Sunday, 14 October 2007

Incentive structures in capital estimation

A capital model creates an incentive structure: if a firm's estimate of the capital required to support its business rises, then that implies it is taking more risk. At some point increasing risk becomes unacceptable given the firm's desired soundness standard, and so positions are cut.

Recently there have been some discussion by Gillian Tett in the FT (quoted by Naked Capitalism) of this effect with regard to VAR models. The basic problem in VAR is that risk estimates can increase either because the portfolio has changed or because market volatilities and correlations have increased. Thus with a regularly updated VAR model the same portfolio in a crisis produces a higher capital charge and hence banks are incentivised to cut at the worst moment. Similarly risk estimates are lower in calm markets, encouraging banks to over-leverage.

The effect can be significant. As Ms. Tett points out

[The Bank of England] estimated that a typical bank’s VAR might theoretically double, with the same assets, if volatility increased.

A similar problem occurs in Basel 2 IRB models - in an economic downturn, banks' estimates of PD and LGD rise, increasing capital, and so discouraging lending. This may intensify the intensity and duration of the downturn.

The phenomenon is known as pro-cyclicality, and it is clearly undesireable. One problem here is that regulators have confused two different kinds of risk sensitivity. Clearly at any point in time having a larger capital estimate for a riskier portfolio than for a less risky one is a good thing: let us call this portfolio risk sensitivity. (Basel 2 doesn't completely satisfy this either, but we will ignore that for the moment.) Then there is temporal risk sensitivity: here the risk estimate of the same portfolio changes over time as market factors used as inputs to the capital model change. It is much less clear that complete temporal risk sensitivity is a good thing. Using long term average inputs to VAR or IRB models might produce better incentives than short term current market estimates. Such models would have the helpful (in a crisis) property of failing to respond quickly to changes in market conditions.

It might be argued that this means that banks are under-capitalised during tough markets. That would be a reasonable argument if VAR produced capital estimates which reflect possible losses in these markets - but it doesn't (and it was never designed to). One needs only examine Morgan Stanley's latest 10-Q to see the phenomenon: their VAR was very roughly $100M yet they suffered a one day loss of $390M. This does not mean that their VAR is broken: VAR is not intended to give an account of how big losses might potentially be. But it does illustrate that modern trading activities can generate losses far in excess of VAR capital estimates, and hence that other risk measures such as stress tests are important too. This relegates VAR to its proper place, as one risk measure amongst a number. In this setting market risk capital would not be based on the VAR alone, and shows that there is no need to have overly temporally risk sensitive capital estimates.

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