Background: Much has been written about how common risk-management techniques such as Value at Risk (VaR) failed to guide financial institutions around the potholes that have been revealed by the current global financial crisis. A common theme in this criticism is that the techniques are based on statistical models, fitted to historical data. Thus, they can be said to be "always managing the last crisis instead of the next one." The suggestion is that each new crisis has its own dimensions, and history can provide no guide to managing the accompanying risk.
However, the failure of current methods to outline the magnitude of the risks to which banks were exposed in recent years may not be caused by their dependence on statistical models fitted to historical data, but rather by the way those models were specified. The incorporation of normal distributions is clearly inappropriate because of the well known non-normality of most financial data, and yet it still appears to be widely used. Most methods can be modified, without huge complication, to replace the normal distribution by a member of Student's t family of distributions, with sometimes dramatic effects on the resultant estimates of risk.
VaR is also open to the criticism that it measures the size of a loss that will be exceeded with a given probability (such as .05), but ignores the magnitudes of losses that exceed that amount. This weakness has been known and discussed in the academic community for over a decade, and simple alternatives (Expected Shortfall, for example) that are not open to the same criticism have been developed. Regardless of these developments, VaR still seems to be the method of choice.
Task: Explore the types of probability distribution that best fit the day-to-day or month-to-month changes in various financial data (stock prices and bond yields, for example). Examine the consequences of the choice of distribution on the value of commonly used measures like VaR and Expected Shortfall. Determine whether more appropriate analysis of historical data could have provided better estimates of risk.
Data Sources: Databases with historical stock and bond data can be accessed through the NCSU Libraries. Ideally, price data for structured products like Mortgage Backed Securities, Collateralized Debt Obligations, and Credit Default Swaps would also be used; access to these is still being explored.
