Downside Risk Optimization with Random Targets and Portfolio Amplitude

Dr Jing Yao, Heriot-Watt University


In this paper, we rationalize using downside risk optimization subject to a random target in portfolio selection.  In context of normality, we derive analytical solutions to the downside risk optimization with respect to random targets and investigate how the random target affects  the  optimal  solutions.   In  doing  so,  we  propose  using  portfolio amplitude, as a new measure in literature, to characterize the investment strategy.  Particularly, we demonstrate the mechanism by which the  random  target  inputs  its  impact  into  the  system  and  alters  the optimal portfolio selection.  Our results underpin why investors prefer holding some specific assets in following random targets and provide explanations for some special investment strategies, such as constructing a stock portfolio following a bond index.  Numerical examples are presented to clarify our theoretical results.