There are various measures of potential losses: Expected loss (EL), loss percentiles, unexpected loss (UL) and exceptional losses. Some other measures can also be defined, one of them being the "expected shortfall," or the expected loss beyond a loss percentile. All such measures are defined formally later on, and we provide here broad definitions.

Expected Loss

Expected loss is the probability weighted average of all possible losses. It is widely used for credit losses, notably when there is a large portfolio of loans. In retail financial services, the portfolio is "granular," meaning that all exposures are small compared to the portfolio size and that none has a "large" value.

Expected loss is the mean of the loss distribution. Expected loss provides the foundation for economic provisioning. The expected loss measure used in Basel 2 as a benchmark for provisioning, applies to credit losses. For market risk, the horizon is shorter than with credit risk and expected P & L from the trading portfolio is usually not considered.

Credit losses will never equal such expectation. Sometimes they will be higher and sometimes lower. For a single exposure, the real loss is never equal to the average, since it would be either zero or the loss under default. On the other hand, for a portfolio, the expected loss is the mean of the distribution of losses. It makes sense to charge this average to each transaction, because each one should contribute to the overall loss.

Loss Percentiles

A potential loss is a loss percentile defined with the preset confidence level. The loss threshold is L(a), where a is the one-tailed2 probability of exceeding L(a), or percentile. For example, if L(l%) equals 100, it means that the loss will not exceed the value of 100 in more than 1%, or 1 out of 100 possible scenarios. Determining potential losses at various confidence levels requires the loss distribution of the portfolio. The loss distribution provides the frequency of the various possible values of losses. It is highly sensitive to dependencies between positions. This is the major technical challenge raised by measuring loss percentiles in credit portfolio models, and addressed in Section 9 (dependencies) and Section 12 (credit portfolio models).

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