Second Round Effects
Stress tests can be improved by including secondround effects. In particular, most stress tests assume no realignments of portfolios in response to risk factors. Stress tests are typically applied to balance sheets at a point in time or in conjunction with a forecast over a specific horizon, and the effect is calculated as if the shock were “markedtomarket” or were valued at market prices. This approach is valid if the time horizon is short or if changes in the portfolios take time to implement. For example, assuming only a limited behavioral response in a large loan portfolio over a 1month horizon may be a reasonable assumption, because it is often difficult to restructure a portfolio in a short time without incurring losses from “firesale” prices.22
Such an assumption may also be justifiable for an individual institution that does not have a large effect on the financial system or the macroeconomy, that is, the feedback effects are relatively small. However, once the time horizon of a scenario or shock extends beyond a year or more, the assumption of no behavioral response becomes harder to justify. Similarly, for systemically important institutions or systems as a whole, the assumption of no feedback effects may be an oversimplification. The policy environment may also change over a longer horizon as monetary or supervisory authorities react to shocks.
One approach that is often used to consider secondround effects and linkages between institutions is the use of contagion models.23 Those models attempt to estimate the effect of the failure of key institutions on other institutions and, hence, the overall financial system. The models have so far been used mostly for the analysis of risks arising from the interbank market, even though the same concept can be used for contagion analysis more broadly. The following example shows an analysis of interbank contagion.
There are two general types of interbank contagion stress tests: (a) pure interbank stress test, in which the shock is the failure of one bank, triggered, for example, by fraud, and the effect on other banks in the system is through the interbank exposures; and (b) integrated interbank stress test, in which the banking system is first subjected to macroeconomic shocks or scenarios. If those shocks or scenarios trigger a failure of a bank or
Bank 1 
Bank 2 
Bank n1 
Bank n 

Bank 1 
— — 
E 1,2 
E1,n – 1 
E1,n 

Bank 2 

— 

Bank n – 1 
En,1 
En – 1, 2 
— — 
— — 

Bank n 
En 
En, 2 
E, n – 1 
— — 
Note:The diagonal elements of this n x n matrix marked "—" are zero; the off diagonal element Ej indicates net uncollateralized lending from bank i to j. 
a group of banks, the interbank stress test is run to assess the effect of additional failures through interbank exposures. The basic methodology of the two approaches is the same; the difference is that the integrated stress test is run through a system that is already weakened by an external shock.
The key input to the interbank contagion stress tests is a matrix of bilateral exposures (see table D.1). In this matrix, the cell in the ith row and jth column contains the net uncollateralized lending from bank i to bank j, E.., defined as a difference between all loans and similar exposures (including offbalancesheet exposures) from bank i to bank j, minus all loans and similar exposures from bank j to bank i. Note that E.. = —E.
The “pure” interbank contagion stress test aims to estimate the effect of the failure of a bank or group of banks on the system. The test assumes that there is a failure in a bank (say, Bank 1), for instance, caused by a fraud. The first round of the contagion calculation would derive the direct effect of Bank 1’s failure on each of the other banks, assuming Bank 1 would not repay its uncollateralized interbank exposures (or a part of the exposures). If some banks fail as a result of Bank 1’s failure,24 the second round of the calculation would derive the effect on each of the remaining banks of those newly failed banks’ not repaying their uncollateralized interbank exposures. The process can be repeated for a third time if there are new failures after the second run, and so on. Concrete examples of such interbank contagion tests and their results can be found in Furfine (1999) for U. S. banks; in Wells (2002) for United Kingdom banks; in Blavarg and Nimander (2002) for Swedish banks; and in Elsinger, Lehar, and Summer (2002) for Austrian banks. In the case of the United Kingdom, Sweden, and Austria, the tests presented in the articles are very similar to those carried out under the FSAP.
The results of the contagion calculations can be presented in a number of ways. Figure D.1 provides an example of such a presentation in a case of a system with four banks. For an interesting example of presenting the network structure of the interbank market with a large number of banks, see Boss et al. (2004).Two indicators of systemic risk can be calculated from the output of the pure interbank stress test: (a) a frequency of bank failure indicator, which is the ratio of the cumulative number of failures to the number of banks in the system, and (b) statistical measures of the effect on bank system capital (e. g., mean, distribution, and quartiles). Specifically, one can define a “systemic risk index,” which is the average reduction in capital ratios of banks in the system triggered by a failure of a












bank. Such a measure could be computed for all banks in the system and used to rank them by their systemic importance.
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