Improved Risk Reporting with Factor-Based Diversification Measures

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

3. Empirical Analysis for Equity Indices

for each index and their facial number of constituents. Note that in Figure 4, we do not include the FTSE All World because it has too many constituents (around 3,000) which does not allow for a clear comparison with the other indices. Also, the number of constituents of some indices may vary over time, so we estimate that the SPI 200 constituents and that the Hangseng has 45 constituents, which corresponds to the average value over their respective historical periods. Unsurprisingly, we find in Table 2 that there is a strong linear relationship between the number of constituents of an index and its average ENB measure. This means that there is a positive proportional relationship between the level of diversification of an index in terms of uncorrelated risk factors and the number of constituents that this index contains. However, if we consider the relationship between the ENC of an index and its number of constituents, we see that the relationship is not as linear, since it seems to grow sublinearly. Intuitively, this is explained by the fact that cap-weighted indices are highly concentrated. Therefore, increasing the number of constituents will not decrease the concentration of cap-weighted in a linear way. Next, we test whether a link exists between the performance of the 14 equity indices in bear markets and their respective diversification measures at a given date before the start of the bear market. As each of the 14 equity indices does not have the same length of historical data, we need to find a period that is common to every index in order to cross-compare their performance. In addition, we want to compute our analysis on a period of particularly severe market correction in

order to test if the indices that were the best diversified in terms of uncorrelated risks (that is to say with the highest ENB) at a date prior to the start of the crisis are the ones that performed the best during this period of bear market. To find a period of harsh market downturn that was common to every equity index, we naturally focus on the period ranging from the beginning of September 2008 to the end of February 2009. The reasons for this choice are the following. If the 2007-2009 crisis has started on July 2007 with the massive default on subprime mortgages in the United States, it is in the automn of 2008 that it started to spread to the banking sector and turned into a global financial crisis. Indeed, automn of 2008 witnessed a rise of the confidence crisis, the discovery of toxic assets in bank accounts, a rise of the interbank interest rates, and credit constrictions to firms and households which exacerbated the global economic recession. In this context, the crisis hit stock exchanges all over the world, and financials were particularly badly hit with several banks being acquired by competitors, saved by the US Federal Reserve, or simply declared bankrupt. For instance, on 6 September 2008, the US government nationalised Freddie Mac and Fannie Mae and on 15 September 2008, Lehman Brothers collapsed triggering a massive drop in stock prices for many financial institutions. It is also during this period that Bernard Madoff, former non-executive chairman of the NASDAQ, was arrested for a large scale Ponzi scheme (on 12 December 2008) and that Iceland and Ukraine became insolvent. We chose to end the period at the end of February 2009, when the worst of the shock had passed and when governments (United States, Great Britain, etc.) issued

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An EDHEC-Risk Institute Publication