An Empirical Study of Correlation and Volatility Changes of Stock Indices and their Impact on Risk Figures

During world financial crisis it became obvious that classical models of portfolio theory significantly under-estimated risks, especially with regard to stocks. Instabilities of correlations and volatilities, the relevant parameters characterizing risk, led to over-estimation of diversification effects and consequently to under-estimation of risks. In this article, we analyze the relevant risk parameters concerning stocks during different market periods of the previous decade. We show that parameters and risks significantly change with market periods and find that the impact of fluctuations and estimation errors is ten times larger for volatilities than for correlations. Moreover, it turns out that diversification between sectors is more efficient than diversification between countries.