Downside loss aversion: Winner or loser?

We study the asset allocation of a quadratic loss-averse (QLA) investor. First, we derive conditions under which the QLA problem is equivalent to the mean-variance (MV) and conditional value-at-risk (CVaR) problems. Then we solve analytically the two-asset problem of the QLA investor for one risk-free and one risky asset. We find that the optimal QLA investment in the risky asset is finite, strictly positive, and minimal with respect to the reference point for a value strictly larger than the risk-free rate. Finally, we implement the trading strategy of a QLA investor who reallocates her portfolio on a monthly basis using 13 EU and 13 US assets. Using risk-adjusted performance measures that do not target specific types of utility we find that QLA portfolios mostly outperform MV and CVaR portfolios; and that incorporating a conservative dynamic update of the QLA parameters, which is based on the historical patterns of bull and bear markets, improves the performance of QLA portfolios. Compared with linear loss-averse portfolios, QLA portfolios display significantly less risk but they also yield lower returns. (author's abstract)