The System’s Distribution of Losses

The first case described here is the estimation of the SDL by using 30,000random shocks originated from a parametric distribution.

Such a distribution can be seen in Figure 7 where it can be seen that it behaves closely to a normal distribution, which is not surprising given that underlying the macroeconomic shocks was the assumption of a normal distribution.

This is precisely one of the main problems in measuring systemic risk, events which threaten the system (systemic events) are located far in the tail of the SDL. One way to cope with such issue is to generate a huge number of simulations in order to populate properly the tail of the distribution. This is the way in which we proceed in the past¹¹; nevertheless, under the current framework is not possible anymore as the valuation of the market portfolios for each bank takes a considerable computing effort.

Fortunately, given that we are able to generate the consistent scenarios from a normal random shock, it is possible to bias such generation process to more extreme regions and more importantly, it is possible to estimate the probability of such an event to happen. This characteristic of the simu­lation model is as important as the consistency aspect of the generation process as it is possible to bias the distribution of the generation process to focus on the tail of the distribution without simu­lating a large number of scenarios and preserve the consistency (in terms of the generated model) of the scenarios. Having said so, we can generate scenarios that, although they are highly unlikely, at least they are in the region of possible things. We believe that this approach is more promising that the individual idiosyncratic defaults which found little evidence of contagion in previous studies.

Figure 9 shows together the 30,000 “normal” scenarios next to the 5,000 “tail” scenarios. These figures illustrate in a stylized fashion the processes of biasing the scenario generation process to the tail of the distribution. A very important remark is that the tails of such distributions do not cor­respond to the same generation process, and the graphs are not actual histograms. However, we took such liberty for illustration purposes. In this distribution, we can observe the amplified¹² losses, which were generated by biasing the scenario generation process. Losses corresponding to such scenarios are derived from extreme movements in economic variables.

Figure 8 shows the realizations of some risk factors (Cete interest rate, output, delinquency rate, and the stock index) under these extreme conditions.

The resulting distribution from the merging of the above-described distributions can be observed in Figure 9. From this figure, we can observe how it is possible to populate the tail of the joint distribution with coherent scenarios.

Even though the capitalization levels of banks in the Mexican financial system is high, contagion under the 5000 “extreme” scenarios did occur and the case is worth exploring in detail. Figure 10 shows the distribution of losses under different types of shocks. From this figure, it is possible to see the sensitivity to different factors under stress as well as to determine which factors have larger impact for the system as a whole.

3.2.