FRM Part II · FRM Exam Part II

The Failure Mechanics of Dealer Banks: formula sheet

Full chapter guide

Key formulas

Leverage ratio (balance sheet): Leverage = Total assets ÷ Equity; Higher leverage means a smaller asset price fall wipes out equity.
Equity loss from asset decline: Equity loss % = Asset fall % × Leverage; Valid before any new capital raised or assets sold; wipe-out occurs when asset fall % = 1 ÷ Leverage.
Repo haircut: Haircut = (Collateral value − Cash lent) ÷ Collateral value; The haircut is the dealer's own funding per unit of collateral.
Cash raised in repo: Cash lent = Collateral value × (1 − Haircut); A rise in haircut cuts cash raised from the same collateral.
Funding gap from haircut increase: Gap = Collateral value × (New haircut − Old haircut); Dealer must fund this gap from other sources or by selling assets.
Leverage ratio (balance sheet): Leverage = Total assets ÷ Equity; Higher leverage means a smaller asset fall wipes out equity.
Equity loss threshold: Fall in assets that wipes out equity = Equity ÷ Total assets = 1 ÷ Leverage; With leverage of 25, a 4% fall in asset value eliminates equity.
Repo haircut and cash raised: Cash borrowed = Collateral value × (1 − haircut); A higher haircut means less cash for the same collateral, so the dealer needs more own funding.
Funding gap from a haircut increase: Extra funding needed = Collateral value × (new haircut − old haircut); The dealer must replace this cash immediately or sell assets.
Solvency vs liquidity test: Insolvent: assets < liabilities. Illiquid: cannot pay obligations when due, even if assets ≥ liabilities.; A run can turn illiquidity into insolvency through fire sales.
Haircut: Haircut = (Market value of collateral − Cash lent) ÷ Market value of collateral; The haircut is the borrower's equity in the trade. A rise in haircut is a loss of funding even if the repo rolls.
Cash raised in repo: Cash = Collateral market value × (1 − haircut); Use the same collateral value and the new haircut to find funding lost.
Funding shortfall from a haircut rise: Shortfall = Collateral value × (new haircut − old haircut); Assumes the repo rolls and collateral value is unchanged. If prices also fall, recompute cash raised from scratch.
Leverage from haircut: Maximum asset-to-equity multiple on repo-funded assets = 1 ÷ haircut; This applies to a position funded entirely by repo at that haircut, with the haircut portion funded by equity. A 2% haircut allows 50 times; at 10% it falls to 10 times. This is why haircut shocks force deleveraging.
Liquidity survival check: Liquidity buffer − (repo not rolled + extra haircuts + client withdrawals + collateral calls) ≥ 0; A negative result means the bank cannot survive the stress horizon without outside help.
Leverage ratio (simple): Leverage = Total assets ÷ Equity; Higher leverage means a small asset fall wipes out equity. Dealers ran very high leverage before 2008.
Liquidity pool adequacy: Survival horizon = Liquidity pool ÷ Daily net stressed outflow; Use unencumbered, liquid assets after haircuts. This is a simple approximation, not a regulatory formula.
Haircut and funding: Cash raised = Market value of collateral × (1 − haircut); Higher haircuts in a stress mean less cash per unit of collateral, so the dealer must fund the gap.
Equity wipe-out: Asset fall that wipes out equity = 1 ÷ Leverage; At 30 times leverage, a fall of about 3.3% in asset value eliminates equity.
Liquidity Coverage Ratio (LCR): LCR = Stock of high-quality liquid assets ÷ Total net cash outflows over the next 30 days ≥ 100%; Short-term resilience under a 30-day stress. Net outflows = outflows − min(inflows, 75% of outflows).
Net Stable Funding Ratio (NSFR): NSFR = Available stable funding ÷ Required stable funding ≥ 100%; Structural, one-year horizon. Targets reliance on short-term wholesale funding.
Loss absorption order in resolution: Equity first → then TLAC-eligible long-term debt (written down or converted) → operating liabilities protected; Under SPOE, losses at subsidiaries are passed up to the parent's equity and debt holders.
Key rule: why bankruptcy is disorderly: Safe harbours for repo and derivatives → immediate termination and collateral sale → fire sales and funding freeze; Contrast with the automatic stay, which normally delays creditor action.

Quick revision

Dealers hold large trading inventories funded mostly by short-term secured borrowing and thin equity.
High leverage means a small fall in asset value causes a large loss relative to equity.
Maturity mismatch: assets may be hard to sell quickly, while funding rolls over daily or in days.
A repo is a secured loan; a higher haircut means the dealer must put up more of its own funding for the same assets.
Rising haircuts force asset sales, which push prices down and cause more losses and more haircut increases.
Prime brokerage clients can withdraw cash balances and free credits quickly when they worry about the dealer.
A run can happen even when the collateral is good, because lenders only need to doubt the dealer's survival.
Bear Stearns lost secured funding access quickly and was sold with central bank support.
Lehman Brothers filed for bankruptcy and its failure spread stress through counterparties and funding markets.
Dealer failure creates fire sales, counterparty losses and frozen collateral for other firms.
Reforms target the failure points: higher capital, liquidity rules, stronger resolution tools and better repo practices.
In an exam scenario, identify the funding channel first, then the feedback loop, then the policy remedy.

Common mistakes

Treating repo as unsecured borrowing Fix: Remember repo is a collateralised loan. Lender risk depends on collateral value and haircut, not only on dealer credit.
Confusing haircut with the interest rate Fix: The haircut is the equity-funded part of the collateral. The repo rate is the cost on the cash lent.
Treating a dealer run like a retail deposit run. Fix: Remember that dealer runs involve professional lenders, repo haircuts and collateral calls, with no deposit insurance.
Saying a liquidity failure means the firm is insolvent. Fix: Define each by its test. Insolvency compares assets with liabilities. Illiquidity is about meeting payments on time. Fire sales can link them.
Treating the haircut as the amount the lender loses. Fix: The haircut is the borrower's own funding in the trade. The lender is protected by it.
Assuming secured funding cannot run. Fix: Secured lenders run by not rolling or by raising haircuts. They do not need to wait for default.
Saying Lehman was rescued like Bear Stearns. Fix: Remember Bear was sold to JPMorgan with Fed support; Lehman filed for Chapter 11.
Treating the liquidity pool as a fixed safe buffer. Fix: Check whether assets are unencumbered and how quickly stressed outflows can drain them.
Saying bankruptcy is disorderly because creditors are paid too slowly. Fix: For dealers the problem is the opposite: repo and derivative counterparties can act immediately, causing fire sales.
Treating LCR and NSFR as the same rule. Fix: LCR is a 30-day stress ratio on liquid assets. NSFR is a one-year structural funding ratio.

Exam tips

Expect short case vignettes that give assets, equity and a haircut. Do the arithmetic first, then interpret.
Know the loop: haircut rise, forced sale, price fall, further haircut rise. Questions often ask which step amplifies the run.
Distinguish funding liquidity risk from market liquidity risk, and say how they reinforce each other.
Read options carefully. Wrong options often describe repo as unsecured or ignore the haircut.
Link the topic to Bear Stearns and Lehman: both relied on short-term secured funding that lenders stopped rolling.
Expect case-style questions describing a dealer's funding mix. Name the feature (maturity mismatch, leverage, wholesale funding, opacity) before looking at the options.
Know the liquidity versus solvency definitions precisely. Distractors often swap them.
Use equity ÷ assets for loss thresholds. Check that you did not use the leverage multiple as a percentage.