Pension Fund Canton Luzern
The graph above plots performance, rebased to 100 at the end of 1999. It shows the featured pension fund, together with the most highly correlated benchmark index, and the legal minimum rate. As a novelty, the graph also includes the factor-modified benchmark ‘C40 VA-M’, a proxy for conceivable expectations of performance achievable by skilled investment management under the exact circumstances described be the underlying benchmark index. Read more on Factor-Modified Benchmarks.
Pension Fund, Risk -Tiers, and Peer Group
In the upper section of Table 01, starting and end values are shown for the pension fund, three contiguous risk-tier benchmarks, the Swiss Pension Fund Composite, and the factor-modified benchmark ‘C40-VA-M’. Performance is listed cumulative and annualised. As simple comparison of risk management and measure of investment efficiency, the table gives sums of annual gains and losses. Finally, the table includes the values of worst and median yearly changes related to these 20 years.
In the lower section of the table, Alpha (intersect) and Beta (slope of linear regression) are indicated. In all regression calculations LPP-C40 (the medium risk tier benchmark) was used as independent variable (x-value). This is different from the regressions in Table-02 (Exhibit G), where the featured pension fund is always the dependent variable (y-value) and each of the benchmarks serve as independent variable.
Highlighted in the graph’s title, overall change in value is given, as well as the resulting normalised rate of return. The chart itself plots four different annualised rates: 31.12.1999 to date (anchored), and trailing three, five, and ten years.
Performance & Financial Market Context
A carousel of exhibits shows performance in the context of benchmark indices, and major financial markets, both domestic and foreign. Use the cursor to stop auto-play and navigate manually. Exhibits refer to year 2019, 3-years to date, 10-years to date (value plot).
M4 describes a global, equal-weight, basket of four countries: USA, Japan, Eurozone-Europe, and Great Britain. The term ‘bonds’ refers to return indices for zero-coupons, 10-year government bonds, calculated from benchmark bond yields.
The main purpose of the table is to make transparent the choice of most correlated benchmark used in several other illustrations. Regression data for the full array of six benchmark indices are shown.
The table gives annualised rates of return. In addition, the pension fund’s return is expressed relative to that of each benchmark. Values for ‘Alpha’, ‘Beta’, and R-squared are shown in grey, but the highest R-squared is emphasised. The benchmark so determined will not necessarily be identical to the benchmark chosen by the pension fund.
Having identified the highest congruence to one of the indices, the table then performs a more detailed analysis of annual return differentials between the featured pension fund and that specific benchmark index.
The ratio shown at the extreme lower right of the table is the frequency-weighted average performance differential in a year. It is shown in green if better, or red if worse than the most correlated benchmark.
Close-Up View Of Yearly Changes
In this exhibit, yearly rates of change are split into cumulated gains and cumulated losses. The charts show values for the most correlated benchmark index and the featured pension fund. A line plots the ratio of the pension fund’s cumulated gains or losses relative to those of the benchmark.
Visualising The Width Of One Standard Deviation
The graph illustrates the three most important components of distribution analysis:
- median value
- upper inflection point (= median plus one standard deviation)
- lower inflection (median minus one standard deviation)
To the left,the featured pension fund is positioned alongside its most correlated index. Grouped separately are plots for all six benchmark indices.
The table below the graph shows the extend of horizontal distortion (of the distribution). Distortions exceeding 10% on either side are emphasised. Vertical distortion is not shown.
Here, cumulated gains and losses are positioned in a grid. The vertical axis refers to the net balance of cumulated annual gains, with cumulated annual losses subtracted. The horizontal axis gives cumulated annual losses. The further up and left a fund is positioned, either overall, or relative to any given reference, the better.
Regression of Annual Rates of Change
This carousel displays graphically selected regressions already seen in numerical format in Table-02. Each time, the featured pension fund’s annual rates of change (y-values) is plotted against a specific reference (x-values). Use the cursor to stop auto-play and navigate manually using the arrows.
In addition to the regression formula, the total change in value of the featured pension fund compared to the reference is calculated, showing the differential in green if positive, or red if negative.
The regression graphs show the pension fund with the following x-values:
- most correlated benchmark index
- Swiss Pension Fund Composite Index (peer group analysis)
- LPP-C40 (the medium risk-tier benchmark)
Please note that the most correlated benchmark index may coincide with LPP-C40, in which case that particular regression would be shown in two graphs.