The square root of time

12 Feb 2016 | Richard Kemmish

The square root of time might sound like a concept from Doctor Who but it is actually used in the pfandbrief regulations. Section 5(2) of the net present value regulations if you really want to investigate further.

Without getting too mathematical here (there may be some readers who are not maths-obsessed nerds), the idea is that the likely variation in, say, an interest rate over a time period is related to the likely variation in the same interest rate over a different time period according to the ratio of the square roots of the respective time periods.  Just take my word for it, ok?

What on earth has that got to do with Pfandbrief?

One of the many nice touches of the pfandbrief regulations – one that regulators in other countries might want to make note of - is that it frequently works with existing bank regulations. If an issuer needs to do something as part of its general supervisory framework and there is something analogous in the covered bond law it saves a lot of time and effort if the methodologies could be aligned.

Specifically, if a pfandbrief issuer uses the IRB approach to capital then they must have had their interest rate stressing model signed off by the BaFin. Why adopt a simplistic approach to interest rate stresses (plus or minus 100 basis points) when there is something much more sophisticated (3 standard deviation moves) already approved?

Of course the basis for the calculation of IRB models is different from the basis on which cover pools must be stressed, in particular the time period (10 days and six months), which is where the square root of time becomes useful to translate the numbers generated form one model to use in the other.
This is a much wider topic than simple interest rate stresses. There are many cases where regulators have adopted one approach for bank regulation and one for covered bond regulation. The most obvious (annoying?) of which is where a property has to be valued on one basis for internal capital purposes and another for LTV purposes in a cover pool, more often than not market value and mortgage lending value respectively. From a practical point of view that requires every bank to revalue every property on a new set of criteria.

But there are plenty of other examples.

I think there are two reasons for the reinvention of methodologies. Firstly, (my personal bete noire) an attempt to copy regulations from other countries without taking into account local specificities: ‘if it works well in Germany, then surely it must work well here?’.

Secondly an excess of caution: we should take a more conservative approach for covered bonds because covered bond regulations ostensibly set a higher bar for investor protection.

But as the pfandbrief example shows, the output of a model can be adjusted when it is used differently, even if that involves obscure mathematical concepts like the square root of time.

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