Well, a little bit.

Quite a few posts recently have argued against higher *capital requirements*. That doesn’t mean I don’t believe banks don’t need higher *capital*, just that it should not be a minimum requirement (because only capital above the minimum can be used to absorb losses). I do think, though, that those capital increases should be delayed.

Given this, you might think I would be pleased when The Clearing House produced a document suggesting that a capital ratio above 7% was not necessary. Unfortunately, part of this document made me suspicious. They

*Analyzed the relationship between Basel III capital ratios of large global banks at the onset of the financial crisis (defined as December 2007), and subsequent Bank distress during the crisis.*

123 banks were in the sample, representing 65% of global banking. The document reports the following results:

Pre crisis Basel III capital ratio |
Probability of distress |

<4.5% |
43% |

4.5% – 5.5% |
29% |

5.5% – 7% |
22% |

>7% |
0% |

It was that zero that worried me. It was too convenient, and it didn’t seem to fit with the other data points. So I did some modelling.

Warning: what comes next is very, very crude.

For rather general (i.e. not very good) reasons, we would expect this distribution to be fat tailed. Given the three data points – not very many – we can’t fit anything sophisticated, so you will have to make do with this:

Note that the fit to the data points isn’t terrible. Now, obviously we are extrapolating a long way beyond what we know, but still, using the fit we get

Basel III capital ratio |
Probability of distress |

8% |
13% |

10% |
7% |

12% |
4% |

99% safety comes at a capital ratio of 18% and 99.9% at 25%.

Now, I would be the first to say that this ‘analysis’ is far more than the data will support. But still, it is interesting that this work suggests that you would have needed a very high capital ratio to get a low probability of failure during the 2008 crash. (Of course it tells us nothing about what might be needed in other, as yet unforeseen market events.)

Just as a final riff, what is the liklihood that the clearing house observed zero failures in the >7% bucket if our fit was correct? They say that there are roughly the same number of banks in each bucket, so the >7% bucket should contain roughly 31 banks. We will assume all these banks have a Basel III ratio of 8%. Then we would expect to see 13% x 31 = 4 distress events. Assuming a binomial distribution, the chances of seeing zero events when you would expect 4 from 31 is 1.5%. This is not low enough to conclude that our fit is wrong. Moreover if even one out of the those 31 is questionable and should really be counted as distress, then the probability jumps to 6.5%. So, to be charitable, the Clearing House might be unlucky rather than mendacious if the analysis above is broadly correct.

Posted in:
Basel, Probability Theory
by
David /

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