Growth Maximization and Downside Protection Using Power-Log Utility Functions for Optimizing Portfolios with Derivatives

The tremendous growth in derivative markets around the world and the high quality of information about these instruments that is widely available, offers us a new opportunity harness their unique return distribution characteristics for building portfolios that conform more closely to investor preferences than is possible with mean-variance analysis and portfolio insurance techniques for downside protection. This study shows how portfolio optimization with Power-Log utility functions can be used to optimize portfolios containing derivatives, to produce portfolios with high growth potential and built-in downside protection. It also compares this method of portfolio construction with portfolio insurance, which has been used for providing downside protection to portfolios.