Anatomy of the Great Financial Crisis of 2007-2009: formula sheet

Key formulas

Loan-to-value (LTV) ratio

LTV = Loan amount ÷ Property value

A higher LTV means less borrower equity and bigger losses if prices fall. Subprime lending often used LTV at or near 100%.

Borrower equity

Equity = Property value − Loan balance

Equity turns negative (negative equity or "underwater") when the house is worth less than the loan.

Core causal chain to remember

Low rates → easy credit → house price rise → looser standards and subprime growth → securitization → hidden risk and leverage → price fall → defaults and losses

Use this as a memory frame for cause-and-effect questions. It is a summary, not a formula.

Loss allocation in tranching

Tranche loss = min(max(Pool loss − Attachment point, 0), Detachment point − Attachment point)

Attachment and detachment points are in the same unit as pool loss (% or amount). Equity tranche attaches at 0.

Subordination (credit enhancement) of a tranche

Subordination = Attachment point of the tranche

The share of the pool that must be lost before this tranche takes any loss.

Tranche thickness

Thickness = Detachment point − Attachment point

Thin tranches are very sensitive to pool losses and to default correlation.

Pool balance identity

Σ tranche principal = Collateral pool principal (plus any overcollateralization)

Tranches are claims on the same pool, so total principal cannot exceed the assets backing them.

Excess spread

Excess spread = Pool interest income − Tranche coupons − Fees

First line of defence against losses before the equity tranche is hit.

Tranche loss rule

Tranche loss = min(max(Pool loss − Attachment point, 0), Detachment point − Attachment point)

Losses are measured as a share of the pool. Divide by the tranche width to get the loss as a percentage of that tranche.

Tranche loss as % of tranche

Loss % = min(max(L − A, 0), D − A) ÷ (D − A)

L = pool loss, A = attachment point, D = detachment point. Thin tranches lose value quickly once L passes A.

Subordination (credit enhancement)

Subordination for a tranche = Attachment point

It is the share of pool losses absorbed by junior tranches before this tranche loses anything.

Correlation effect (rule of thumb)

Higher default correlation → fatter tail of pool losses → senior tranche riskier, equity tranche often less risky

State this as a general pattern, not a law. It explains why low assumed correlation overrated senior and CDO tranches.

Leverage ratio

Leverage = Total assets ÷ Equity

Higher leverage means a smaller fall in asset value wipes out equity.

Equity wipe-out threshold

Asset fall that eliminates equity = 1 ÷ Leverage

With leverage of 20, a 5% fall in assets eliminates equity.

Return on equity under leverage

ROE ≈ Leverage × Asset return − (Leverage − 1) × Cost of debt

Use it to show how leverage magnifies gains and losses.

Repo haircut

Haircut = (Collateral value − Loan amount) ÷ Collateral value

Loan amount = Collateral value × (1 − haircut).

Equity needed to fund collateral

Equity needed = Collateral value × haircut

A higher haircut forces a borrower to fund more with its own capital or sell assets.

Maturity mismatch (concept)

Long-term illiquid assets funded by short-term liabilities that must be rolled

This is a rollover risk, a form of funding liquidity risk.

Leverage ratio

Leverage = Total assets ÷ Equity

Higher leverage means a smaller fall in asset value wipes out equity.

Equity wipe-out threshold

Asset decline that eliminates equity = 1 ÷ Leverage

At leverage of 30, a decline of about 3.33% in assets eliminates equity.

Money fund net asset value

NAV per share = (Assets − Liabilities) ÷ Shares outstanding

Funds target $1.00. Breaking the buck means NAV below $1.00.

Collateral call on a swap

Collateral required = Mark-to-market loss on position − Collateral already posted

Applies when a CSA or rating trigger requires posting. Concept-level, rarely computed in full.

Leverage ratio

Leverage = Total assets ÷ Equity

Used to size the forced asset sale in a loss spiral.

Haircut and financing

Haircut = (Collateral value − Loan) ÷ Collateral value; Loan = Collateral value × (1 − Haircut)

A higher haircut cuts the funding available against the same asset and creates the margin spiral.

Equity funding need from a haircut increase

Equity needed = Asset value × Haircut

A rise in the haircut forces the borrower to fund the difference with equity or sell assets.

Asset sale to restore target leverage after a loss

New assets = Target leverage × (Equity − Loss); Sale = Assets − Loss − New assets

Assets fall by the loss first, then the firm sells enough to reach the target while using proceeds to repay debt.

Liquidity Coverage Ratio (LCR)

LCR = Stock of high-quality liquid assets ÷ Total net cash outflows over 30 days ≥ 100%

Short-term resilience. Tests a 30-day stress.

Net Stable Funding Ratio (NSFR)

NSFR = Available stable funding ÷ Required stable funding ≥ 100%

Long-term structural funding over a one-year horizon. Limits reliance on short-term wholesale funding.

Basel III leverage ratio

Leverage ratio = Tier 1 capital ÷ Total exposure measure ≥ 3%

Not risk-weighted. A backstop to risk-based capital. The 3% is the minimum; some jurisdictions add surcharges for large banks.

Basel III minimum capital ratios

CET1 ≥ 4.5% of RWA; Tier 1 ≥ 6%; Total capital ≥ 8%; plus conservation buffer 2.5% of RWA (CET1)

With the conservation buffer, CET1 must be at least 7%. The countercyclical buffer (0-2.5%) is added by national authorities when credit growth is excessive.

Quick revision

• The crisis began with US mortgage losses, especially subprime, after house prices fell.
• Originate-to-distribute weakened lenders' incentive to screen borrowers because risk was sold on.
• Tranching creates senior and junior claims on a pool; losses hit the junior tranches first.
• Structured product ratings relied on weak assumptions about default correlation and house prices.
• Shadow banks funded long-term assets with short-term borrowing, creating maturity mismatch.
• High leverage meant small asset declines caused large equity losses.
• Repo haircuts rising and lenders refusing to roll over funding acted like a bank run.
• Fire sales push prices down, which forces more selling and margin calls: a loss spiral.
• Interconnectedness means one failure can cause counterparty losses across the system.
• Procyclicality: capital and margin rules tighten in downturns and deepen the stress.
• Policy responses included central bank liquidity support, rescues of institutions and later stronger capital and liquidity rules.
• Always name the risk type: credit, liquidity, market, model or systemic.

Common mistakes

• Treating low interest rates as the only cause. Fix: Remember it was a combination: low rates, housing boom, weak standards, securitization and leverage. Reject options that say "solely".
• Saying subprime defaults alone caused the whole crisis. Fix: Subprime losses were the trigger. Opaque securitization, high leverage and short-term funding spread and magnified them.
• Saying securitization removes risk from the financial system. Fix: Say risk is redistributed. Banks retained senior tranches and gave liquidity support, so losses returned to them.
• Confusing MBS and CDO collateral. Fix: MBS collateral is mortgage loans. CDO collateral is a pool of securities or bonds, often MBS tranches. CDO-squared holds CDO tranches.
• Saying agencies rated CDOs AAA only because they were paid to. Fix: Give model failure (low correlation, rising house price assumption) and incentives together. Both contributed.
• Thinking the senior tranche of a CDO has the same risk as an AAA corporate bond. Fix: Remember structured ratings were far more sensitive to correlation and systematic shocks, so downgrades were sudden and severe.
• Treating a repo run as the same as a retail bank run Fix: Remember the repo run is by wholesale lenders, on secured and uninsured funding, and it shows up as higher haircuts or refusal to roll.
• Saying repo lenders lose money because the borrower defaults on an unsecured loan Fix: Repo is secured by collateral. Lenders ran because collateral values were uncertain and hard to sell, so they demanded bigger haircuts.
• Saying Lehman was rescued like Bear Stearns. Fix: Remember Bear was sold to JPMorgan with Fed support, while Lehman filed for bankruptcy.
• Treating AIG's problem as insurance underwriting losses. Fix: The trouble came from its financial products unit selling CDS and facing collateral calls.

Exam tips

• Learn the causal chain and be able to place any statement in it. Most conceptual questions test one link.
• Watch for words like "only", "solely" and "always". They usually mark a wrong option here.
• Be ready to separate the trigger (falling house prices and subprime defaults) from the amplifiers (leverage, opaque securitization, short-term funding).
• For numeric questions, LTV and equity are quick calculations. Do them first and check the direction of the answer.
• Study this topic together with securitization and the credit rating agency failures, since questions often mix them.
• Expect tranche waterfall questions: practise computing loss as a share of thickness, not of the pool.
• Be ready to define MBS, CDO, CDO-squared and synthetic CDO in one line each and spot the collateral difference.
• For crisis-cause questions, pick the answer built on misaligned incentives and opacity, not on a single actor.