A proposed fat-tail risk metric: disclosures, derivatives, and the measurement of financial risk.

• Author: Conti-Brown, Peter

INTRODUCTION

Accurately and precisely modeling financial risk is something of a Holy Grail for financial theorists, regulators, and market participants. But like the Holy Grail, the location of a comprehensive model of risk remains unknown; some have even suggested that such a model is a figment of financial theorists' imaginations. (1)

Nowhere has that disaster been more fully evident than in the recent failure of risk models to adequately prepare the marketplace for the collapse of the market for mortgage-backed securities and credit derivatives, and the financial crisis that followed. Because of the mistaken assumptions associated with some risk models, otherwise vigilant market participants were blinded to the risks that brought the global financial system to the brink of collapse.

One of the modeling critics' primary targets is the Value-at-Risk (VaR). In the 1980s, practitioners created a model to focus on the risk exposure experienced by a single firm.2 VaR is meant to give traders--and, eventually, investors and regulators--a snapshot of how much money a firm might lose in a single day. That dollar figure is easy to comprehend and straightforward in its application; if a firm is uncomfortable with that exposure, the firm can make appropriate adjustments to its trading strategies and positions. As VaR continued to develop, traders and academics weren't the only ones paying attention. Soon, regulators from the U.S. Federal Reserve, (3) the U.S. Securities and Exchange Commission (SEc), (4) the Basel committee on Banking Supervision, (5) and the UK Financial Supervisory Authority (6) endorsed it as an adequate tool for setting banking capital adequacy requirements, and for appropriate risk disclosures to shareholders. (7)

The financial crisis reveals, however, an application of Mencken's aphorism: for the complex problem of risk measurement, VaR produces an answer that is "neat, plausible, and wrong." (8) VaR is not useful in times of unforeseen volatility, as extreme events occur far more frequently than a 95% confidence level would suggest. In statistical terms, the tails of the distribution become "fat." When model-altering events occur more frequently than originally anticipated, the model itself becomes useless. So it is with VaR in times of financial crisis.

None of these observations is new. (9) And, in light of these weaknesses, financial economists have filled the literature with revisions and refinements that seek to improve the model. (10) In offering an alternative, this Comment makes no attempt to enter that mathematics-intensive fracas. Instead, I propose a lawyer's solution: use a form of mandatory disclosure for off-balance-sheet guarantees and over-the-counter (OTC) derivatives to provide the data necessary to describe the risk of a firm's economic footprint in the unlikely event of catastrophic collapse. With this data, regulators and firms could compute what I preliminarily call a FatTail Risk Metric (FTRM), or a metric for determining the impact of the most financially devastating high-impact, low-probability events. Such a disclosure requirement could have three principal benefits. First, requiring mandatory disclosure of contingent liabilities--namely, derivatives and off-balance-sheet guarantees--will resolve the ongoing difficulties in record keeping that have plagued the industry. Second, a scale that measures the size of a firm's impact upon catastrophic collapse provides a relative measure with which regulators can compare firms of equal market capitalization and/or balance sheet assets that have differing remote-risk profiles. Third, and most importantly, the FTRM will provide a steady stream of data that has, until now, been impossible to gather and could prove essential in understanding risk measurement at the firm level over the coming decades. With that information, defining "too big to fail" may simply become a question of basic econometrics.

VaR-WHAT IT DOES, WHY IT FAILS

VaR is, essentially, an expansion and application of modern portfolio analysis as developed over the last half century by Harry Markowitz and many others. (11) Portfolio analysis uses mathematical models of the covariance between assets within a portfolio to predict the risk inherent to that portfolio. (12) VaR uses these models and historical data to report information in three parts: (1) a specific dollar amount lost, (2) within a fixed time period, and (3) with a specific level of confidence.13 For example, a risk-management officer in a bank or hedge fund might report to a CEO or board member, with 95% certainty, that market conditions are such that the firm could lose $50 million in a given day. If market volatility increases during the day, that figure could change. VaR therefore gives clear, comprehensible information that is easily operational; it's very easy to conceptualize the prospects of losing $50 million, and if a manager or investor objects to that level of risk, the firm can adjust accordingly. Alternatively, if VaR sinks too low, the firm can make those necessary adjustments as well. (14) The promise of VaR is that risk can be projected, adjusted, and controlled according to an investor's or firm's appetite for risk.

VaR's key assumptions are two: (1) that, for asset-price volatility, past is prologue, and (2) that such variations are normally distributed around a mean; i.e., they follow a "bell curve." (15) Unfortunately, in times of crisis neither assumption is appropriate. The distribution of asset-price volatility has much fatter tails--that is, the likelihood of extreme events in asset-price swings is much higher than the normal distribution models, including VaR, would predict. (16) And, as became painfully apparent in the fall of 2008, volatility today can exceed anything in the history books. These failed assumptions mean that reliance on such models can lead to disastrous consequences.

Goldman Sachs' Chief Financial Officer David Viniar offers an illustrative example of what this means in practice. In August of 2007, after one of the firm's hedge funds lost 27% of its value in a matter of days, Goldman injected the fund with $2 billion of its own capital. In defense of this dramatic action, Viniar explained: "We were seeing things that were 25-standard deviation moves, several days in a row." (17) Viniar makes explicit the assumption that such price swings are normally distributed, and says--whether accurately or for dramatic effect--that these events are 25 times the average variation around the mean change in prices.

To put this in perspective, a 2-standard deviation loss event should occur only approximately 2.5% of the time, or roughly once every 44 days; a 5-standard deviation event should occur only once every 13,932 years; a 10-standard deviation event only once every 525 quadrillion millennia (the universe, incidentally, is estimated to be between 12 and 14 billion years old); (18) and a 25-standard deviation event should occur roughly once every 1.309 X 10136 years. (19) Thus, the expected time between two 25-standard deviation events has more millennia than the universe has number of particles. (20) And yet, according to Viniar, it occurred day after day, in August of 2007, well before the fire sale of Bear Stearns, the collapse of Lehman Brothers, or the bailout of the financial sector, with all the associated market upheaval that followed. (21) Thus, the VaR models Viniar and others used to explain such 25-standard deviation moves, day after day, were not only wrong; they were catastrophically wrong.

Thus, in addition to the flawed assumptions mentioned above, VaR has two other weaknesses. First, in times of crisis, VaR fails to provide any clear content on risk exposures in the long tail, especially when those tails are fat. When high-impact, low-probability events--what trader and bestselling author Nassim Taleb calls "Black Swans"9--occur with such frequency that they dominate a firm or portfolio, VaR loses its utility. (23) Second, VaR's presentation of the risk statistic as a dollar figure has deceptively precise appeal. Any manager, investor, or regulator knows what it means to lose $50 million in a day; adjusting a risk portfolio to adapt for that kind of risk is a relatively straightforward enterprise. The problem, as seen in the August 2007 example, is that that dollar figure is nearly meaningless in a time of crisis. The VaR statistic masks that reality.

Resolving the VaR problem--and, indeed, the problem with nearly all mathematical models of...