Journal of Finance and Accountancy Black swans and

There are two general classes of probability domains; each is very distinct, both qualitatively and quantitatively. The first distribution is referred to as a "Gaussian-Poisson distribution " – thin tail, the second, a “fractal ” or Mandelbrotian distribution- fat tail. In thin-tail distributions, statistical exceptions occur but they don't carry unusually large consequences. In fat-tail distributions, when significant deviations (black swans) occur, the consequences are usually catastrophic in nature. Standard deviation is a useful statistical measurement of risk, if the underlying asset returns are distributed in a normal fashion about the mean. However, if the asset returns deviate significantly from what would be expected in a Gaussian distribution, standard deviation is often an inadequate and poor measurement of total risk and can often result in the serious underestimation of potential losses. Albeit, VaR is fairly accurate in predicting small daily losses with high probability, it breaks down completely in forecasting large catastrophic losses that exist in the tail of the distribution – black swan events. A glance at the Dow Jones Industrial Average's biggest one-day gains and losses confirms the existence of black swan events: On each of two different days in October 2008, the Dow surged more than 10%. On each of eight different days in late 2008, the Dow gave back more than 5%. 2008 was a particularly volatile year, but big moves can happen any time. In this article, the theoretical normality assumption is empirically tested (and clearly rejected) using time series of stock returns for the U.S. stock market for the last 30 years. The purpose of this study is to illustrate the existence of black swan events and their historical frequency, paying particular attention to the time period 1980-2010