Markowitz with regret

Providing a framework to integrate regret as an additional decision criterion in Markowitz’s model of portfolio selection, we propose two different views on regret: An investor might feel regret with respect to the ex-post best alternative either in terms of return or in terms of preference value. Under both views, regret can be captured by adjusting the vector of expected returns or alternatively by adjusting the return covariance matrix, retaining the tractability of the Markowitz model. The regret model, however, has very different implications for how asset characteristics affect optimal portfolios. While the impact of the skewness of an asset is strengthened, the impact of the variance shrinks. Moreover, we show for a variety of real portfolios that the effects of regret on optimal portfolio weights and the ex-ante return distribution are large.