When specifying your next risk model for asset returns there are a number of properties, or stylised facts, to keep in mind.

A stylized fact is an empirical finding that is believed to hold for a diverse collection of instruments, markets and time periods.

A number of authors have studied stylised facts for asset returns over the last 30 years, and thereare a few common themes that can be concluded: non-normality (fat tails) and features giving rise to various dependence structures.

Cont (2001) summarises the most important stylized facts of assets returns as:

  1. Absence of autocorrelations: (linear) autocorrelations of asset returns are often insignificant, except for very small intraday time scales

  2. Heavy tails: the (unconditional) distribution of returns possess heavy tails, i.e. the distribution has more mass in the tails than in the entre. Even if the precise form of the tails often is difficult to determine the normal distribution can be readily excluded

  3. Gain/loss asymmetry: it can observed in stock prices and stock market indices that upward movements tend to be smaller than, the often large, drawdowns

  4. Aggregational normality: as the time scale is increased over which returns are calculated, their distribution becomes more and more Gaussian; in particular the shape of the distribution varies across time scales

  5. Intermittency: returns display, at any time scale, a high degree of variability. This is quantified by the presence of irregular bursts in time series of volatility estimators

  6. Volatility clustering: many measures of volatility display a positive autocorrelation over several days, which quantifies the fact that high-volatility events tend to cluster in time

  7. Conditional heavy tails: even after correcting returns for volatility clustering, e.g. via GARCH-type models, the residual time series still display heavy tails. However, the tails are less heavy than those of the unconditional distribution

  8. Slow decay of autocorrelation in absolute returns: the autocorrelation function of absolute returns decays slowly as a function of the time lag. This is sometimes interpretedas a sign of long-range dependence

  9. Leverage effect: most measures of volatility of an asset are negatively correlated with the returns of that asset

  10. Volume/volatility correlation: trading volume is correlated with all measures of volatility

  11. Asymmetry in time scales: coarse-grained measures of volatility predict more granular volatility better than the other way around

Now that we are aware of these empirical findings, the next step is to figure out what features we need our model to possess in order to be able to reproduce some of these stylised facts. That way we will be able to simulate the behaviour of the asset returns we are investigating, and then produce an estimate of the distribution of the future value of the assets on our balance sheet.

Further reading

Cont - Empirical properties of asset returns, Quantitative Finance, vol. 1, Institute of Physics Publishing, 2001.