Improved Risk Reporting with Factor-Based Diversification Measures

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

4. Empirical Analysis for Pension Funds

representing an asset class in our universe in order to estimate these pension fund performances at any future date following the date t of diversification measurement. We use this methodology for two main reasons. The first reason for our choice is more practical. We want to look at performances at different points in time. However, most of the time, we cannot get this information from pension funds’ releases as they display their returns at the end of calendar years or at the end of fiscal years (end of June). Secondly, this approach allows us to preserve a stronger link between diversification measures computed at a date t and pension funds’ performances at t + n months. Indeed, pension funds are free to change their asset allocation after the date of computation of the diversification measures. In the end, depending on the degree of modification of these allocations, the diversification measures computed at date t are likely to bear little, if any, relation to pension fund performance at date t + n months. Depending on the policies adopted by a fund, its actual performance at date t + n months may therefore have nothing to do with its diversification measure at date t . In our test, we compute the fund returns over two different periods: over the year directly following the date of computation of the diversification measures (from 28/09/2007 to 26/09/2008), and over the worst period of the subprime crisis for the financial sector (from 05/09/2008 to 27/02/2009). For each diversification measure, we first plot the relationship between the US pension funds’ annualised performances at date t +n months according to their level of diversification measure at date t (end of September 2007). Then, we

notice that public pension funds always have, on average, a higher ENC than corporate pension funds. This is confirmed by looking at panel (b) of Table 10, where we see that the t-test of the equal mean hypothesis is rejected with a 95% confidence for each of the three years. However, this tends to be the opposite when we look at the ENB measure. Indeed, it is statistically impossible to identify in 2002 and 2007 whether the public or corporate pension funds had the higher ENB measure. Moreover, the t-test of panel (b) in Table 10 shows that in 2012 corporate pension funds had, on average, higher ENB measures than public funds. This shows that the 2007-2009 subprime crisis led corporate funds to increase their level of diversification in terms of risk factors, which made them more comparable if not better diversified than public funds. In the empirical analysis for equity indices which we performed previously, we tested for the cross-sectional relationship between diversification measures and subsequent performance. In this section, we replicate the same analysis on the 1,000 largest US pension funds, and we analyse whether the diversification measures computed over these pension funds at the end of September 2007 can give insights on the returns of US pension funds performance several months after. In order to perform our test, we need to make several assumptions. We actually do not use pension fund actual performance in our analysis and assume instead that the fund asset allocation remains constant over the months following the computation of the diversification measures at date t . Then, we use the performances of each benchmark

46

An EDHEC-Risk Institute Publication