Improved Risk Reporting with Factor-Based Diversification Measures

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

4. Empirical Analysis for Pension Funds

statistically test the degree of significance of our results. We replicate this test for each diversification measure and for the two periods of time considered. We display our results in Figure 12, and panels (a) and (b) of Table 11. In Figure 12, it is first striking to see that the relationship between US pension fund performances and their level of ENC is negative, while this relationship is positive for the ENB. This is true for the two periods of performance computation. We test the degree of significance of these results for the two periods and note that the coefficients between performances and diversification measures are indeed positive for the ENB and negative for the ENC whatever the period of performance chosen, and that t-stats and p-values are always significant. These results mean that, at the end of September 2007, a pension fund that had a higher ENB was more likely to reach higher performances during 28/09/2007-26/09/2008 and during 05/09/2008-27/02/2009 (which translates into lower losses because we are looking at performances during the subprime crisis) than a pension fund that had a lower ENB, assuming the policy portfolio weights remaining constant. However, higher levels of ENC for a pension fund at the end of September are likely to have no impact if not negative effects on its performances during 28/09/2007-26/09/2008 and during 05/09/2008-27/02/2009 compared to another pension fund with lower levels of ENC, all weights remaining equal. Nevertheless, in Figure 12, we notice that the pension funds that performed best during the two periods considered seem to behave differently to the others. For these pension funds, there seems to be a negative, as opposed to positive, relationship between

their performances and their level of ENB at the end of September 2007. For the annualised performances observed during 28/09/2007-26/09/2008, this observation applies to the pension funds that performed over -5%; for the annualised performances observed during 05/09/2008-27/02/2009, it applies to the pension funds that performed over -20%. Therefore, for each period, we split up our population and test the link between performances and diversification measures on the US pension funds that performed over -5% (respectively over -20%) on the one hand, and the ones that performed under -5% (respectively under -20%) on the other hand during 28/09/2007-26/09/2008 (respectively during 05/09/2008-27/02/2009). For each diversification measure and for each period, we scatter plot these relationships and test their levels of significance. We display our results in Figure 13, and panels (c) and (e) of Table 11 for performances computed during 28/09/2007-26/09/2008; and in Figure 14, and panels (d) and (f) of Table 11 for performances computed during 05/09/2008-27/02/2009. We always display annualised performances expressed in percentages. For each period and for the US pension funds that performed under the threshold of -5% (or -20%), the results of our linear regressions are very close to the ones obtained on the whole sample and their scatter plots look similar to the scatter plot obtained on the whole sample. However, results are very different for the US pension funds that performed over the threshold of -5% (or -20%). Indeed, we see that for the two periods considered, the relationship between pension funds performances and ENB becomes negative. This relationship

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An EDHEC-Risk Institute Publication