Predictions vs Probabilities

A key distinction for any investor is the difference between predicting a price and calculating the probability of a price change. While both use historical data, they represent fundamentally different approaches to market analysis. Using 180 days of price and volume data, let's explore this distinction.

The Myth of Price Prediction 🔮

A price prediction is a specific forecast of a future price. For instance, "Stock X will be $150 in three months." This is a definitive statement that can either be right or wrong. While tempting, relying on these types of predictions is often a mistake. Financial markets are chaotic and influenced by an endless number of unpredictable factors, from geopolitical events to a company's unexpected earnings report.

Traditional models for price prediction, even those using 180 days of data, often fall short. They include:

• Moving Averages: A simple moving average (SMA) calculates the average price over a set period. An exponential moving average (EMA) gives more weight to recent prices. You can plot a 180-day moving average to identify a long-term trend, but it's a lagging indicator and doesn't predict a specific future price.

• Linear Regression: This model tries to find a straight line that best fits the historical data. It can project a future price based on a past trend, but it assumes the trend will continue, which is rarely a safe bet in the financial world.

• Machine Learning (ML) Models: More advanced models like Long Short-Term Memory (LSTM) networks can identify complex, non-linear patterns in data. While they can be powerful, their predictions are still based on the assumption that past patterns will repeat, and they can be complex to set up and interpret.

These models aim to tell you what will happen, which is a significant challenge in a non-linear system like the stock market.

The Power of Price Change Probabilities 📊

Instead of trying to predict the future, a more effective approach is to work with probabilities. A probability-based analysis tells you the likelihood of a certain outcome occurring. For example, "Based on historical volatility, there's a 70% chance that Stock X's price will be between $120 and $160 in the next three months." This approach acknowledges the inherent uncertainty of the market and provides a more realistic framework for making decisions.

To calculate these probabilities using 180-day data, you can use models based on historical volatility and statistical distribution.

1. Calculate Historical Volatility: Volatility is a measure of how much a security's price has fluctuated in the past. To do this, you first calculate the daily logarithmic returns for the past 180 days. Then, find the standard deviation of those returns. This gives you the daily volatility. To get the annualized volatility, you multiply the daily standard deviation by the square root of 252 (the approximate number of trading days in a year).

2. Model Price Changes: Financial theory, particularly the Black-Scholes model, often assumes that stock prices follow a log-normal distribution. This means that while the raw price changes might be all over the place, their percentage changes (returns) are more predictable and often fall into a bell curve.

3. Calculate Probabilities: With the volatility calculated, you can use statistical functions to determine the probability of a price ending up in a specific range. For example, a common rule of thumb is that there's about a 68% chance a stock's price will end up within one standard deviation of its mean over a given period, and a 95% chance it will be within two standard deviations. This isn't a guarantee, but it provides a quantifiable measure of risk and potential reward.

This method shifts the focus from a single, rigid prediction to a flexible, probabilistic view of the market. It doesn't tell you the price, but it gives you the odds, allowing you to manage risk and size your positions accordingly.

The Verdict: Probabilities over Predictions 🧠

While both methods use historical data, price predictions are a quest for certainty that doesn't exist, while price change probabilities are an acceptance of uncertainty that provides actionable insight. Using 180-day data is a great starting point for both, but the true value lies in how that data is used. By focusing on probabilities, you can make more informed, risk-aware decisions rather than chasing an elusive crystal ball.