In academic finance, “stylised facts” simply means “Universal Rules of Thumb”. These are the behaviours that happen so consistently across all markets and all decades so that we accept them as facts.
Let’s start to explain harsh realities of stock market:
- Lack of stationarity: Past performance does not guarantee future results.
- Volatility clustering: Calm periods breed calm; crazy periods breed crazy.
- Absence of autocorrelations: Yesterday doesn’t predict today.
- Heavy tails: Crashes happen way more than they should (not like a bell curve).
- Gain/loss asymmetry: Markets tend to grind upward slowly, but it drops fast and violently.
- Positive correlation of assets: In a crisis, everything crashes together.
How do we choose our data then? There are 3 ways to look at the market data:
- Low frequency (Looking at Monthly/Yearly data): Risk of underfit.
- Medium frequency (Looking at Daily data): Sweet spot, though we must build mathematical nets for violent crashes.
- High frequency (Looking at Minute-by-Minute data): Risk of overfit.
Resources
Portfolio Optimisation: Theory and Application by Daniel P. Palomar, Page 19, 20.