Uncertainty Principle of Stock Price Trend

Uncertainty Principle of Stock Price Trend

Atsufumi Ichinoseki

May 19, 2018

A stock price, though randomly fluctuating, is often said to be rising or falling. Consider the following graph.

The S&P 500 is rising in terms of its MA 500 (the 500-day moving average) in 2015 although the deviation of the MA 500 from the S&P 500 is inordinately large. While the trend is well-defined (precise), the MA 500 is an extremely imprecise approximation of the S&P 500.

When a moving average approximates the position (level) of the S&P 500 better, the trend defined over the same period may become uncertain (imprecise). For example, consider the MA 5.

Although the MA 5 closely approximates the S&P 500, it keeps swinging up and down. This makes the overall trend of the year 2015 quite uncertain.

What these observations signify is the uncertainty principle of the trend of randomly fluctuating stock price, which states, “The more precise the approximation of randomly fluctuating stock prices, the less precise their trend, and vice versa.”

How well this uncertainty principle of the trend is handled determines the depth of the insight into and the understanding of the nature of the random stock price fluctuation. To this end, this site focuses on the approximation of a stock price index by the Fourier series. When the Fourier series approximation of the stock price index is rising, its trend is said to be up. When it is falling, the trend is down. It is found that the uncertainty principle leads to a superior method of the Fourier series approximation of random fluctuation, resulting in a more reliable trend. This is demonstrated by the graphs that represent the trend of a stock index under the uncertainty principle. These graphs posted in this site testify the excelling value of analyzing the randomness by means of the uncertainty principle.