Central Limits and Financial Risk

Abstract

Systematic model bias has been implicated in the global recession that began in 2007, and this bias can be traced back to assumptions about the normality of data. Nonetheless, the normal distribution continues to play a foundational role in quantitative finance. One reason for this is that the normal often emerges, without prompting, as the distribution of sums or averages of large collections of random variables. Precise statements of this miracle are known as Central Limit Theorems, and they appear throughout the physical and social sciences. In this note, we review some of the most widely-used Central Limit Theorems. Subsequently, we explore the gap between the normal distribution and financial risk. This can be traced to a failure of the financial data to satisfy the assumptions of even the most liberal versions of the Central Limit Theorem.

Keywords: Systematic model global recession quantitative finance random variables central limit theorem normal distribution financial risk