MEASURING BLACK SWANS: THE IMPORTANCE OF THE HIGHER-ORDER MOMENTS OF THE EQUITY RETURNS DISTRIBUTION

Open Access
Author:
Tallman, Gregory D
Area of Honors:
Finance
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Oleysa, Thesis Supervisor
  • Olesya Grishchenko, Thesis Supervisor
  • James Alan Miles, Honors Advisor
Keywords:
  • kurtosis
  • skewness
  • Gaussian
  • bell curve
  • distribution
  • sector
  • returns
  • Taleb
  • Black Swan
Abstract:
Nassim Nicholas Taleb introduced the notion of the Black Swan in his best-selling book, “The Black Swan: The Impact of the Highly Improbable” in 2007. A Black Swan is an event that is characterized as being extremely rare, having an extreme impact, and being explainable after the fact. Taleb points out that the predictive models used in many statistical fields do not account for the probability of these events, including the financial world. This thesis breaks down the issues with the use of a traditional Gaussian, or normal distribution and the measure of volatility with stock returns. Using the third and fourth moments of a distribution, skewness and kurtosis respectively, I compute market and 9 sectors’ daily and monthly returns over the sample period from 1990-2009. Using Fisher’s cumulant test for normality, I investigate whether sectors follow the patterns of a normal distribution. I find that there is little evidence that all stock returns are negatively skewed, while I find substantial kurtosis across all sectors.