Aug 24

Friday’s Movie: Advanced Credit Risk (1st of 2)

by David Harper, CFA, FRM, CIPM

FRM | Risk |

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For members, we just published Advanced Credit Risk-Part 1 (we will publish Part 2 Monday). For non-members, the first ten minutes can be sampled here. This (Part 1) is a review 2007 FRM Learning Outcomes 51.x to 52.8.

  • Merton model
  • The estimation of probability of default (PD)
  • Scoring models, decision rules, performance measures (ROC, CAP)
  • Credit risk portfolio Models (e.g., CreditMetrics, CreditRisk+)
  • Economic capital (important!)

Merton model

FRM candidates only need to refer to the Black-Scholes-Merton option pricing model. The key insight of the Merton model is that equity holders hold a call option on the firm's assets. Shareholders "exercise their option" by retiring debt instead of paying the strike price; if they do that, they own the firm. So the Merton model for equity is the Black-Scholes, except V = firm value (total assets) and F = the face value of debt:

 mertonmodel2

KMV's EDF

Moody's KMV model applies the Merton model to calculate estimated default frequencies (EDF). The EDF is a probability of default (PD). For example, assume the following:

  • Our firm's assets are worth $130 today but have an expected future value (end of year one) of $134
  • The firm's asset volatility is 20%
  • The firm has an expected default point of $100 (short-term liabilities plus 50% of long-term liabilities; or maybe 75% of liabilities)
  • The model estimates that the expected future value of the firm's asset's will be about 29% greater than the default point
  • This 29% is 1.46 standard deviations (29%/20%) from the firm's estimated default point
  • We could use this distribution to estimate a default (i.e., the probability that asset value drops more than 1.46 standard deviations from its expected mean)
  • However, KMV Moody's maps the distance to default (DD) based on its database: what is the historical default frequency for companies, in the relevant class, that have similar distance to defaults? In short, they map DD-to-EDF empirically rather than parametrically.

 

kmvEDF

Scoring Models

Altman's Z is the classic linear discriminant: a multiple regression "draws a line" which segregates firms into subgroups. In Altman's case, a low score (less than 1.8) predicts default; a high score (above 3.0) predicts no default

 

linearDiscrim1

 

The k-nearest neighbor is non-parametric. The firm's characteristics (e.g., market cap-to-debt) are used to locate its neighbors (the "nearest neighbors"): what happened to firms with similar characteristics, did they tend to default or not?

 

kNearest1

 

Decision rules

The classification models are not perfect because they cannot predict the future. While we cannot predict the future (whether a firm will default or not), we can decide our orientation and preference toward the different error types. We may prefer to seek minimum error (i.e., assign firm's to their most likely class). But this gives no regard to the cost of our error. If we are a bank, mistakenly declining a good borrower (a borrower who will not default) is less costly than mistakenly making a loan to a bad borrower (who will default). The former, what de Servigny calls a Type II error is just an opportunity cost (a false alarm). The latter is a Type I error that" damages the wealth of the bank."

decisionRules

 

Credit risk portfolio models

For the exam, you don't need to take a deep dive on these models. But you do need to understand their high-level approaches, strengths and weaknesses. For example, KMV Portfolio manager's "definition of risk" only pertains to defaults; but CreditMetrics measures market-to-model losses based on migrations and spreads.

riskModels

 

Economic capital

Expected losses (EAD x PD x LGD) are a "cost of doing business:" as such, they are priced into loans by way of higher rates (and their expectation is covered by loss provisions).

Unexpected losses (UL) are the standard deviation of portfolio losses. If we consider the difference between value at risk (VaR) for a given confidence level and expected losses, we get economic capital. Economic capital is the amount of capital buffer, set aside to cover losses (in excess of the expected losses), up to the value at risk (VaR):

econCapital

 

But unexpected losses, and VaR, are still less than expected shortfall (ES). ES gives information that VaR does not. VaR says nothing about the distribution of losses in excess of VaR; i.e., no information about the worst losses, when we most need it! Expected shortfall fills this gap, superbly complementing VaR. It gives the expected loss given that (conditional on) the loss exceeding VaR.

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