# Swiss Pension Fund Composite Index Performance Monitor

### Swiss Pension Fund Composite Index

From 31.12.1999 onward, Credit Suisse calculate the first pension fund aggregate index, based on some 100 Swiss pension funds to whom Credit Suisse acts as global custodian. While the index is calculated monthly, it is published quarterly. With an inception date of 31.12.2005, UBS Group began to also publish a family of pension fund indices based on custody. In contrast to Credit Suisse, UBS publish calculate and publish indices monthly. Unsurprisingly, against minor and often temporary differences, both groups of pension fund aggregates are highly representative of the entire population of Swiss pension funds.

Based on the Credit Suisse and the UBS Pension Fund Index families, Agathos calculate the Swiss Pension Fund Composite Index, merging two highly similar references into a single aggregate. Credit Suisse pension fund data yet to be published are temporarily represented by statistically based estimates. Hence, the Pension Fund Composite Index may contain a combination of published data and estimates.

The performance of this Pension Fund Composite is assessed either against a medium risk benchmark (LPP-C40), or is shown alongside all three risk-tiers (C25, C40, and C60).

Performance benchmarks in asset management (with the exception of peer group references) are free from any attempt to generate ‘value-added’. Thus, benchmark indices must not be read as quality reference. Rather, they should be seen as a simplified description of circumstances under which pension funds operate.

### Taking Advantage Of Monthly Performance Updates

The calculation of many quantitative and qualitative metrics requires large data samples to generate meaningful results. Unlike the data for specific pension funds, any of the aforementioned aggregate indices is available with monthly frequency, thus permitting a depth of analysis and comparisons not possible with quarterly, or annual data. As individual pension funds show a very high degree of congruency with the aggregate indices used here, the analysis of monthly data for the composite index can be taken as advance insight into pension funds investment performance released much later and with lower frequency.

**Exhibit-02** looks only at a fairly short period, the most recent 18 months of history. The graph shows the PF Composite index as grey columns and the three risk-tier references as lines. The plot consists of percentage changes from the starting value 18 months ago. Some additional statistics are given in the table to the left of the graph.

**Exhibit-03** gives an express glance of contextual pension fund performance across several time frames, each calculated to date. It shows annualised rates of return since 31.12.1999 as well as over trailing ten, five, and three years. Simple rates of change are shown for periods of 12 months and less.

**Exhibit-04** shows the figures underlying the graph in the previous exhibit. As additional information, the current distance from the all time high is also calculated.

In the split graph of **Exhibit-05**, a closer look is taken at relative performance of pension funds since inception. Relative performance is calculated separately for each risk-tier benchmark. The lower portion of the graph plots the relative performance of LPP-C60 (the higher risk-tier benchmark) versus LPP-C25 (the lower risk-tier). If that ratio rises (black line), a more aggressive policy achieves higher returns than a more cautious stance.

**Exhibit-06** gives selected metrics describing the distribution of monthly rates of change since inception. Variance of the data can be gauged by Standard Deviation (also referred to as ‚Volatility’, and by the Interquartile value a bit further out from the centre than standard deviation. Skew, (calculated according to Fisher-Pearson) and kurtosis ,a measure of vertical distortion here calculated according to Cochran) are quotients that show to which degree the distribution differs from ‚Normal’. Normally distributed data have a skew of 0.0 and kurtosis also at 0.0. All methods for calculating skew have zero as ‚normal’, albeit with different sensitivities. Various methods to determine kurtosis use either zero, or 3.0 as reference for ‚normal’.

**Exhibit-07** shows the actual distribution of monthly rates of change (columns) together with the corresponding normal distribution (thin black line). This ‚bell curve’ reflects mean and standard deviation as per actual distribution and it is drawn (positioned) to coincide with the mean of the actual distribution. But in any normal distribution, mean, median, and mode are always identical. When generating an overlay of theoretical ‘normal’ and ‘observed’ (actual) distributions, it is arguably just as be legitimate to place the mean of the normal distribution to coincide with the mode, or the median, of the actual distribution. Each option would generate an interpretation distinct from the one in the exhibit.

**Exhibit-08** investigates the congruence between the Pension Fund Composite and all three risk-tier benchmarks, picks the one which generates the highest correlation. The benchmark so selected serves as independent variable (x-axis) in the scatter plot. The line of best fit is shown in red. The underlying regression equation is shown to the right of the graph, supplemented by the accrued performance differential between the PF Composite and the selected benchmark index for all the history included. In the equation, the intercept value of the graph ‚alpha’ has been annualised. Based on that equation, the table shows scenarios of predicted annual returns for pension funds, given assumed returns of the most highly correlated benchmark index.

**Exhibit-09** plots fixed-length (120 months) trails of r-squared values between the PF Composite and each risk-tier. A reading of 100% would indicate perfect correlation and thus a completely lethargic investment approach. Readers should bear in mind that each point on any line of that graph reflects 10 years of history to that point in time.

The table in **Exhibit-10** makes an analysis of risk efficiency by comparing annualised returns with risk. Pension funds require absolute returns more than all else. While the absolute level of risk and the risk-adjusted return are indeed important, they are arguably not as important as a test of consistency across risk tiers. Higher risk may well be tolerated, even at lower risk efficiency, for as long as it produces a higher absolute return than a lower risk strategy and/or a more risk efficient strategy. In this table all relatives have been calculated using the lowest risk tier as reference.

**Exhibit-11** illustrates the extent of loss (drawdown) from the emerging all time highs. That erosion is put into perspective by including the mean drawdown value of each risk-tier as a constant ( = floor).

The final three exhibits focus on displaying normalised values for risk and return:

**Exhibit-12** shows both values calculated across the entire time since inception as a scatter, with return on th vertical axis and risk on the horizontal axis. **Exhibits-13** shows only normalised return over 36 months trailing, while **Exhibit-14** does the same for normalised risk.

### Data Sources

Raw data underlying all calculations and illustrations was sourced from: