Improved Risk Reporting with Factor-Based Diversification Measures

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

4. Empirical Analysis for Pension Funds

statistics in Table 7 over the entire period. We notice that the US bonds, US IL bonds, and the mortgage backed securities display on the sample period the highest Sharpe ratios among all the asset classes. This comes from a lower volatility compared to the other asset classes. On the other hand, the asset classes with the lowest Sharpe ratios over the sample period are commodities (close to 0) and equities (their Sharpe ratios is close to 0.13 for all types of equities: US, international, or global). In panel (b) of Table 7, we compute the correlations between each asset class over the entire period of time, and observe, as expected, that the correlations among similar asset classes remain high: the three equity benchmarks are highly correlated, and so are the four bond benchmarks. However, across very different asset classes, correlations can be quite low. From the covariance matrix estimated over the entire sample period (we do not robustify the covariance estimator here since there are only a few constituents), we compute the factor exposures for both the PCA and the MLT methods, and report these numbers in Tables 8 and 9. From Table 8, one can provide some interpretation for the factors obtained through the PCA approach: F1 seems to be a factor related to equities, F2 to commodities, F3 to real estate, F4 to ex-US equities, F5 to bonds, F6 to large cap equities (vs.) small caps, F7 to high-yields, etc. As often, it becomes increasingly difficult to interpret factors that start to have an exceedingly low explanation power. Similarly, we display in Table 9 factor exposures for the MLT approach. A quick look at the diagonal of the table displaying the asset classes’ exposure to the different factors confirms

that each factor seems to be related to one particular asset class, which is consistent with the focus of the MLT approach. For reasons outlined in the section dedicated to equity indices, we focus in what follows on the minimum linear torsion approach, which is better suited for our purpose than the principal component analysis. In Section 4.3, we use another, smaller, set of pension funds, which is a selection of the ten largest pension funds in the world, according to Towers Watson’s 2012 ranking. 8 For our selection, we exclude the 8th largest pension fund, the Central Provident Fund (Singapore) is a comprehensive compulsory saving plan for Singapore citizens and permanent residents which is essentially dedicated to domestic fixed income investments, thus making it an outlier in the analysis. We also exclude the 10th largest pension fund, which is the Employees Provident Fund (Malaysia) because of the difficulty to find relevant domestic fixed- income benchmark with sufficient history. Instead, we include PFZW (Netherlands) and California State Teachers (U.S.A.), which are ranked 11th and 12th, respectively. These funds are ranked by decreasing order of assets under management (amount evaluated at year-end 2011) in the list that follows: 1. Government Pension Investment Fund (Japan); 2. Government Pension Fund (Norway); 3. Stichting Pensioenfonds ABP (Netherlands); 4. Korea National Pension Service (Korea); 5. Federal Retirement Thrift Investment Board (U.S.A.); 6. California Public Employees (U.S.A.); 7. Chikyoren Local Government Officials (Japan);

8 - The survey is available at http://www.towerswatson. com/en-AE/Insights/IC-Types/ Survey-Research- Results/2012/11/ international-pension-plan- survey-2012.

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