Financial Risk Modelling and Portfolio Optimization with R

3

Financial market data

3.1 Stylized facts on financial market returns

3.1.1 Stylized facts for univariate series

Before we turn to the topic of modelling financial market risks, it is worthwhile to consider and review typical characteristics of financial market data. These are summarized in the literature as ‘stylized facts’ (see Campbell et al. 1997; McNeil et al. 2005). These observed properties have important implications for assessing whether the risk model chosen is appropriate or not. Put differently, a risk model that does not capture the time series characteristics of financial market data adequately will also not be useful for deriving risk measures. For observed financial market data, the following stylized facts can be stated:

• Time series data of returns, in particular daily return series, are in general not independent and identically distributed (i.i.d.). This fact is not jeopardized by low absolute values of the first-order autocorrelation coefficient.
• The volatility of return processes is not constant with respect to time.
• The absolute or squared returns are highly autocorrelated.
• The distribution of financial market returns is leptokurtic. The occurrence of extreme events is more likely compared to the normal distribution.
• Extreme returns are observed closely in time (volatility clustering).
• The empirical distribution of returns is skewed to the left; negative returns are more likely to occur than positive ones.

As an example, we will now check whether these ...