- Stylized facts are generalized, common, qualitative properties based on empirical asset returns across many markets and time.
- Some stylized statistical properties of asset returns:
- Linear autocorrelations are insignificant, except for very small time periods (<20 minutes), where market microstructure comes into play.
- Existence of heavy (power-law or Pareto-like) tails, which are difficult to model.
- Large drawdowns occur but not symmetrical large up moves.
- Times scales of measurement create different distributions. As the time scale increases, the distribution resembles more Gaussian.
- High variability (jumps) in the time series.
- High volatility tends to cluster. Trading volume is correlated with volatility.
- Some challenges to stationarity: various calendar effects (e.g. January effect).
- Well established: (linear) autocorrelation in liquid markets rapidly decays to zero with time intervals as short as 15 minutes. Statistical arbitrage has eliminated autocorrelation in futures and foreign exchange markets to mere minutes.
- Squared returns (volatility) do exhibit autocorrelation. Volatility tends to cluster, and decay slowly for days and sometimes weeks. This nullifies the Random Walk (RW) hypothesis for stock returns, since RW requires linear and non-linear functions of the data to be non-autocorrelated.
- Using autocorrelations statistic may be unreliable for functions of heavy-tailed, non linear (higher moments of returns) time series.
- Covariance has been an ineffective tool to measure risk because it is based on a co-dependence behavior on average, not during extreme (downside) events. Extreme correlations may be a better tool for risk management. Note that two assets can have zero covariance (during normal times), but high extreme correlation.
Finished: 27-Jun-10. Rating 7/10.