Optimal portfolio allocation for pension funds in the presence of background risk

We model the asset allocation decision of a defined benefit pension fund in the UK using a stochastic dynamic programming approach. Our model recognizes the fact that asset allocation decisions are made by trustees who are mandated to act in the best interests of beneficiaries not by sponsoring employers and that trustees face payoffs that are linked in an indirect way to the value of the underlying assets. This is because of the presence of pension insurance which may cover a portion of deficits in the event of a sponsor default and a sponsoring employer who may make good any shortfall in assets, and who may reclaim some pension surplus. Our model includes an allowance for uncertainty both of the future value of assets (because of uncertain investment returns) and liabilities (because of uncertainty in future longevity and in future interest rates). We find that we are able to substantially replicate observed DB pension asset allocations in the UK and conclude that institutional details in particular asymmetries in payoffs to pension trustees are crucial in understanding pension asset allocation. David Miles Morgan Stanley 25 Cabot Square Canary Wharf London, E14 4QA Phone: +44 20 7425-1820 [email protected] David McCarthy Tanaka Business School Imperial College South Kensington London, SW7 2AZ Phone: +44 20 7594-9130 [email protected] Acknowledgements: The authors would like to thank Francis Breedon, Andrea Buraschi, John Campbell, and participants at the Imperial College Finance Workshop, and the Warwick Conference on Pension Funds for comments and suggestions on the paper. All remaining errors are our own.