Abstract
Defined benefit pension schemes accumulate assets with the ultimate objective of honoring their obligation to the beneficiaries. Liabilities should be at the center of designing investment policies and serve as the ultimate reference point for evaluating and allocating risks and measuring performance. The goal of the investment policy should be to maximize expected excess returns over liabilities subject to an acceptable level of risk that is expressed relative to liabilities. In this article, we argue for the use of a liability-relative drawdown optimization approach to construct investment portfolios. Asset and liability returns are simulated using a vector autoregressive process with state variables. We find that drawdown optimal portfolios provide better downside protection, are better diversified and tend to be less equity centric while providing higher expected returns compared to surplus variance portfolios.
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Notes
Some of the uncertainty embedded in pension liabilities, such as mortality risk and wage growth uncertainty, cannot (currently) be hedged away.
Maximizing expected utility over the funded ratio is closely related to maximizing the expected utility of the fund surplus (A T −L T ), as in Rudolf and Ziemba (2004), as the funded ratio is equal to the value of the fund surplus scaled by the value of the liabilities: F T =(A T −L T )/L T +1. An advantage of the funded ratio is that it is non-negative by definition and therefore more suited for traditional power utility functions (including logarithmic utility).
Several studies have shown that historical hedge fund returns are biased upwards because of survivorship bias and other reporting biases. Estimates of survivorship bias in hedge fund returns range from about 1.8 per cent to 2.4 per cent per annum.
For quarterly data, we find that setting λ equal to 0.18 produces the best overall fit to the yield curve data. A value of 0.18 on a quarterly basis is identical to λ=0.06 on a monthly basis, as used by Diebold and Li (2006).
Starting values for the VAR process in the simulation are the latest observed values in our sample (2008:Q3). We use antithetic sampling from the error distribution to generate the scenarios.
The original Calmar ratio is the ratio of compound annualized return to maximum drawdown.
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We thank two anonymous referees for valuable comments and suggestions.
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Berkelaar, A., Kouwenberg, R. A liability-relative drawdown approach to pension asset liability management. J Asset Manag 11, 194–217 (2010). https://doi.org/10.1057/jam.2010.13
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DOI: https://doi.org/10.1057/jam.2010.13