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Show where retail credit risk and corporate credit risk part ways.

FRM® Part II · Credit Risk Measurement and Management · Credit Scoring and Retail Credit Risk Management · FRM2.CR.7.b

The idea

Corporate credit risk is assessed borrower by borrower by analysts using financial statements, ratings and judgement, and exposures are large and lumpy so single-name concentration matters. Retail credit risk is assessed on large pools of small, homogeneous exposures using statistical scorecards, with PD, LGD and EAD estimated for segments from historical data. Let p be each loan's default probability and N the number of independent loans. The standard deviation of the pool default rate is then SD = √(p × (1 − p) ÷ N). It shrinks as N grows, so idiosyncratic risk diversifies away and retail losses are driven mainly by systematic factors such as unemployment and house prices. Under Basel IRB, retail default can be defined at the facility level rather than the obligor level. Retail capital formulas have no maturity adjustment and use supervisory asset correlations by sub-class. The usual error is to apply single-name concentration thinking to a granular pool.

Formulas

Standard deviation of a pool's default rate with independent loans

σ = √(p × (1 − p) ÷ N)

p
the default probability of each loan
N
the number of loans in the pool

Independent, identical loans only. It shrinks with N, which is why idiosyncratic risk vanishes in a granular pool while correlated, systematic risk remains.

A practice question

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

Under the Basel internal ratings-based approach, at what level may default be identified for retail exposures?

  1. Only at the obligor level, because a retail borrower in default on one loan is always in default on all of them.Why not: That is the corporate convention; retail may be applied facility by facility.
  2. Only at the portfolio level, once the pool's loss rate exceeds a supervisory threshold.Why not: Default is a status of an exposure, not of a portfolio whose loss rate crosses a threshold.
  3. At the level of the individual facility, so a customer may be in default on one loan while others remain performing. - correct
  4. At the level of the external rating agency, which declares retail defaults.Why not: Retail borrowers are not externally rated; the bank identifies default from its own records.

Basel allows retail default to be defined at facility level, whereas corporate default is defined for the obligor. This is one of the structural differences between the two books.

A harder one

A bank's card pool has 10,000 accounts. Each has a default probability of 2% and defaults are independent. The standard deviation of the pool default rate is closest to:

  1. 14.00%Why not: Uses the standard deviation of a single loan's default indicator and ignores diversification across 10,000 accounts.
  2. 2.00%Why not: Treats the mean default rate as its own standard deviation.
  3. 0.02%Why not: Divides p by sqrt(N) instead of using sqrt(p x (1 - p) / N).
  4. 0.14% - correct

Std dev of default rate = sqrt(p(1-p)/N) = sqrt(0.02 x 0.98 / 10,000) = 0.14%. With independence, granularity makes idiosyncratic risk very small.

The hardest tier

A card pool begins the year with 2,000 accounts and an average balance of USD 10,000. During the year 60 accounts defaulted. Balances at default averaged USD 12,000 because customers drew down before defaulting, and recoveries were 35% of balance at default. The pool loss rate relative to the starting exposure is closest to:

  1. 1.95%Why not: Uses the starting average balance of USD 10,000 as the loss base per defaulter and ignores the draw-down before default.
  2. 2.34% - correct
  3. 3.00%Why not: Reports the default rate and ignores both the loss severity and the exposure at default.
  4. 3.60%Why not: Ignores recoveries, i.e. assumes an LGD of 100%.

Loss = 60 x 12,000 x (1 - 0.35) = USD 468,000. Starting exposure = 2,000 x 10,000 = USD 20 million. Loss rate = 2.34%. Retail losses are measured at pool level as default rate x EAD x LGD.

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