Risk–Reward Optimisation for Long-Run Investors: an Empirical Analysis∗

This is a draft version and must not be quoted. Comments are very welcome. A common approach in portfolio selection is to characterise a portfolio of assets by a desired property, the ‘reward’, and something undesirable, the risk. These properties are often identified with mean and variance of returns, respectively, even though, given the non-Gaussian nature of financial time series, alternative specifications like partial and conditional moments, quantiles, and drawdowns seem theoretically more appro-priate. We analyse the empirical performance of portfolios selected by optimising risk– reward ratios constructed from such alternative functions. We find that in many cases these portfolios outperform our benchmark (minimum-variance), in particular when long-run returns are concerned. We also find, however, that all the strategies tested (including minimum-variance) are sensitive to relatively small changes in the data. The main theme throughout our analysis is that minimising risk, as opposed to maximising reward, leads to good out-of-sample performance. Adding a reward-function to the selection criterion usually improves a given strategy only marginally