a physicist reflects on market risk measurement

by Paul Nigel Shotton

When I left academia as a CERN physicist more than thirty years ago to join Wall Street as a trader, my physics knowledge was a nice but superfluous skill. Back then, risk management as a distinct and quantitative discipline did not exist. Of course, bankers were held accountable by their employers for the quality of the deals they brought into the portfolio, but risk management as practiced by banks and investment banks such as Goldman Sachs, where I worked (still then a private partnership), was done wholly by the front office, or what is now referred to as the “first line of defense”, and the bank’s managing partners.

In the intervening years, the quantification of risk has developed into a pillar of the financial industry, based primarily on the precepts of classical physics. Yet the degree of success of this practice can best be described as partial because financial market behavior is much more akin to the world of quantum mechanics than it is to the world of classical physics.

The Evolution Of Financial Market Risk Measurement

Although the Basel Committee of Banking Supervision (BCBS) was set up in 1974, it wasn’t until 1988 that the Committee, under the Chairmanship of Peter Cooke of the Bank of England, first prescribed the minimum amount of capital which international banks should hold on the basis of their riskweighted assets, with five categories of riskiness and a 100% risk-weight yielding a requirement to hold a minimum of 8% of the asset value as capital; the so-called Cooke ratio, in what became known as the Basel Accord.

Elsewhere, Dennis Weatherstone, Chairman of JP Morgan, frustrated by the plethora of different metrics used to report disparate risk types such as FX, rate futures, government bonds, corporate bonds, equities, etc. held by the JP Morgan trading desks to the daily 4:15pm Treasury Committee meeting which he chaired, asked that a means be devised to aggregate these various risk types into a single number.

So was born Value-at-Risk, the classic statistical method to aggregate market risk, later adopted by the Basel Committee via the 1996 Amendment to the original Basel Accord, as a means by which sophisticated banks (those allowed to use their internal models) could calculate the amount of capital required to underpin market risk in their trading book, which generally produced a smaller capital requirement than did the standardized approach.

Since its first formulation, the Basel Accord has evolved considerably, as supervisors sought to refine the approach in order to address criticism on both sides: on the one hand that the Basel capital prescription was too onerous and risk-insensitive, resulting in reduced lending to support economic growth; and on the other that it was too lenient and allowed the buildup of dangerous levels of risk which could threaten financial markets and the economy.

In response to these criticisms, and to various market crises, in particular the Global Financial Crisis (GFC) of 2008, quantitative approaches to risk measurement gradually became more codified and more prescriptive, and risk management became established as a distinct discipline. After a decade as a trader, I was at the forefront of what became a trend of having former traders move to the independent risk oversight function, now known as the second line of defense, and contributed to the development of many of what are now standard techniques in the risk manager’s toolbox, such as VaR, Expected Shortfall (ES), Stress Testing and Scenario Analysis.

Complex Adaptive Systems

However, like many frameworks which mediate interactions between people, financial markets are examples of Complex Adaptive Systems (CAS). CAS are characterized by highly non-linear behavior, following power laws, which means that small changes in input parameters can have highly magnified impacts on outcomes. They have deep interconnectivity between different parts of the system, which means that the classic techniques of Stoic philosophers - of taking a complicated problem and breaking it down into its component parts; having experts solve each component according to their specialization; and then reconstitute the whole - do not work.

As I mentioned above, financial market behavior is much more akin to the world of quantum mechanics than it is to the world of classical physics. In classical physics there is complete independence between the observer and the system under observation. Betting on a horse race, for example, is akin to classical physics, because of this independence. Whilst actions in the betting market change the odds for which horse is favored to win, they don’t impact the outcome of the event, which is rather determined by the best horse on the day.

In the realm of quantum mechanics, however, the systems under observation are so small that the act of observation disturbs the system itself, described by Heisenberg’s Uncertainty Principle. Betting in financial markets is like this world of quantum mechanics, because in financial markets the actions of market players are not separate from market outcomes; rather it’s the actions of the market players which produce the market outcomes, a process which George Soros refers to as “reflexivity”.

It’s this interaction between financial markets and participants which results in markets being adaptive. Markets continually evolve over time and adapt to the actions of market players, including changes in market conditions imposed by supervisory bodies like the Federal Reserve and the BCBS.

Invalid Assumptions

Because of this adaptivity, using historical timeseries data to estimate market risk (through Value-at-Risk and Expected Shortfall modeling) and credit risk (through Default Probability and Loss Given Default modeling) is problematic. Implicitly, when using these models, we make the assumption that historical data are a good representation of the distribution from which future events will be drawn, but this assumption is justified only if the timeseries exhibit stationarity, or, in other words, if the statistical properties of the underlying processes generating the timeseries do not change. Since markets are adaptive, this assumption is not valid.

Given these concerns, consider the framework the BCBS uses to determine the capital requirements for sophisticated banks under the Pillar I Risk Weighted Asset formulations. The Committee’s approach is to perform separate calculations of capital required to underpin respectively credit-, market- and operational risks, and the results are then summed to produce the total capital requirement. But as we have discussed, the interconnections between risk types mean that the separation is invalid, and the linear sum of the three components cannot be assumed to produce a prudent level of capital.

Interconnected Risk Types

As an example of the interconnection between risk types, consider the operational risk losses borne by banks and other financial market participants arising from the frauds conducted by Bernie Madoff. Madoff’s frauds had been underway for a long time and the suspicions of some participants had been aroused by the uncannily smooth financial performance of his funds, but what really brought the frauds into the open were the liquidity crisis and market risks arising from the GFC. It should not be surprising that risk of financial fraud may be heightened during stressful market environments, so clearly modeling operational and market risk capital requirements independently is inappropriate.

A forward-looking example of the link between market and credit risk might be the heightened risk of default of so-called zombie companies which have been kept on life support by the extremely low level of interest rates following the GFC and the pandemic. As interest rates are now rising and economic conditions worsening, failing companies will be increasingly unlikely to be able to refinance their debt or grow their businesses, so are at increased risk of default. Moreover, the fact that interest rates have been so low for so long has enabled weak companies to continue to operate far longer than they would have been able to historically, a factor which is likely a driver of the lower productivity experienced in many economies. It is likely that such companies will have been run farther into the ground than would have been the case historically, so that Loss Given Default estimates based upon historical loss data may well prove to be too optimistic, and the credit risk capital so calculated prove to be insufficient.