Stylized Facts of Financial Returns › Summary

This chapter established the empirical foundation for quantitative modeling by documenting the robust statistical properties of financial returns:

Heavy tails and excess kurtosis represent the most dramatic departure from normality. Extreme returns occur far more frequently than the normal distribution predicts, with daily equity returns typically showing excess kurtosis of 5-15. This has direct implications for tail risk measurement and derivative pricing.

Negative skewness characterizes many equity return distributions, which reflects the asymmetric nature of market movements: gradual rises and sudden crashes. Risk models must account for this asymmetry in the loss tail.

Volatility clustering means that market turbulence is persistent. Today's volatility strongly predicts tomorrow's volatility, with autocorrelation in squared returns remaining significant for many weeks. This violates the i.i.d. assumption underlying many classical models.

The leverage effect introduces asymmetry in volatility dynamics: negative returns increase future volatility more than positive returns. This correlation between returns and volatility changes has implications for option pricing and hedging.

Aggregational Gaussianity provides a silver lining: returns become more normal at longer horizons. Daily returns require careful non-normal treatment, but annual risk assessments can rely more heavily on Gaussian approximations.

These stylized facts motivate the sophisticated modeling techniques developed throughout the remainder of this textbook. The Brownian motion framework of the next chapter provides a mathematical foundation for continuous-time price processes, but you'll now understand why extensions like jump-diffusions and stochastic volatility are necessary to capture market reality. The gap between elegant theory and messy reality is precisely where quantitative finance earns its value.