This post is as close as I get to a “rant”.

Some parts of Basel formulas have unnecessary complexity, which involves not just inefficiency but also potential pitfalls.

The specific example is the formula for asset correlation which appears in Basel paragraph [283] and which includes a term 0.12 x (1-EXP(-50 x PD)) / (1-EXP(-50)). There are similar terms elsewhere in Basel formulas, but for focus let’s look at just this case. Surely, this term should be given as simply 0.12 x (1-EXP(-50 x PD)).

Presumably the casters of the formula felt a need to normalise the term to handle PD its full range of [0,1]. This may satisfy academic neatness but, I maintain below, at significant risk of causing error or wasted resource.

The materiality of the normalising denominator is as close to nil as
any banker could imagine. The term EXP(-50) evaluates as 2 x 10**-22
which means 0.0000000000000000000002. When one subtracts this from 1 it
makes no difference and you still end up with 1. In the old days, this
used to cause a computer error known as underflow, whereby the floating
point arithmetic processors rearrangeing numbers for calculation would
discover that during this process one of the quantities had
disappeared, which although not automatically a fatal error, would
probably be something you wanted to know about. In the case of
the above Basel term it’s not an *error* but it is *frivolous formulaic complexity* and in practical terms the denominator equals 1 and the term should be simplified to 0.12 x (1-EXP(-50 x PD)) .

OTOH to make a pedantic point if Basel wants the answer to come out exactly the same, they could change the multiplier from 0.12 to 0.1200000000000000000000024 . Or, add a sentence in the doc saying that, whilst a normalising denominator was academically desirable, it was omitted on materiality grounds.

Whatever, the materiality of the denominator term is less than a thousandth of a cent even when multiplied against a capital figure of $100billion.

What makes this a non-trivial rant is that there is significant cost to extra complexity. In my experience, only the most adept of the technical team would be able to transcribe such a formula without error. Others not directly familiar with the context, such as managers or computer programmers, are prone to transcription errors. But, most perversely, if I were to see such a formula presented by an intermediary – say, for example, as part of a computer program – I would assume strongly that a transcription error had been made because the logic of the formula fails the “sanity test”.

Much as I admire maths, a Basel implementation is fraught with thousands of small hurdles (OK and big ones), and we owe it to the business community to adopt pragmatic stan

dards.
## 1 comment

20 April, 2008 at 21:23

AndrewI love a good rant.