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February 2010

The financial crisis: a question of guilt

By Prof. Paul Embrechts, Professor of Mathematics, ETH Zurich

The current crisis can be partly laid at the door of the flawed choice of risk-metrics used in the Basel framework. More regulation, without rethinking and correcting these flaws, will just be a plaster over the wound.

The recent financial crisis has been a rude wakeup call on how fragile our financial system really is. The media has laid the blame for the crisis on many parts of the financial system, such as the credit rating agencies, mortgage brokers and lenders, special investment vehicles, structured finance products, banks and financial engineers, while exhorting regulators to come up with more stringent regulation to reel in the lack of transparency and conflicts of interests apparent in the finance industry.

However, before placing our faith in further regulation, we should be aware that early caveats about inherent flaws in the system were fully ignored. The warnings by H. Markopolos (a "quant", or a financial engineer), in 2005, that the Madoff fund is a fraud and the academics' critique, in 2001, on some serious flaws of the Basel II Accord had not been heeded by the regulators. Revisiting the flaws of Basel II as stated in P. Embrechts' "An Academic Response to Basel II", we can demonstrate that at least part of the blame for the current crisis can be attributed to the flawed choice of the risk-metrics by the Basel Committee and consequently, more regulation, without rethinking and correcting these flaws, may not be the best solution going forward.

The Basel Accord sets the minimum regulatory capital banks are required to maintain based on their exposure to market, credit and operational risks. For calculating market risk for instance, the Basel II Accord chose the 10-day VaR (Value-at-Risk) at 99% confidence as the risk metric to determine risk exposure. All too often, VaR is communicated as the maximum loss of a particular portfolio at a particular point (confidence interval) in an underlying asset returns' distribution, over a given timeframe (the holding period). Since VaR only measures the losses at the 99% point, say, losses beyond that quantile, along with their respective magnitudes and probabilities, will not be reflected in the VaR measurement. Hence, catastrophic losses beyond the 99% confidence interval can be hidden from sight until events beyond the 99% confidence interval actually occur, such as a global financial crisis. In that respect, one should be careful in communicating the magical word "maximum", especially Zurichas higher and higher up the business ladder, underlying technical details, assumptions and conditions underlying the VaR definition and calculation (estimation!) tend to fade away. In some way, VaR is least useful when it is most needed. This has been pointed out by mathematicians over and over again since the birth of VaR around 1994!

In times of stress

To make matters worse, a portfolio VaR that is sub-additive under normal circumstances may lose this property under stress situations. Under normal circumstances, asset returns are not highly correlated. Holding a portfolio is, hence, less risky than holding individual assets, due to diversification, and the VaR of the portfolio will naturally be less than the sum of the individual VaRs of each asset within the portfolio. However, in times of stress, asset returns start becoming highly correlated as all asset returns are falling. The high correlation of asset returns would reduce diversification effects and cause the portfolio VaR to be much higher. In fact, VaR can even be super-additive when the underlying returns distributions are skewed (such as in the case of credit-default swap portfolios), heavy-tailed (so-called power laws) or when there is special dependence between the asset classes.

Hence, banks will load up on risks during normal periods, when the asset returns distribution are less volatile due to diversification and VaR is sub-additive, only to discover that the same portfolio is actually too risky during distress situations, when the asset returns are fat-tailed and VaR may become super-additive. Banks will then dump their assets into the distressed markets at the same time in a bid to lower their respective VaRs, fueling a further fall in asset prices. Indeed, Basel II may actually contribute to a destabilization of the financial system by causing bank actions to become more homogenous. It is especially this point that was stressed on early in "An Academic Response to Basel II". Further, regulatory arbitrage can also occur by concentrating portfolio risks beyond the 99% confidence interval.

The Basel II Accord also permits banks to measure credit risk using their own internal rating models subjected to the approval of local regulators, in addition to the standardized manner, which is supported by external credit assessments, used since Basel I. Hence, Basel II allows banks to lower their risk-weightings on loans if the bank believes it has taken sufficient steps, such as hedging and diversification, to offset the risks of the loan based on their models. While this regulation circumvents the conflicts-of-interest issues associated with ratings from credit rating agencies, the approach fails to account for the model risks associated with the banks' credit models. The banks can also take up higher leverage as compared to Basel I, since they can justify lower risk-weightings to more risky assets, if their models suggest sufficient diversification. This may result in model arbitrage between external credit assessments and proprietary credit models as well as banks overleveraging in good times.

Despite the best efforts of regulators to stabilize the financial system, imposing more regulation may not necessarily be the best solution going forward. One needs to carefully balance extra regulation with possible market reactions, and definitely make sure that the properties of the quantitative risk metrics used are not only unde stood in normal scenarios, but much more importantly in times of distress. Government intervention is inherently pro-cyclical as regulations will make banks more homogenous. All market participants have to understand the intricacies behind certain risk metrics, causing regulatory arbitrage and allowing banks the chance to over-leverage. Hence, a better response to the financial crisis would be for risk managers to recognize the inherent flaws of the current regulations, and its risk metrics, as well as have a firm grasp of the underlying mathematics to make better adjustments to the handling of extreme, or rare tail events.

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