Outline the lessons from the three model risk case studies.
The idea
The model risk case studies teach recurring lessons. They include JPMorgan's London Whale episode in 2012, the 1998 collapse of Long-Term Capital Management, and the pricing of credit derivatives with a Gaussian copula. Models fail when assumptions calibrated on a short, benign history break in stress, such as stable correlations and constant liquidity. Leverage then magnifies the loss. They also fail when models are built or changed in manual, poorly controlled processes such as spreadsheets, approved in a hurry, and never independently validated. A model change that conveniently lowers a risk number needs extra scrutiny, parallel runs and reconciliation with the old model. Management must understand model limits and not treat a market convention or a single output figure as truth. Exam point: governance, independent validation and stress testing of assumptions are the common remedies.
Formulas
Loss as a share of equity under leverage
equity loss = asset fall × (assets ÷ equity)
- asset fall
- the percentage fall in asset values
- assets
- total assets
- equity
- the equity financing them
Leverage multiplies a modelling error: a fall only modestly larger than VaR implied can wipe out most of the equity.
A practice question
What did investigations into the 2012 JPMorgan Chief Investment Office (London Whale) losses reveal about the new VaR model introduced for the portfolio?
- It was prohibited by regulators and was never used by the office.Why not: The model was used; the failure was in its construction and approval, not a regulatory ban.
- Spreadsheet formula errors and weak validation led it to understate risk. - correct
- It overstated risk, which led the bank to sell positions prematurely at a loss.Why not: The lesson is the opposite: the model understated risk and allowed large positions to build.
- It was a Gaussian copula model that mispriced tranches of securitised mortgage portfolios held at the bank.Why not: This confuses the case with the copula pricing of credit derivatives; the issue here was a VaR model built in spreadsheets.
The key lessons are operational: manual spreadsheet processes, errors in formulae, rushed and cursory model review, and an understatement of VaR. Strong controls and independent validation were missing.
A harder one
A bank values senior tranches of a collateralised debt obligation with a one-factor Gaussian copula and a single correlation parameter calibrated in a calm market. Which lesson from the model risk case studies does this practice most directly violate?
- Stress-test the model's assumptions instead of treating a market convention as validated. - correct
- Always replace the market-standard model with the bank's own proprietary model, which will necessarily be more accurate.Why not: Wrongly assumes a proprietary model is automatically better; the lesson is to understand assumptions, not to avoid standard models.
- Always calibrate to the longest available history, regardless of market regime.Why not: A longer history does not remove the assumption of stable correlation; the problem is the assumption.
- Increase model complexity until no single parameter drives the result.Why not: Complexity can itself add model risk; the issue is unexamined assumptions.
A model used as a market convention can give false comfort. If correlation is unstable and risk is concentrated in the tail, a single calibrated parameter understates senior tranche risk when conditions change.
The hardest tier
A highly leveraged fund holds assets of USD 125 million financed with equity of USD 5 million. Its 99% 10-day VaR model, calibrated on a calm history, gives a maximum loss of 1.2% of assets. In a stress, asset values fall 3.5%. Which statement best describes the outcome and the lesson?
- Equity falls 3.5%, since the loss is a percentage of asset value, and the lesson is that the VaR was accurate.Why not: Ignores leverage: the loss is applied to assets of USD 125 million against equity of USD 5 million.
- Equity falls 30%, in line with the VaR, and the model performed as designed.Why not: This is the VaR-implied equity loss (1.5/5), not the loss in the stress (4.375/5).
- Equity falls 12.5%, and the lesson is that leverage has no effect on model risk.Why not: Misapplies the loss; and leverage is what transforms a modest asset loss into a large equity loss.
- Equity falls 87.5%, not the 30% VaR implied, because leverage magnifies the error. - correct
Stress loss = 3.5% x 125 = USD 4.375 million, which is 4.375/5 = 87.5% of equity. VaR implied 1.2% x 125 = 1.5 million, or 30% of equity. LTCM-type failures combine wrong assumptions and high leverage.
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