Stylized Facts of Financial Returns › Stylized Facts of Financial Returns

When you examine financial return data from different assets, markets, and time periods, certain empirical regularities appear again and again. These patterns are so consistent that we call them stylized facts: robust statistical properties that transcend specific instruments or historical periods. Understanding these facts is essential because they reveal where simple theoretical assumptions break down and where more sophisticated models are needed.

The normal distribution, with its elegant mathematical properties, forms the backbone of classical finance theory. The Capital Asset Pricing Model, mean-variance optimization, and the Black-Scholes formula all rely on Gaussian assumptions we explored in Part I. Yet when you analyze actual return data, you discover systematic departures from normality that affect risk management, derivative pricing, and portfolio construction.

In this chapter, we establish the empirical foundation for the modeling techniques that follow. Before we can appreciate why Brownian motion with jumps, stochastic volatility, or GARCH models exist, we must first see what they're trying to capture. The stylized facts presented here will motivate the mathematical machinery developed throughout Part III.