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Asset–liability modelling and pension schemes: the application of robust optimization to USS

2015; Taylor & Francis; Volume: 23; Issue: 4 Linguagem: Inglês

10.1080/1351847x.2015.1071714

1466-4364

Emmanouil Platanakis, Charles Sutcliffe,

Insurance, Mortality, Demography, Risk Management

AbstractThis paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme's projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.Keywords: robust optimizationpension schemeasset–liability modelSharpe ratioSharpe–TintBayes–SteinBlack–LittermanJEL Classification: G11G12G22G23 AcknowledgementsWe wish to thank Chris Godfrey (ICMA Centre) for help with the data, and John Board (ICMA Centre), Chris Brooks (ICMA Centre), John Doukas (Old Dominion University), Thomas Lejeune (HEC-University of Liege), Raphael Markellos (University of East Anglia), Ioannis Oikonomou (ICMA Centre), Edward Sun (KEDGE Business School), the referees of this journal and participants in the following conferences – International Conference of the Financial Engineering and Banking Society, Portuguese Financial Network Conference, 12th Annual International Conference on Finance and the Annual Workshop of the Dauphine–Amundi Chair – for their helpful comments on an earlier draft.Disclosure statementNo potential conflict of interest was reported by the authors.Notes1. We have used factors not asset classes because it is common practice in robust optimization (see for instance Goldfarb and Iyengar Citation2003; Ling and Xu Citation2012 and other studies). It reduces the number of parameters to be estimated by about 20% in comparison with the classical approaches (e.g. the Sharpe and Tint model) and by much more for Bayes–Stein and Black–Litterman; and there is some evidence that it helps in creating more stable portfolios. Finally, the use of factors plays a significant role in making the robust optimization problem computationally tractable (e.g. a second-order cone problem – SOCP) (see for instance Glasserman and Xu Citation2013; Goldfarb and Iyengar Citation2003; Kim, Kim, and Fabozzi Citation2014).2. For mathematical reasons the expected Sharpe ratio must be constrained to be strictly positive, and so the lower bound on expected returns of the asset–liability portfolio is set to 0.1%, rather than zero. This rules out asset allocations that are expected to worsen the scheme's funding position.3. Bessler, Opfer, and Wolff (forthcoming) show that Black–Litterman results are robust to the choice of reference portfolio.4. This is the mean of the range of values used by previous studies. Bessler, Opfer, and Wolff (forthcoming) show that Black–Litterman results are robust to the choice of c over the 0.025–1.00 range.5. We experimented with different values of δ and found it had little effect on the Black–Litterman performance, and so we followed Meucci (Citation2010) and set δ equal to one.6. This abstracts from the effects on returns of the low liquidity of pension liabilities and the inflation risk inherent in government bond yields, as these effects tend to cancel out.7. The robust optimization ALM model was solved using SeDuMi 1.03 within MATLAB (Sturm Citation1999), and this took 0.67 seconds for each out-of-sample period on a laptop computer with a 2.0 GHz processor, 4 GB of RAM and running Windows 7. The modified Sharpe and Tint model was solved using the fmincon function in MATLAB for constrained nonlinear optimization problems (interior point algorithm) and took less than a second, as did the Bayes–Stein and Black–Litterman models.8. In every case, robust optimization is also the superior technique when the Calmar ratio, Burke ratio and average drawdown performance measures are used (Eling and Schuhmacher Citation2007).