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Describe the stress testing that is possible for a portfolio of loans and for a portfolio of derivatives.

FRM® Part II · Credit Risk Measurement and Management · The Evolution of Stress Testing Counterparty Exposures · FRM2.CR.21.c

The idea

A stress test of a loan portfolio shocks the credit parameters of each exposure: probability of default, loss given default and exposure at default, for example through higher drawdowns on committed lines. The shocks usually come from a macroeconomic scenario such as a recession, with sector or regional concentration shocks and higher default correlation. Loan exposure is fairly well known, being the outstanding balance plus any drawdowns. A derivatives portfolio needs an extra step because exposure itself is uncertain. The scenario first shocks market risk factors such as rates, FX, equity and commodity prices, volatilities and credit spreads. The netting sets are then revalued and collateral is applied to give stressed exposures. Only then are counterparty PDs and LGDs stressed. Further derivative-specific choices are a longer margin period of risk, larger collateral haircuts and wrong-way dependence. The aim is one consistent scenario applied to loans and derivatives and aggregated by counterparty.

Formulas

Stressed exposure of a collateralised netting set

stressed exposure = max(Σ MTMₛ − C, 0)

MTMₛ
each trade's mark-to-market after revaluation under the scenario
C
the collateral held against the netting set

Revalue under the scenario first, then net and deduct collateral. Using base-case values or ignoring collateral are the usual slips.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which set of inputs is typically stressed in a stress test of a loan portfolio?

  1. Probability of default, loss given default and exposure at default, for example through drawdowns on committed lines - correct
  2. Mark-to-market values of rates, FX and equity risk factors, to obtain future exposureWhy not: Describes the derivatives step; loan exposure is largely the known balance.
  3. Only the margin period of risk and collateral haircutsWhy not: Collateral parameters for derivatives; they are not the main loan stress inputs.
  4. Only borrowers' credit ratings, since LGD and EAD are contractual constantsWhy not: LGD and EAD move in stress: collateral values fall and borrowers draw lines.

Loan stress tests shock PD, LGD and EAD, usually from a macro scenario. Exposure is basically known, so there is no market-factor revaluation step as there is for derivatives.

A harder one

A bank has loans and OTC derivatives with the same set of corporate clients. Which stress test design is most appropriate?

  1. Separate scenarios for each book, run by different teams, with the results added togetherWhy not: Without a common scenario the dependencies between exposure and credit quality are missed.
  2. Stress only PDs for both books because market factor moves are a market risk issueWhy not: Ignores that market moves drive derivative exposure.
  3. One coherent macroeconomic scenario that moves PDs, LGDs and market risk factors together, with results aggregated by counterparty - correct
  4. Stress the derivatives for market factors only, since loans are carried at amortised costWhy not: Ignores credit stress for derivative counterparties and the combined counterparty view.

Consistency matters: the same scenario should drive credit parameters and market factors, so that exposure, PD and LGD are linked and the total stressed loss per counterparty is meaningful.

The hardest tier

In a stress test of a loan portfolio, which change raises the tail of the stressed loss distribution while leaving portfolio expected loss unchanged?

  1. Raising default correlation among borrowers, with PD, LGD and EAD held fixed - correct
  2. Doubling every borrower's PDWhy not: Expected loss is proportional to PD, so this raises expected loss.
  3. Cutting recovery rates so LGD risesWhy not: Expected loss is proportional to LGD, so this raises expected loss.
  4. Higher draw-downs of committed linesWhy not: Expected loss is proportional to EAD, so this raises expected loss.

EL = sum of EAD x PD x LGD, so it does not depend on correlation. Correlation changes how losses cluster, which fattens the tail (unexpected loss) but not the mean.

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