the subset of “Banks at Risk” as the most vulnerable banks that collectively represent at least 20% of banking system assets.<sup>10</sup> We use total assets to break DBP ties.

Next, for the “Banks at Risk” we compute the consolidated values at the country level for the Consolidated Break Point (CBP) and the Consolidated Distance from Break Point (CDBP). The weight of each bank is proportional to its gross loans. The CDBP summarizes a country’s vulnerability to an increase in NPLs focusing on the weakest banks. Higher values indicate that a banking system is more resilient.

Table 1 summarizes the steps followed using an illustrative example. Note that the CBP (17.4%) minus the CDBP (13.6%) does not correspond to the weighted NPL ratio (4.0%) for “Banks at Risk” reported in Table 1. This is because the value of the DBP is 0 for one bank (Bank A) which is already undercapitalized.

# **Table 1. Illustration of the computation of CBP and CDBP**

_Column “Bank ID” shows the “Banks at Risk”. These banks have the smallest DBP values (Column C) and jointly represent at least 20 percent of banking assets (in fact they cover 30%, see Column E). The consolidated Bank’s Break Point (CBP) of “Banks at Risk” is 17.4% (of gross loans) (Column G). The consolidated Distance from Break Point (CDBP) is 13.6 percentage points (Column H)._

|||**’**|**B**<br>|**ank-level an**|**alyses**<br>**Cumulative**||**Country-leve**<br>|**l analyses**<br>**Consolidated**|
|---|---|---|---|---|---|---|---|---|
||||||||||
|**Bank**<br>**ID**|<br>**ratio**<br>**(% gross**<br>**loans)**|**ans**<br>**Break Point**<br>**(BP) (% of**<br>**gross loans)**|**sance rom**<br>**Break Point**<br>**(DBP) (%**<br>**points)**|**Total**<br>**assets ($**<br>**millions)**|**banking**<br>**assets (% of**<br>**total banking**<br>**system assets)**|**Gross**<br>**loans ($**<br>**millions)**|**onsoae**<br>**Break Point**<br>**(CBP) (% of**<br>**gross loans)**|**Distance to**<br>**Break Point**<br>**(CDBP) (%**<br>**points)**|
||**(A)**|**(B)**|**(C)=(B)-(A)**|**(D)**|**(E)**|**(F)**|**(G) =**<br>**[sum(B×F) /**<br>**sum(F)]**|**(H) =**<br>**[sum(C×F) /**<br>**sum(F)]**|
|A|19.3|1.8|0.0|2699.6|0.38|1,793.7|||
|B|4.1|10.2|6.1|41321.3|6.24|40,282.5|||
|C|3.5|11.4|7.9|2456.5|6.58|1,987.3|||
|D|2.4|18.4|16.0|74323.6|17.11|53,387.0|||
|E|4.9|21.5|16.6|94968.7|**30.57**|69,889.1|**17.4**|**13.6**|

The results of the bank-level reverse stress testing are computed under the following assumptions, some of which can be relaxed:

- **Negative impact from increased provisioning.** The decrease in total regulatory capital is generated by an increase in loan loss provisioning associated with the increase in NPLs. The increase in NPLs occurs because of a re-balancing of the loan portfolio, where performing loans turn to NPLs due to a credit shock.

- **No profits.** We make the conservative assumption that banks have no profits. Hence provisions are fully absorbed by capital. This assumption can be relaxed by adjusting Equation (1) as follows: −M

- = (6)

- ) + M ii ii CC ) −Mii ]

- ii TTM + PPrrTTPPMMcc MM × MMR ii

- BBPP ii cc ii cc ii + NNPPNN rrc MMTT [(55% × GGrrTTP NNTTccMMPP MM × (55% × GGrrTTP NNTTccMMPP MM × MMR TTr MMPP

where _Profit_ could be current profits or a hypothetical value (for example the average or minimum value of a bank’s profit over a 10-year period). In a robustness test presented below, we compute the BP as per equation (6) and then the consolidated values (CBP and CDBP) as described above.

> 10 As discussed in Laeven and Valencia (2013), a systemic banking crisis could be defined as the collapse of a relevant fraction of the banking system. Among several other criteria, the authors identify the collapse of banks representing 20% of banking system assets as a sufficient condition to classify a crisis episode as “systemic”.

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