One of our pet interests has been how the use of mathematics and models can unwittingly enable people to fool themselves. We see this regularly when working on deals. The model for the target business’ performance somehow becomes more real than the company. When the numbers don’t work, if you can come up with a good sounding rationale for tweaking them, presto! Suddenly everything in hunky dory. No wonder over 60% (some studies say as high as 75%) of all deals fail.
Our colleague Susan Webber, in an article about the corporate obsession with metrics, made some pertinent observations:
Metrics presuppose that situations are orderly, predictable, and rational. When that tenet collides with situations that are chaotic, nonlinear, and subject to the force of personalities, that faith—the belief in the sanctity of numbers—often trumps seemingly irrefutable facts. At that point, the addiction begins to have real-world consequences. Business managers must recognize the limitations of metrics.
Mind you, I’m not arguing that metrics and measurement are inherently bad things. To note just one example, a well-structured performance measurement system is essential to the well-being of large enterprises. But quantitative measures can be and frequently are used naively. It’s all too easy to abdicate judgment to the output of a model or scorecard.
Jon Danielsson at VoxEU takes this viewpoint further in an article that discusses a pervasive cognitive dissonance among trading operations and their regulators. They know that statistical models have major shortcomings, particularly in underestimating the odds of catastrophic losses, which is precisely what they are supposed to help avoid. While the conventional response has been to try to devise better models, Danielsson argues that that line of thinking is wrongheaded.
For Danielsson makes a fundamental point: what matters is management; the models are secondary. For reasons I cannot fathom (perhaps the rise of the PC and the ease of slicing and dicing data), qualitative assessments are seen as inferior to quantitative ones. But for a regulator to understand the robustness of a company’s management practices requires more scrutiny than has been fashionable of late. And it also requires better regulators.
In response to financial turmoil, supervisors are demanding more risk calculations. But model-driven mispricing produced the crisis, and risk models don’t perform during crisis conditions. The belief that a really complicated statistical model must be right is merely foolish sophistication.
A well-known American economist, drafted during World War II to work in the US Army meteorological service in England, got a phone call from a general in May 1944 asking for the weather forecast for Normandy in early June. The economist replied that it was impossible to forecast weather that far into the future. The general wholeheartedly agreed but nevertheless needed the number now for planning purposes.
Similar logic lies at the heart of the current crisis
Statistical modelling increasingly drives decision-making in the financial system while at the same time significant questions remain about model reliability and whether market participants trust these models. If we ask practitioners, regulators, or academics what they think of the quality of the statistical models underpinning pricing and risk analysis, their response is frequently negative. At the same time, many of these same individuals have no qualms about an ever-increasing use of models, not only for internal risk control but especially for the assessment of systemic risk and therefore the regulation of financial institutions.1 To have numbers seems to be more important than whether the numbers are reliable. This is a paradox. How can we simultaneously mistrust models and advocate their use?…..
Underpinning this whole process is a view that sophistication implies quality: a really complicated statistical model must be right. That might be true if the laws of physics were akin to the statistical laws of finance. However finance is not physics, it is more complex, see e.g. Danielsson (2002).
In physics the phenomena being measured does not generally change with measurement. In the finance that is not true. Financial modelling changes the statistical laws governing the financial system in real-time. The reason is that market participants react to measurements and therefore change the underlying statistical processes. The modellers are always playing catch-up with each other. This becomes especially pronounced when the financial system gets into a crisis.
This is a phenomena we call endogenous risk, which emphasises the importance of interactions between institutions in determining market outcomes. Day-to-day, when everything is calm, we can ignore endogenous risk. In crisis, we cannot. And that is when the models fail.
This does not mean that models are without merits. On the contrary, they have a valuable use in the internal risk management processes of financial institutions, where the focus is on relatively frequent small events. The reliability of models designed for such purposes is readily assessed by a technique called backtesting, which is fundamental to the risk management process and is a key component in the Basel Accords.
Most models used to assess the probability of small frequent events can also be used to forecast the probability of large infrequent events. However, such extrapolation is inappropriate. Not only are the models calibrated and tested with particular events in mind, but it is impossible to tailor model quality to large infrequent events nor to assess the quality of such forecasts.
Taken to the extreme, I have seen banks required to calculate the risk of annual losses once every thousand years, the so-called 99.9% annual losses. However, the fact that we can get such numbers does not mean the numbers mean anything. The problem is that we cannot backtest at such extreme frequencies. Similar arguments apply to many other calculations such as expected shortfall or tail value-at-risk. Fundamental to the scientific process is verification, in our case backtesting. Neither the 99.9% models, nor most tail value-at-risk models can be backtested and therefore cannot be considered scientific.
We do however see increasing demands from supervisors for exactly the calculation of such numbers as a response to the crisis. Of course the underlying motivation is the worthwhile goal of trying to quantify financial stability and systemic risk. However, exploiting the banks’ internal models for this purpose is not the right way to do it. The internal models were not designed with this in mind and to do this calculation is a drain on the banks’ risk management resources. It is the lazy way out. If we don’t understand how the system works, generating numbers may give us comfort. But the numbers do not imply understanding.
Indeed, the current crisis took everybody by surprise in spite of all the sophisticated models, all the stress testing, and all the numbers. I think the primary lesson from the crisis is that the financial institutions that had a good handle on liquidity risk management came out best. It was management and internal processes that mattered – not model quality. Indeed, the problem created by the conduits cannot be solved by models, but the problem could have been prevented by better management and especially better regulations.
With these facts increasingly understood, it is incomprehensible to me why supervisors are increasingly advocating the use of models in assessing the risk of individual institutions and financial stability. If model-driven mispricing enabled the crisis to happen, what makes us believe that the future models will be any better?
Therefore one of the most important lessons from the crisis has been the exposure of the unreliability of models and the importance of management. The view frequently expressed by supervisors that the solution to a problem like the subprime crisis is Basel II is not really true. The reason is that Basel II is based on modelling. What is missing is for the supervisors and the central banks to understand the products being traded in the markets and have an idea of the magnitude, potential for systemic risk, and interactions between institutions and endogenous risk, coupled with a willingness to act when necessary. In this crisis the key problem lies with bank supervision and central banking, as well as the banks themselves.