Improved Risk Reporting with Factor-Based Diversification Measures

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

4. Empirical Analysis for Pension Funds

and make several assumptions. Firstly, in the 2002 original database, we gathered the portion allocated to “Sponsoring Companies Stock” and to “Other Domestic Equity” into a single asset class: “Domestic equity”. Secondly, we did not always have the same partition of asset allocation for the three years. Therefore when one of the asset classes from our list was missing in one database, we added it and filled it with zeros. This is why we have 0% asset allocation for the “Global equity” asset class for the years 2002 and 2007, 0% asset allocation for the “Mortgage” asset class for the year 2012 and 0% asset allocation for the “Commodity” asset class for the year 2002. Thirdly, in each of the three original databases we did not have access to the percentage allocated to high-yield bonds and to inflation-linked bonds. However, we had their amount in dollars, and consequently we managed to deduct their percentage asset allocation. Then, in order to remain at 100% total allocation, we removed the calculated portions from the “Domestic fixed income” percentage allocation. By doing so, we assumed that the high-yield bonds and the inflation- linked bonds in which the US pension funds invest are all domestic bonds. We applied this methodology for most of the pension funds but there were some exceptions. When it was specified that high-yield bonds and inflation-linked bonds had been counted in the portion allocated to “Other investments”, we withdrew the portion of high-yield bonds and inflation-linked bonds from “Other investments”. Fourthly, as for the high-yield bond and the inflation- linked bond asset classes, the portion allocated to commodities was never specified. We just had its amount in dollars for the years 2007 and 2012 and knew that

this asset class was part of the “Alternative investments” asset class for the year 2012. Therefore, using the same method as for the high-yield bond and the inflation- linked bond asset classes, we deducted the portion allocated to commodities and subtracted it from the “Alternative investments” asset class in 2012 or from “Other investments” for the years 2007 and 2012 when it was specified. Finally, we removed from our partition the portion allocated to “Other investments” (and to “Alternative investments” for the year 2012) and we normalise the percentages in order to obtain a total of 100% allocation. These “Other“ or ”Alternative“ investments that we discard represent in average 4.50% of the total investment in 2002, 11.33% in 2007, and 8.65% in 2012. Once the three databases were homogenised, we still had some small remaining discrepancies. First, for some pension funds we had negative percentages allocated to the domestic fixed income asset class, to the “Other investments” asset class and to the “Alternative investments” asset class. This happened because these pension funds did not carefully fill the original databases. In some cases, they classified all their bonds under “International/global fixed income” whereas they should have been part of the ”Domestic fixed income”; in some other cases they classified all their other investments (and/or alternative investments) under the “Private equity” asset class. However these discrepancies happened to be a negligible portion of the universe (around three out of 1,000 pension funds for each year). Secondly, the sum of the percentage allocated to each asset class did not always equal 100%. This was due to a wrong approximation of the amount

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An EDHEC-Risk Institute Publication