Improved Risk Reporting with Factor-Based Diversification Measures

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

4. Empirical Analysis for Pension Funds

historical weekly returns before the date at which we perform the computation. We also compute the ENC measure at the same dates. As our universe is made of roughly 1,000 pension funds (it is less than 1,000 because some funds did not fill out the P&I form, or did so but not with enough details to be included in our analysis), we obtain 1,000 diversification measures at each date. In Figure 9, we display the distributions of the ENC, and ENB computed using a PCA and ENB computed with an MLT approach. We first notice that the distribution of the ENB computed through a PCA is on average close to one for all pension funds and for the three years, just as was already the case for the equity indices. We thus decide to focus on the ENB computed with an MLT approach in order to cross-compare the diversification measures. When looking at the evolution of each diversification measure, it seems that a change occurred between 2007 and 2012, as most US pension funds seem to have increased the diversification level in their portfolio between these two dates. For instance, between 2002 and 2007, the mean of the distribution of the ENCs increases by 1.3% while between 2007 and 2012, it increases by 40.7%. Therefore, it seems that US pension funds dedicated some effort between 2007 and 2012 to improve their level of diversification. However, we note that when US pension funds increase their ENC by 40.7% in five years, they only increase their ENB by 14.4% between 2007 and 2012. We then test whether the distributions displayed in Figure 9 depend on the US pension funds’ characteristics such as the amount of assets under management or their status (public or private). In Figure 10,

we look at the distribution of the ENC and the ENB computed using a PCA approach and the ENB computed using an MLT approach according to the amount of assets under management of the pension funds. For each diversification measure and for each date, we compute two distributions: one for the pension funds managing the lowest 30% of assets under management (in red in the figure), and one for the pension funds managing the highest 30% of assets under management (in blue in the figure). We note that the ENC of the 30% pension funds managing the lowest amount of assets under management are on average higher than the ENC of the 30% pension funds managing the highest amount of assets under management at the end of September 2002, 2007 and 2012. We test the level of significance of the average of the two distributions of ENC for the three years using a two-sample t-test and report the results in Table 10. We find that the mean of the distribution of the pension funds managing the lowest amount of assets is always significantly different (higher) at a 95% confidence interval from the mean of the distribution of the pension funds managing the highest amount of assets (except in 2012 for the ENB computed with the MLT, where we find that bigger funds are slightly better diversified). This means that smaller funds tend to be less concentrated than larger funds, which could be explained by liquidity constraints preventing some of the largest fund to invest significant fraction of their assets in some alternative asset classes.

In Figure 11, we look at the distribution of public versus corporate pension funds’ diversification measures. It is interesting to

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An EDHEC-Risk Institute Publication