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Unformatted text preview: en take the default set D to be consecutive pairs of banks. The ﬁrst default
set under BNP Paribas consists of Deutsche Bank and HSBC, the next default set consists of HSBC and
Barclays, and so on.
Under “WR” (weak ratio), we report the ratio of the left side of inequality (20) to the right side.
Contagion is weak whenever this ratio exceeds 1, as it does in most cases in the table. Contagion fails to
be weak only when the banks in the default set are much smaller than the triggering bank. Moreover,
the ratio reported for each bank shows how much greater βi would have to be to reverse the direction
of inequality (20). For example, the ﬁrst ratio listed under BNP Paribas, corresponding to the default
14 Based on Federal Reserve Release H.8, the average value of β for commercial banks in the U.S. is about 3%, so our
i
estimates for European banks would appear to be conservative. 32 of Deutsche Bank and HSBC, is 18.64, based on a βi value of 4.6% (see Table 2). This tells us that
the βi value would have to be at least 18.64 x 4.6% = 85.7% for the weak contagion condition to be
violated. In this sense, the overall pattern in Table 1 is robust to our estimated values of βi . Expanding
the default sets generally makes contagion weaker because of the relative magnitudes of wi and λ−1 ; see
i
(20) and Table 2.
Under “LR” (for likelihood ratio), we report the relative probability of failure through independent
direct shocks and through contagion, calculated as the ratio of the right side of (22) to the left side.
This is the ratio of probabilities under the assumption of a uniform distribution p = q = 1, which
is conservative. An asterisk indicates that the ratio is inﬁnite because default through contagion is
impossible.15 The value of 6.68 reported under BNP Paribas for the default set consisting of Banco
Santander and Societe Generale indicates that the probability of default through independent shocks is
6.68 times more likely than default through contagion. Raising the LR values in the table to a power of
q > 1 gives the corresponding ratio of probabilities under a shock distribution having parameters p = 1
and q .16
Table 2 reports a similar analysis by country. Within each country, we ﬁrst consider the possibility
that the failure of a bank causes the next two largest banks to default – the next two largest banks
constitute the default set D. (In the case of Belgium, there is only one bank to include in D.) For each
bank, the column labeled “Ratio for Next Two Banks” reports the ratio of the left side of inequality
(20) to the right side. As in Table 1, contagion is weak whenever this ratio exceeds 1. The table shows
that the ratio is greater than 1 in every case. As in Table 1, the magnitude of the ratio also tells us how
much larger βi would have to be to reverse the inequality in (20).
The last column of the table reports the corresponding test for weak contagion but now holding D
ﬁxed as the two smallest banks...
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This document was uploaded on 02/20/2014 for the course ECON 101 at Pontificia Universidad Católica de Chile.
 Spring '11
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