This paper presents a framework for portfolio optimization that makes three departures from the traditional mean-variance approach. First, we optimize the portfolio over multiple horizons, reflecting the belief that long-term investors care about intertemporal gains and losses, as well as cumulative performance, rather than simply long-run performance (expressed as a terminal value at the end of the optimization period). Second, rather than approximate through variance, which includes upside performance too, we account for loss aversion by simulating more severe shock events than those captured in historical samples, as well as through a specification of investor utility that sharply penalizes loses beyond a specified threshold. Finally, our framework allows investors to express forward-looking expectations (or make Bayesian adjustments) around how future performance may differ from those observed in the past.
We demonstrate the value of the framework and how it could be implemented through a consideration of the problem faced by sovereign wealth funds with long-term investment horizons. While this implementation exercise is illustrative, we find that these adjustments – which more realistically capture the observed behaviour of sovereign wealth funds as long-term investors than the traditional mean-variance heuristic – result in meaningful shifts in optimal portfolio weights.