Asset returns have certain statistical properties, also called stylized facts. Important ones are:
- Absence of autocorrelation: basically the direction of the return of one day doesn’t tell you anything useful about the direction of the next day.
- Fat tails: returns are not normal, i.e. there are many more extreme events than there would be if returns were normal.
- Volatility clustering: basically financial markets exhibit high-volatility and low-volatility regimes.
- Leverage effect: high-volatility regimes tend to coincide with falling prices and vice versa.