Business 21C - Published by UTS Business

In the fall out from the global financial crisis, mathematicians and their financial models have received a good deal of attention – not much of it flattering. Are they the fall guys or the felons? Professor Erik Schlögl considers the evidence.

In the recent financial crisis, the use of mathematical models in finance has received quite a bit of attention, most of it unflattering. An article in Wired Magazine titled ‘Recipe for disaster: the formula that killed Wall Street’ is not even the most extreme example. A lot of the criticism tends to be sensationalistic and oversimplified, but this shouldn’t blind one to the serious arguments hidden in the polemic.

Academics often assume that practitioners are sceptical of models, as they should be. In the lead-up to the crisis, this doesn’t seem to have been the case. Models have their uses, and in an ever more efficient, faster-moving, interconnected and thus more volatile financial system they are indispensable tools.

However, one must be careful to use them for what they can deliver, rather than for what would be nice to have. Quantitative methods were misused, highly leveraged positions were built on vulnerable assumptions, and quantitative models were called upon to provide a veil of security.

So which arguments apportioning some of the blame for the present crisis to the use (or misuse) of quantitative methods should be taken seriously (though not necessarily endorsed)? At the risk of also becoming guilty of oversimplification, I would state them thus:

1. The models don’t work when they are most needed.
2. Models that give a false sense of security are worse than no models at all.

It is hard to argue with the first point: When they were most needed, the models did fail – and not for the first time. Dynamic hedging strategies (based on quantitative models) failed during the crash of 1987, and ten years later quantitative strategies eventually failed for the hedge fund, Long Term Capital Management (LTCM). Thus the consequences were well known, those of ignoring the limitations of models, and of failing to ask what would happen if the model assumptions no longer hold.

But the lesson hadn’t been learned. The models with the most simplest formulas and thus with the most restrictive assumptions remained the most attractive to practitioners and VaR (‘Value at Risk’) remained the standard metric for measuring risk, because it ostensibly allows the risk of a complex financial position to be expressed as a single number.

Unwarranted simplification aside, the problem wasn’t as much the use of quantitative methods, as the seeking of inputs where there were none to be obtained reliably. To have at least some semblance of reality, the models must be calibrated to the market, so additional modelling assumptions were made up to a point where calibration was possible. Subsequently the oversimplification was forgotten – obscured by the illusion that something was rigorous and exact simply because it was expressed in equations.

The pressure for ‘simpler is better’ came from the trading and the management side and attempts by quantitative analysts to model the more complex were not helped by the fact that such models are impossible to calibrate reliably. There was an adverse selection among quantitative models: If you have one model which tells you you can’t do this and one that says you can, as a manager, which one (and which quant that came up with it) do you pick?

The problems faced in model calibration/estimation are particularly dire when trying to reflect any type of extreme and rare event. Theoretically, one might fix the models to better take these events into account. However, the best one can do is to demonstrate what we don’t know, and to generate extreme scenarios for stress tests. There is simply not enough data to do more. Blaming a particular model rather than its misuse makes it likely that the same mistakes will be repeated when a supposedly better model comes along.

Which brings us to the second argument, that models which give a false sense of security are worse than no models at all. Exponents of this point of view essentially presume that it is not possible to use quantitative models in finance correctly, because people will succumb to the temptation to misuse them.

Based on recent experience, this has some merit – as an empirical observation. The business decisions that led to the present crisis were not made by people who queried the assumptions underlying the models, but by people who wanted to know only what was needed to ‘get the job done’. In such an environment, there are strong disincentives to using the models properly, and they become little more than a fig leaf hiding highly speculative positions under a cover of respectability.

The key question is, do the metrics need to be simple enough for the managers to understand or the managers sophisticated enough to understand proper metrics? To date, the line followed in practice has been mainly the former: Most prominently, VaR is a dangerous oversimplification, which had resounding success in the industry, driven by the need to have something that can be easily understood by top management. If this is the best we can do, then yes, we might be better off without the false sense of security that VaR in particular imparts.

However, although we are likely to see more regulation of financial markets, the complexities of the global financial system will not go away. Models can help navigate these complexities and identify the pitfalls – which is helpful as long as the potential pitfalls are treated as such, and not glossed over by heroic assumptions when expedient. The bottom line is to calibrate to what you know, and stress test for what you don’t know. Risks which we can calibrate, we can manage and even hedge, while risks for which we can stress test, we can at least identify.

Nevertheless, even calibrated models will only reflect the market consensus and therefore will not take into account risks currently not perceived by the market. In 2005 or 2006, the possibility of a crisis (beginning 2007) wasn’t priced in, except perhaps with so low a probability as to be negligible. The market did not predict the crisis, so a model calibrated to the market could not – and it shouldn’t be expect to.

Of course, the market can be wrong, and unfortunately the consequences are asymmetric: It is dangerous to bet against the market (as Warren Buffett likes to quote John Maynard Keynes, ‘The market can stay irrational longer than you can stay solvent.’), but also dangerous to rely blindly on market-implicit information, possibly betting on the market remaining irrational.

So where do we go from here? Future financial crises won’t be prevented by outlawing killer formulas. The system needs more transparency, less leverage, more appropriate accounting for risk, and incentive structures which do not undermine these principles. In the context of the application of quantitative methods, this means:

1. An awareness of and a constant vigilance with respect to the validity of the assumptions underpinning the models:

• Calibration only where possible, extensive stress-testing wherever necessary.
• No illusions of rigour and precision when these are based on unrealistically restrictive assumptions. Move away from the deceptively simple (single number) approaches to risk.
• Identification and recognition of tail risks which cannot be calibrated, estimated, or engineered away.

2. Use of quantitative methods to dampen risk, not magnify it:

• More focus on static rather than dynamic hedging arguments.
• No hugely leveraged positions to exploit minute arbitrage opportunities.
• More effort on proper risk management of simpler products, rather than valuation of ever more complicated derivative financial instruments.

3. Proper accounting for risk

• No valuation separated from hedging costs or required economic capital.
• Proper accounting not just for market risk, but also counterparty credit risk and liquidity risk – i.e. addressing the hard problems, rather than assuming them away.

You can also leave a response, or trackback from your own site.