VALIDATION OF CREDIT PORTFOLIO MODELS
Portfolio credit risk models give a probability distribution for portfolio credit losses. Validation of the model includes testing whether observed losses were consistent with the model’s predictions. The main focus when testing credit portfolio models is on the “high loss” end of the distribution, which, assuming normal distribution, means “low probability”. Normally one or five percent Value at risk is used, which means that a given loss within specified time will be observed with a probability of one or five percent respectively.
“A risk manager has two jobs: make people take more risk the 99% of the time it is safe to do so, and survive the other 1% of the time. Value at risk is the boarder.”1
One common way to validate portfolio models is to verify wether the experienced losses exceeded the models predictions over a certain period. Exceeding losses, assuming a 1% one day- Value at risk can be observed, assuming 250 trading days, (1 — .99) * 250 = 2, 5 trading days on average.
Credit risk portfolios usually have a much longer time horizon, usually one year. To get the same amount of excedding periods and therefore obtin the same statistical significance when testing, one would have to wait 250 years, which is clearly more than few lifetimes and therefore not really useful.
A way to obtain an idea about the validity of the model and its consistency with the observed losses is to test whether the the observed losses were consistent with the models prediction over the whole distribution- and not only if a certain Value at risk mark was exceeded.
Testing distributions with the “Berkowitz Test”
For testing the distribution with the berkowitz test the models forecast of the loss distribution at the beginning of the period is needed. The cummulated distribution of the probability of portfolio losses might loook as the figure below.
The distribution returns for a given loss, L the cummulated probability, F(L) with which this loss is not exceeded.
Furthermore experienced losses for a certain amount of period (say, five years) are required for validating the portfolio.
1 Aaron Brown (2008) in: Private Profits and Scialised Risk; GARP Risk Review
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