance guide, and Rules 15c6-1, 15c6-2 and 204-2. [Free] [Intermediate]
• SEBI circulars on T+1 (2021–2023) and on the optional T+0 beta cycle (March 2024, enhanced December 2024). [Free] [Intermediate]
• RBI, Concept Note on Central Bank Digital Currency (7 October 2022) and the Digital Rupee (e₹) FAQs. India's CBDC design, two-tier distribution, legal-tender status and non-remuneration. [Free] [Beginner–Intermediate]
• GENIUS Act (S.1582, 119th Congress; signed 18 July 2025), permitted issuers, the 1:1 reserve list, monthly examined disclosure, the prohibition on paying yield. Read the statute; the summaries disagree with each other. [Free] [Advanced]
• SEC Rule 2a-7 and Form N-MFP: the money market fund rule and its monthly position-level holdings filing; the benchmark against which any stablecoin reserve disclosure should be judged. [Free] [Advanced]
• CLS Group product documentation and CCIL settlement FAQs and PFMI disclosures, the operators' own descriptions, including CLS's 18 currencies, 75+ settlement members and >96% funding compression, and CCIL's PvP and multilateral netting for USD/INR. [Free] [Intermediate]

Analysis worth your time (commentary, not sources):

• Du, Tepper and Verdelhan, Deviations from Covered Interest Rate Parity, Journal of Finance (2018), the foundational treatment of the basis and why arbitrage does not close it. [Free working papers] [Advanced]
• Perry Mehrling, The New Lombard Street and his open money-view lectures. MS1.01's hierarchy applied internationally. [Paid book; free lectures] [Intermediate]
• Hélène Rey, Dilemma not Trilemma (Jackson Hole, 2013), the global-financial-cycle challenge to the trilemma. [Free] [Advanced]
• BIS Working Paper No 1164, Public information and stablecoin runs, a careful treatment of the March 2023 USDC episode. [Free] [Advanced]
• Circle and Tether transparency pages: the issuers' own reserve reports. Read them as disclosures by an interested party: check the as-of date and engagement type first, then compare against a 2a-7 fund's N-MFP for the same month. [Free] [Intermediate] (perishable, always read the latest)

Perishable specifics, as of 2026-07; verify current. The mechanisms in this module are durable; almost every number attached to them is not. Re-check before quoting: BIS turnover and settlement figures (triennial, so the next round supersedes them); BIS global liquidity indicator levels (quarterly); CLS's daily settled value, member count and currency list; India's foreign-exchange reserves and the e₹ pilot's scope, participants and holding caps; any stablecoin's reserve composition, size and attestation cadence; the scope and phase of SEBI's optional T+0 cycle; and the list of central banks with standing Fed swap lines. Rate levels used in this module's arithmetic (SOFR/OIS, €STR, TONA, INR) are stated inputs for the exercises, not quotations, and must never be cited as market data.

Do this, not just read: download one global liquidity indicator series from the BIS Data Portal; read CLS's funding-compression claim in its original wording; find the sentence about interest in the RBI e₹ FAQ. Thirty minutes with three primary sources will do more for your judgement here than any commentary, because the whole skill is knowing which document answers which question.

Teach it back & journal

Feynman prompt. Explain to a sharp colleague who follows markets but has never thought about plumbing why the sentence "the Federal Reserve can print dollars, so a dollar shortage is impossible" is wrong: using nothing but balance sheets. Start with what a eurodollar actually is (a non-US bank's dollar liability), show why no central bank can issue another institution's liability, and land on why swap lines and the FIMA repo facility had to be invented. Then, in the same breath, explain why an FX swap is a loan and why the world's debt statistics do not contain tens of trillions of dollars of it. Your colleague has understood if they can, unprompted, predict that a negative cross-currency basis will widen at quarter-end for reasons that have nothing to do with the euro, and say why.

Journal prompt. For one week, take every cross-border or digital-money claim you encounter (research note, news story, podcast, AI answer) and, before reacting to it, write down the four things this module says you must have: whose liability is it, whose balance sheet expands, what settles it and when is that final, and who is the backstop. Log how many claims you could answer all four for from the source itself, and how many needed you to open a primary document. Then write a paragraph on this: in every other region of this program a wrong number can be caught by recomputing it; here a wrong mechanism reads exactly like a right one, and only a document distinguishes them. Which single habit, naming the BIS table before quoting an aggregate, drawing the T-accounts before accepting an explanation, or reading an attestation's as-of date and engagement scope before its numbers, would most change how a portfolio manager or a regulator judged the quality of your work? What will you do this week to make it automatic, and what will you stop doing?

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.