Monthly Archives: November 2011

Topic 2: Value at risk

The recent crisis has highlighted the inadequacy of the approaches to risk management adopted by financial institutions; risk modeling by and large failed to provide a true and fair representation of the degree of risk of many financial instruments, leading financial institutions and investors to take on more risk than they could bear. So how is risk modeled and managed? In the run up to the financial crisis, the standard framework adopted within the industry was the value-at-risk (VaR) model: the model provides the monetary value that the mark-to-market loss on an instrument will not exceed over a given time period and with a given level of probability (usually 95% or 99%). With the benefit of hindsight, it is quite clear that the model has a fundamental shortcoming in that it disregards the potential losses “hidden” in the tail and their magnitude. When the profit-loss distribution is normal, the probability that the loss will exceed three standard deviations from the mean is only 0.15%; however, the assumption of a normally distributed profit-loss curve does not hold in many cases (this phenomenon is called tail-risk).


As pointed out by Nocera (2009) in the New York Times, in the case of a CDS with a probability of default lower than the level of significance at which the VaR is computed, the downside potential of the instrument is not properly accounted for by VaR. In this sense, risk management with VaR is biased towards positions that have small probability of big losses. Furthermore, Yamai and Yoshiba (2005) find that VaR leads utility-maximizing investors to increase the concentration of their portfolio; they conclude that:

“if investors can invest in assets whose loss is infrequent but large, the problem of tail risk can be serious. Furthermore, investors can manipulate the profit-loss distribution using those assets, so that VaR becomes small while the tail becomes fat”.

Danielsson (2002) questions the assumptions of VaR even further: VaR is computed on using historical data on past market behavior of a financial instrument. However, he argues, the ‘normal’ market behavior in which some investors sell and others buy, changes markedly under stress. The market becomes more volatile and driven by forces that are not entirely rational. In this sense, the VaR computed under normal market conditions may be a poor indicator of the risk of an instrument in a moment of crisis: one particular weakness of the model is its sensitivity to market volatility, which is likely to increase significantly under stress, thus reducing the validity of the indicator computed under ‘normal’ conditions.

Despite its shortcomings, VaR remains the most widely adopted risk management model within the industry and is likely to maintain this role in the near future. In fact, it may be the role of risk management models, rather than the models themselves that needs re-thinking. In his book ‘A colossal failure of common sense’, McDonald describes the risk management approach adopted at Lehman Brothers in the run up to its collapse: according to his description, the firm relied solely on VaR as a measure of the risk, without any sort of critical approach towards the results produced by the model. As described above, VaR is designed to provide the maximum value of the loss that can be incurred in a certain period: in this sense, the model may suffer from a confirmatory bias and as such should at least be integrated by additional models, such as expected shortfall, that focus on the risk hidden in the tails. Not only does the array of quantitative approaches to risk management need to be extended, but it should also be supplemented by qualitative analyses of the results obtained by the models. Such approach allowed Goldman Sachs to detect the risks associated with CDOs ahead of the market and to unwind their positions in December 2006, when the price for these instruments was yet to fall. At the individual level, comparatively better risk management represents an advantage in the sense that it allows to avoid taking on unwanted risk or to minimize losses by exiting a market before it collapses; however, financial institutions are also exposed to a significant level of systemic risk that is more difficult to manage or diversify. In this sense, while sound risk management is extremely important at the individual level, it matters little at the aggregate level; going back to the example of CDOs, their toxicity represented an issue at the macro level and for this reason it was of little importance who got caught holding these instruments in their books when the market collapsed, since everyone had to endure the indirect consequences of the crisis they triggered. In the case of financial institutions, systemic risk has been enhanced in recent times by the fact that market behavior is prone to sudden and irrational changes under conditions of stress (Akerlof and Shiller provide an interesting account of this topic). Moreover, as Danielsson notes, the risk models employed by different institutions are much the same and, in this sense, they are likely to be enacting similar trading strategies at the same time, modifying the distribution of risk in the market.

To conclude, I have looked briefly at the mainstream approach to risk management currently adopted by financial institution and at its shortcomings. I have highlighted how it may be the case that what needs to be thoroughly re-thought are not the models employed, but the blind faith that was paid to the models before the financial crisis. Not only is it the case that the models (and VaR in particular) are as good as the information that is fed into them, but as Triana discusses they can also be easily manipulated to yield the results desired. Finally, it is important to highlight the interconnectedness of the financial sector and its potential impact on the real economy: for this reason, although risk management can help to protect an investor or a financial institution from the direct risk associated with its investment decisions, it is unlikely to be beneficial in the absence of an adequate regulatory framework.










  • Akerlof, G. and Shiller, R. (2009). Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism. Princeton University Press;
  • Danielsson, J. (2002). The Emperor Has No Clothes: Limits to Risk Modelling. Journal of Banking and Finance Vol.26, p.1273-1296;
  • McDonald, L. (2009). A Colossal Failure of Common Sense: The Inside Story of the Collapse of Lehman Brothers. Crown Business;
  • Nocera, J. (2009). Risk Mismanagement. The New York Times, 02/01/09;
  • Yamai, Y. and Yoshiba, T. (2005). Value-at-risk Versus Expected Shortfall: A Practical Perspective. Journal of Banking and Finance Vol.29, p.997-1015.