# Credit Risk

Credit risk is the risk that counterparties or obligors will default on their contractual obligations. It refers to the risk that the cash flows of an asset may not be paid in full, according to contractual agreements. Stress testing of credit risk typically begins with the collection of data on different credit qualities, usually the categories of performing loans and NPLs (e. g., substandard, doubtful, and loss) tracked by the supervisor.

Alternatively, if banks are providing their own data and estimates that are based on their internal models, then the different credit quality measures that they employ can be used. A variety of stress tests can be applied to those data, depending on the underlying quality of banking supervision. For example, if underprovisioning is an issue, a scenario that applies more stringent provisioning criteria to existing balance sheets can be performed.

For other countries, assumptions about the growth rate of different qualities of credit can be applied, or assumptions about the migration between categories can be made. Those scenarios can be based on previous recessions or episodes of rising defaults and increases in NPLs. Cross-sectional regressions of NPL ratios on various macroeconomic variables (e. g., interest rates, growth rates, exchange rates) can provide benchmark sensitivities of NPLs to different macroeconomic shocks. Once a set of adjusted data on credit quality is derived, existing provisioning rates can be applied to determine the effect on bank balance sheets.

An example of implementation of the credit risk stress test is given in the following paragraphs, which are based on a recent FSAP. The methodology proposed in Boss (2002) was used to link default frequencies and macroeconomic conditions. This model is particularly suited for macroeconomic stress testing because it explicitly models credit risk in relation to macroeconomic variables. Some models include a Monte Carlo simulation approach to calculate the loss distribution of a credit portfolio.21 However, more frequently, including the case discussed here, a simpler regression approach was used to link historically observed default frequencies to macroeconomic variables.

The expected loss at time t, E[L], is given by the volume of the credit portfolio at time t, V, times the average default probability in the economy at time t, p, times 1 minus the recovery rate, RR, which is typically assumed to be a fixed number.

E[L,] = V>,(1-RR) (10)

The average default probability at time t is modeled as a logistic function of a macroeconomic index, which depends on the current values of the macroeconomic variables under observation:

(11)

where yt denotes the macroeconomic index at time t. The pt can be estimated directly (substituting yt by a linear combination of macroeconomic variables and then using logistic regression in order to get estimated average default probabilities £>,). Or it is possible to calculate first the “observed” values for the macroeconomic index yt by taking the inverse of the logistic function using the historically observed default frequencies

(12)

and then use linear regression to explain the index yt by a combination of macroeconomic variables. If one is to get estimated average default probabilities /. ., the output of the macroeconomic model explaining yt has to be plugged into the logistic function of default probabilities. In the particular FSAP case, the following regression was estimated:

. / у

A v, = In — = A, + ptxui + p2x2, + … + PKxK, + e, with esl ~ N(0,ac), (13) bt-i)

where

Д’V, = In

is the logarithmic change or growth of the macroeconomic index, calculated according to the respective equation above and xx t, x2t, … xKt denote the set of macroeconomic variables at time t and P^ P2, – вк stand for the parameters that determine the direction

and extent of the effect that those factors have on the index or, eventually, the sector – specific default probability. The parameters are estimated by means of a linear regression, where the error term e is assumed to be an independent, normally distributed random variable.

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