I’ve been meaning to learn the math behind stock trading for a while, but I’ve found it’s hard to find quality information. Most of the stuff online is (1) non-technical, (2) trying to sell you something, or (3) both. So I decided to collect my own notes on modern portfolio theory (MPT). Here’s the pdf: Notes on Itô calculus and quantitative trading.

The information comes from various lecture slides and articles. I didn’t put specific references in there, since it’s standard, textbook stuff. Just search for any piece you’d like more information about.

Here is a rough outline:

- How to select stocks, given their risk and return statistics
- How to model risk and return in the first place

The first part takes the “Minimum Variance” approach due to Markowitz. To model stock prices, I give an overview of Itô calculus (one form of stochastic calculus) and geometric Brownian motion (GBM). This is the model used by the Black-Scholes formula for pricing derivatives.

I suspect that a simple index fund might beat a portfolio selected with this recipe. In the future, I’d like to test on historical data and find out if there really is an advantage to picking your own stocks.