Math and Statistics

Math and Investing

Math, and especially statistics, plays two key roles in trading:

  1. Statistical models help in determining the theoretical spot price of a security.
  2. Basic math using various parameters is used to assess the risk of a portfolio.

Beyond these two things, there is limited utility in understanding the behavior of securities over time; however, and I cannot stress this enough, there is no way to regularly and accurately predict the price of any stock or option.

This is important:

Note

There is no way to regularly and accurately predict the price of any stock or option.

Because of that fact, use of mathematics should be strictly limited to two activities when investing:

  1. Determining your portfolio’s risk
  2. To generate heuristics to guide a trading strategy, rarely to decide one, and never with the assumption that a computed price is accurate

How to approach this material

This material is separated into two groups.

Basics

This material covers the bare minimum necessary to understand the items presented in the advanced material. There are a lot of diagrams, examples, and problem walk-throughs that make it approachable (and I hope fun!). Once you finish this material, you should have a fairly basic conceptual understanding of the statistics necessary to move on, even if you haven’t mastered the actual mathematics behind statistics.

Formal Statistics

It is important to note that a lot of the material in the Math and Statistics course is presented without the depth and “formalism” that one would find in a textbook on the subject. Proofs are rare, and some of the definitions for terms used are much less formal than a mathematician might use. This is intentional, as this course is meant to be a conceptual introduction, not a formal course as might be taught in a university.

Advanced

The advanced material draws on a number of texts and other readings from the world of quantitative finance, which is the academic discipline covering the world of mathematics as applied to investing and other financial matters. For the most part, results are presented without the mathematical proofs or derivations one would find in a textbook, unless it would truly help understand what the result is. There are, again, a lot of explanatory diagrams, scenarios, and worked examples to help make it more approachable. The goal in this section is to give you an understanding of the mathematics used by professionals that ultimately are used to determine the values of parameters and prices associated with stocks and options.

Note

Much of the material presented in this Math and Statistics primer is presented without proof. The references I’ve used to generate this material can be consulted if you want to see proofs for various things. The material will note where to look!