•We investigate the performance of behavioural investment strategies.•We propose a new behavioural investment objective function.•We compare the behavioural portfolio with rational and naïve portfolios.•We use both EUT-based and CPT-based evaluation criteria. In this paper, we investigate the performance of behavioural portfolio strategies. We incorporate the short-term and long-term memory of the investor, thus recasting the behavioural portfolio choice process in a dynamic setting. We evaluate the out-of-sample performance of a behavioural investor in relation to both a naïve investor who invests in an equally weighted portfolio and a rational investor, who maximises expected mean-variance utility. We report a number of findings. First, from an expected utility perspective, neither the rational investor nor the CPT investor achieves a risk-adjusted return or certainty equivalent return that significantly outperforms that of the naïve investor. Second, from a CPT utility perspective, the behavioural investor outperforms both the rational and naïve investors. Third, the CPT investor typically displays highly concentrated, lottery-like asset allocations, low turnover and highly stable portfolio allocations. Fourth, the addition of the investor's memory into the portfolio choice process increases both diversification and turnover, leading to improved investment performance. Finally, by allocating more weight to positively skewed assets and increasing portfolio concentration, the probability weighting function has more impact than the utility function on the behavioural investor's performance. Our results are robust to the choice of reference return, estimation sample size, probability estimates, the probability weighting function and portfolio weight constraints.