In 1989, I had used statistics regularly to solve process problems in semiconductor manufacturing while working as an assistant process engineer for NEC Semiconductors. I had received many awards for solving wire bonding problems and my solutions were presented at the NEC Headquarters in Tokyo, Japan.
Image: My NEC Award Certificates
In 1992, I left NEC to further my studies in Scotland at the University of Glasgow. At the University of Glasgow was where I first heard about the Central Limit Theorem.
The Central Limit Theorem defined that "the sampling distributions of the mean from non-normal populations approach a
normal distribution as the sample size increases" (Schumarker and Tomek 2013, 96).
Dennis McNicholl (2002) had applied the Central Limit Theorem on DJIA closing prices from 24 Mar to 25 Oct 1999 and resulted in a DJIA bell shaped curve which indicated normal distribution.
Fast forward to June 2021, can the Central Limit Theorem still apply to Dow Jones Industrial, Nasdaq and the S&P500 indexes? I followed McNicholl's (2002) way to apply the central limit theorem on DJI, Nasdaq and S&P500 closing prices from a year ago starting from yesterday. Getting the DJI, NASDAQ and S&P500 data from Yahoo Finance into my excel spreadsheet, I generated the following curves using the concept of Central Limit Theorem:
My conclusion is that the Central Limit Theorem has proven to make the DJI, Nasdaq and S&P500 into a bell shaped curved that indicated normal distribution. Since the prices of the indexes are distributed normally, we can apply statistics on stock picking effectively. I will talk about stock picking later. Stay tune...
McNicholl, Dennis. 2002. "Old statistical methods for new tricks in analysis." Futures, 31(5), 30.
Schumacker, Randall, and Sara Tomek. 2013. Understanding statistics using R. New York: Springer.
