FRM Part II · FRM Exam Part II

The US Dollar Shortage in Global Banking and the International Policy Response: formula sheet

Full chapter guide

Key formulas

Dollar funding gap: Funding gap = US dollar assets − US dollar liabilities from stable sources (e.g., non-bank deposits and long-term debt); The gap must be met by short-term wholesale dollars or FX swaps. A larger gap means more rollover risk.
Net dollar position: Net USD position = USD assets − USD liabilities (on-balance-sheet); Can look small or zero while gross positions are huge. Gross size drives rollover need, not only the net.
FX swap as dollar funding: Spot: sell home currency, receive USD. Forward: pay USD, receive home currency back at the agreed forward rate; Economically a collateralised dollar loan. Dollars must be repaid at maturity, so it carries rollover risk.
Cross-currency basis (concept): Basis = the spread added to the non-USD leg's rate so the swap is fairly priced; a negative basis means dollars cost more than the CIP-implied rate; Use direction only unless numbers are given: more negative = tighter dollar funding.
Covered interest parity (CIP): F ÷ S = (1 + r_local) ÷ (1 + r_USD) (F, S in local currency per USD; same tenor); Holds with no frictions. Forward premium or discount reflects the interest rate difference.
Cross-currency basis (common quote): Basis x = r_USD − r_synthetic USD, quoted as a spread added to the non-USD rate in the swap; Negative x means synthetic dollars cost more than direct dollar borrowing. Conventions vary, so read the question.
Implied (synthetic) USD rate from an FX swap: With S and F in local per USD: 1 + r_synthetic USD = (1 + r_local) × (S ÷ F). With S and F in USD per local currency (for example USD per EUR): 1 + r_synthetic USD = (1 + r_local) × (F ÷ S); Use for tenor of one period. For tenors over a year, annualise. Check the quote direction first, because the ratio flips with it.
Deviation from CIP: Deviation = r_USD − r_synthetic USD observed; This has the same sign as the basis x. A negative deviation means an extra cost to obtain dollars through the swap.
LIBOR-OIS spread: LIBOR-OIS spread = 3-month LIBOR − 3-month OIS rate; Read as a gauge of perceived bank credit and liquidity risk. OIS reflects expected overnight policy rates with little credit risk.
Covered interest parity (CIP): F ÷ S = (1 + i_USD) ÷ (1 + i_foreign), with S and F as USD per unit of foreign currency; Holds when arbitrage is unconstrained. Quote conventions matter. Check how the question defines S and F.
Cross-currency basis: Basis = (rate to borrow USD via FX swap) − (direct USD rate), expressed in basis points; Convention: a negative basis means a premium to borrow USD synthetically. It widened sharply in the crisis.
Funding gap: USD funding gap = USD assets − stable USD funding (such as USD deposits); The gap must be covered by wholesale markets or FX swaps, so it is exposed to rollover risk.
Swap line, initial leg: Dollars delivered by the Fed = Foreign currency received × spot rate (USD per unit); The Fed receives foreign currency at the spot rate on the start date.
Swap line, reversal: Foreign currency returned = same amount, at the same initial rate; The reverse trade uses the original rate, so the Fed has no exchange rate risk on the principal. It still bears credit risk to the foreign central bank, which is mitigated by holding the foreign currency.
Cost to the borrower: Interest = USD amount × swap rate × days ÷ 360; Interest is paid in dollars at a rate fixed relative to a policy benchmark. Use the day count given in the question.
Who bears the credit risk: Fed exposure = foreign central bank; central bank exposure = its commercial banks; The Fed does not lend to foreign commercial banks directly.
Liquidity Coverage Ratio: LCR = Stock of HQLA ÷ Total net cash outflows over the next 30 days ≥ 100%; Net outflows = outflows − min(inflows, 75% of outflows). Inflows are capped at 75% of outflows.
Net Stable Funding Ratio: NSFR = Available stable funding (ASF) ÷ Required stable funding (RSF) ≥ 100%; Horizon is one year. ASF weights liabilities and capital by stability. RSF weights assets and off-balance-sheet items by liquidity and maturity.
Currency-specific LCR: LCR(USD) = USD HQLA ÷ USD net cash outflows over 30 days; Monitored for each significant currency. Significant means liabilities in that currency are 5% or more of total liabilities. It is a monitoring metric, not a separate Basel minimum.
Dollar funding gap: Gap = USD assets − USD stable funding (e.g. USD deposits and long-term USD debt); The gap must be filled with short-term wholesale USD or FX swaps. This is the core vulnerability.

Quick revision

Dollar shortage = non-US banks cannot roll over short-term dollar funding against dollar assets.
The core problem is a currency and maturity mismatch: long dollar assets, short dollar liabilities.
FX swaps let banks raise dollars against other currencies, but the swap must be rolled over.
FX swaps are off-balance-sheet, so the mismatch can be hidden from simple balance sheet views.
A more negative cross-currency basis means dollars are more expensive to obtain via swaps.
In the crisis, counterparty fears and frozen money markets cut off dollar rollover funding.
Swap lines: the Fed provides dollars to a foreign central bank, which lends them to its local banks.
The foreign central bank, not the Fed, carries the credit risk of its local bank borrowers.
Swap lines work by supplying dollars directly, which eases pressure on the basis.
LCR and NSFR address funding liquidity, but dollar-specific mismatches can remain.
Remaining vulnerabilities include continued reliance on short-term dollar funding and swap market stress.
Always name the channel: mismatch, rollover, basis, or policy tool.

Common mistakes

Saying the shortage was caused by a lack of US dollars in the world. Fix: It was a funding access problem: banks could not roll over short-term dollar debt, not an absolute lack of dollars.
Judging risk from the net dollar position only. Fix: Look at gross dollar assets and liabilities. Large gross books mean large rollover needs even with a small net.
Saying an FX swap removes all risk from a currency mismatch. Fix: It fixes the exchange rate but not rollover risk. If the swap cannot be renewed, the bank faces a funding shortfall.
Treating the FX swap as a derivative with no funding role. Fix: Think of it as a collateralised loan of one currency against another.
Treating the shortage as a US bank problem only. Fix: Remember that non-US banks with big USD assets and thin USD deposits were most exposed.
Saying a wider LIBOR-OIS spread means expected policy rates rose. Fix: The spread isolates the bank credit and liquidity premium, because OIS already reflects expected policy rates.
Saying the Fed lends dollars directly to foreign commercial banks. Fix: Remember the chain: Fed to foreign central bank to local banks. The foreign central bank takes the bank credit risk.
Thinking the Fed bears exchange rate risk on the swap. Fix: The reversal rate equals the initial rate, so exchange rate risk on the principal is removed. The Fed still bears credit risk to the foreign central bank, which is mitigated by holding the foreign currency.
Saying Basel sets a binding 100% LCR minimum in each currency. Fix: Remember that currency-level LCR is a monitoring requirement for significant currencies. Supervisors may add limits, but Basel does not.
Using total inflows in the LCR denominator without the cap. Fix: Cap inflows at 75% of outflows. Net outflows are at least 25% of gross outflows.

Exam tips

Always name both mismatches: currency and maturity. Examiners reward the exact pairing.
Remember the sources of dollars: money market funds, interbank, FX swaps. Questions often ask which one ran.
Expect an attribution to McGuire and von Peter: large gross dollar books, funded via interbank and FX swaps.
If a stem gives a net position near zero, check gross sizes before calling the bank safe.
Link the shortage to its symptom: a more negative cross-currency basis and a need for central bank swap lines.
Questions often hide the mismatch: look for derivative footnotes or off-balance-sheet items beside a balance sheet with no USD liability.
Read exchange rate quotes carefully. USD per EUR versus EUR per USD changes the answer.
Link the basis to its drivers: USD funding demand, limits on arbitrage, and central bank swap lines as a backstop.