The Math Behind Stock Market Predictions
Let’s face it: Wall Street sometimes seems like a magical place, full of mysterious numbers and inside information. The truth is that for the most part, many of the real prediction tools are grounded in pretty straightforward math. So let's dive into the fascinating math behind making sense of stock prices without adding a glaze to your eyes
The important point is that predicting a market is not an intuitive thing—it is about pattern recognition, using data sets, and thinking in numbers. Whether you are an independent trader, or creating algo strategies, simple math can set you apart- allowing you to literally quantify risk, trends, opportunities, etc.
Here is the standard toolbox that traders and quants typically have open on their desktops:
Descriptive Statistics- the mean, median, mode, etc. quick ways to summarize data.
Probability and Regression- modeling how likely an event is, or how one trend predicts the other.
Linear Algebra - to handle large data sets quickly, especially if you are concurrently managing portfolios with many moving pieces.
Calculus and Stochastic Math- required to model how prices behave in relation to time.
Once you have combined the descriptive statistics with the other tools, you will have strategies that do not make a guess estimation, they simply calculate it.
Okay, so calculus isn't just something you did to cringe through in class - in fact, it's a big part of how these price models work. One of these concepts is stochastic calculus, which combines simple trends with randomness.
If we think of price changes as originating from two sources: an overall trend, and a bit of randomness (the market doesn't always make sense).
Stochastic calculus simply combines both of these into one equation (including both multiple definitions of volatility and surprise) and helps quants to model and predict market volatility without being surprised. Stochastic calculus is also the principle behind some of the high-tech option pricing models (like Black-Scholes in providing a cost to “hedge” an investment to manage risk).
Let's de-mystify what the average person thinks of as "trading" as a real trader:
Model Price Movement: Trading is not "it's going up or down," it is "here's how likely it moves X size in Y way and Z volatility."
Optimizing Trade Execution: All right, you have a big order. Algorithms use formulas such as VWAP (Volume Weighted Average Price) and TWAP (Time Weighted Average Price) to break big trades into smarter pieces of trade and help reduce bad price impacts.
Forecasting Trends: Linear regression helps your model modeling forecast stock A moves then forecasts stock B moves, useful for pairs trading and forecasting.
Risk Management: Consider models that stress test or run different volatilities and get “what-if” scenarios, in effect modeling how much money you might lose based on some mathematical methodology before it happens.
The emotion is removed - there is no fear, greed or FOMO. Just decision making based on known data.
It is often way faster than you - algorithms don't fall asleep or get tired. The model is always learning - as the model gets smarter with training data, it improves. But let’s be honest – models will be wrong. (Markets can be quite unpredictable). This is part of why trading is as much art as science. Its intelligence is knowing when to accept a model's price forecast and when not to.
The math behind stock predictions isn't a mystery—it is a kit. Descriptive stats, probability, calculus, and algebra all come together to make noisy, and somewhat random, market data actionable. If we strip off the mystery, we see that trading is partly a clear-headed calculation, and partly a precise act of bravery, in actual practice.
Sources:
https://www.quantinsti.com/articles/algorithmic-trading-maths/