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# Unexpected Loss and VaR

Unexpected losses are loss percentiles in excess of the expected loss. The expected loss is an average used for provisioning. The unexpected loss is the additional loss beyond the expected loss and up to the loss percentile used for defining VaR.

VaR applies both to market and credit risk. For market risk, for example, where the 1% confidence level is used, 1% of all 250 trading days would designate a loss not exceeded in more than 2 to 3 days within a year. The expected tail loss or expected shortfall is the expectation of the losses beyond the VaR. All these measures are discussed in the chapters dedicated to market risk and credit risk (Sections 10 and 11).

# Exceptional Losses

Unexpected loss does not include exceptional losses beyond the loss percentile defined by a confidence level. Exceptional losses are in excess of the sum of expected loss plus the unexpected loss, which is equal to the loss percentile L(a). Only stress scenarios, whereby we need to consider all effects of extreme situations, help finding out the order of magnitude of such losses.

# Loss Distributions, Potential Losses and VaR

If we assemble those definitions in a single graph, the three measures would appear as in Figure 18.3. The distribution is asymmetric, with a fat tail extending to the right, and matches the general shape of portfolio losses for credit risk. For market risk, the loss distribution would be an earnings distribution truncated towards losses only.

Losses appear on the right-hand side of the zero level along the x-axis. The VaR at a given confidence level is a loss percentile in excess of expected loss. The area under the curve between

FIGURE 18.3 Unexpected loss and VAR

EL and VaR value on the x-axis represents this probability. The maximum total loss at the same confidence level is the sum of the expected loss plus the unexpected loss (or loss percentile).

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