Improved Risk Reporting with Factor-Based Diversification Measures

Improved Risk Reporting with Factor-Based Diversification Measures — February 2014

3. Empirical Analysis for Equity Indices

Table 6 displays the results obtained from the six linear regressions for the S&P500 index. These predictive powers of the diversification measures are statistically significant for both ENC and ENB measures as they have a p-value close to 0 for every period of computation of the annualised performance. These results suggest that there is a positive relationship between the level of diversification (measured via the ENC or ENB indicator and the subsequence performance of the S&P500 index, whatever its period of computation. It should be noted, however, that the coefficients of proportionality remain low (between 0.21 and 0.42). In addition, we find for both diversification measures that the R-squared and the t-stats of the linear regressions increase with the length of the period of annualised performance computation, which shows that the diversification measures have better forecasting power over long horizons. Lastly, if we only focus on the quarterly and the semi-annually performance computation, we notice that the t-stat of the ENB is higher than the one of the ENC with a higher level of significance. From the point of view of an investor who seeks to use diversification measures for short-term tactical purposes, it is therefore more interesting to look at the evolution of the ENB measure rather than focusing on the ENC measure. 3.2 Cross-Sectional Analysis of Diversification Measures In the previous section, we analysed the diversification measures from a time-series analysis based on long-term historical return data for the S&P500 index. In this section, we test the link between diversification measures of risk and the performance

of equity indices from a cross-sectional perspective instead. To do so, we conduct an analysis of the relationship between the performance of the 14 equity indices during the sub-prime crisis and their diversification measures computed at some point before the crisis started. The indices we consider in this analysis are the S&P500 and 13 other equity indices mentioned before: the CAC 40 index, the DAX 30 index, the Dow Jones 30 index, the Euro Stoxx 50 index, the Euro Stoxx 300 index, the FTSE 100 index, the FTSE All World index, the Hang Seng index, the Nasdaq 100 index, the SPI index, the Stoxx Europe 200 index, the Stoxx Europe 600 index and the Topix 100 index. Therefore, we consider equity indices of different sizes and different universes. For each of them, we compute the ENC measure and the ENB measure using an MLT approach on the largest time period available. These time periods vary from 17 years of historical data for the longest to six years of historical data for the shortest. Figures 5 and 6 respectively display the ENC and the ENB using an MLT approach for the CAC40 index and for the Stoxx Europe 600 index computed following the same protocol than for the S&P500. We choose to present two indices with different sizes on purpose. We notice that the figures we obtain for these two indices are very close to those of the S&P500 (except for a shorter time period), which suggests that the conclusion we have obtained so far are relatively robust with respect to the choice of the index. We then analyse in Figure 4 the relationship between the average ENB computed using an MLT approach and the average ENC computed on the whole historical period

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An EDHEC-Risk Institute Publication