The relationship between concentration and realised volatility: an empirical investigation of the FTSE 100 Index January 1984 through March 2003

Abstract

Few studies have examined the impact of portfolio concentration upon the realised volatility of stock index portfolios, such as the FTSE 100. Instead, previous research has focused upon diversification across industries, across geographic regions and across different firms. The present study addresses this imbalance by calculating the daily time series of four concentration metrics for the FTSE 100 Index over the period from January 1984 through March 2003. In addition, the value weighted variance covariance matrix (VCM) of daily FTSE 100 Index constituent returns is decomposed into four sub-components: two from the diagonal elements and two from the off-diagonal elements of the VCM. These consist of the average variance of constituent returns, represented by the sum of diagonal elements in the VCM, and the average covariance represented by the sum of off-diagonal elements in the VCM. The value weighted average variance (VAV) and covariance (VAC) are each subdivided into the equally weighted average variance (EAV) the equally weighted average covariance (EAC) and incremental components that represent the difference between the respective value-weighted and equally weighted averages. These are referred to as the incremental average variance (IAV) and the incremental average covariance (IAC) respectively. The incremental average variance and the incremental average covariance are then combined, additively, to produce the incremental realised variance (IRV) of the FTSE 100 Index. The incremental average covariance and the incremental realised variance are found to be negative during the 1987 crash and the 1992 ERM crisis. They are also negative for a substantial part of the study period, even when concentration was at its highest level. Hence the findings of the study are consistent with the notion that the value weighted, and hence concentrated, FTSE 100 Index portfolio is generally less risky than a hypothetical equally weighted portfolio of FTSE 100 Index constituents. Furthermore, increases in concentration tend to precede decreases in incremental realised volatility and increases in the equally weighted components of the realised VCM. The results have important implications for portfolio managers concerned with the effect of changing portfolio weights upon portfolio volatility. They are also relevant to passive investors concerned about the effects of increased concentration upon their benchmark indices, and to providers of stock market indices.