Downside risk in multiperiod tracking error models

The recent crisis made it evident that replicating the performance of a benchmark is not a sufficient goal to meet the expectations of usually risk‐averse investors. The manager should also consider that the investors are seeking downside protection when the benchmark performs poorly and thus they should integrate a form of downside risk control. We propose a multiperiod double tracking error portfolio model which combines these two goals and provides enough flexibility. In particular, the control of the downside risk is carried out through the presence of a floor benchmark with respect to which we can accept different levels of shortfall. The choice of a proper measure for downside risk leads to different problem formulations and investment strategies which can reflect different attitudes towards risk. The proposed model is tested through a set of out‐of‐sample rolling simulations in different market conditions.