Every event in life can be classified as either deterministic or probabilistic. In actuality nearly everything can be argued to be probabilistic except for maybe death and taxes (sounds morbid I know, but I didn’t make it up).
When it comes to stocks most people would argue that the movement of stock prices is more probabilistic than most things. If someone tells you that they know for certain that a stock will go up or down, take it with a large grain of salt. One of the first things I usually ask when someone says this to me is “so did you mortgage your house and invest all your money in it?”
Usually the answer to this question is no which indicates their certainty is not as certain as it sounds. The reality of the stock market is its probabilistic nature make the future completely uncertain. Luckily mathematics provides us with an important framework to deal with this sort of situation!
Statistics, which I know makes many people cringe, is the most important mathematics subject anyone interested in the stock market should study. While the field can become incredibly complicated using tools such as multi-variate calculus to analyze probability density functions, lower-level statistical analysis can be incredibly useful in the world of finance too. In order to set a foundation for effective stock trading, I believe every trader should know and understand the following general statistical concepts.
This is something many of us learn in high school, but often forget by the time we begin to invest. If you read enough finance articles people will talk about the average (mean) return of an asset over some time frame. It is important to realize that reporting an average can be way different than reporting a median value or a mode. Reader beware…
This is one of the most important statistical relationships that is used in many stock modeling equations. The most common correlation variable is \(\beta \) which is used in the Capital Asset Pricing Model (CAPM) for evaluating the risk-reward in stocks. Before you trade any individual stock understanding its correlation to the overall market and other assets in your portfolio is crucial in hedging risk.
We’ve probably all heard of the bell curve, but did you know that the Central Limit Theorem dictates most things become bell curves with enough trials (including stock market returns too!). Knowing this helps explain why diversification works and individual stock picking can be so risky.
It is important to note that these terms and concepts are just the tip of the iceberg when it comes to statistics in finance. Throughout this blog we will utilize many other statistical properties (Bayes Theorem, cointegration and many others) to help achieve market success!