Covariance Structure and Systematic Risk of Market Index Portfolio

A set of 18 stocks, selected as the current components of the Dow Jones Index, for which the historical daily closing data quoted at the US market are available for over four decades, is studied. Within this portfolio, we construct a market index with static weights, defined as the relative aggregate trading amounts for each stock. This market portfolio is studied by means of correlation and covariance analysis for the times series of logarithmic returns. Although no measure defined at the correlation/covariance matrices could be found as a definite precursor of market crashes and bubbles, which thus appear as a rather sudden phenomenon, there is an increase in the covariance measures for large absolute values of the logarithmic return of the index. This effect is stronger for the negative values of the log return, corresponding to the market crash case, during which the first principal component of the covariance matrix tends to describe larger proportion of the total market volatility. Periods of low volatility in the market can be characterized by rather significant spread of the relative importance of the first principal component. This finding is common also for the case of dynamically constructed market index, for which the weights are computed as the coordinates of the first principal component eigenvector using short-term covariance matrices.