Higher Moments in Postmodern Portfolio Asset Allocation

While modern portfolio theory (MPT) uses standard deviation as the measure of risk;PostModern Portfolio Theory (PMPT) develops the idea of risk further to only include that of downside-risk. Intuitively this makes sense;because investors are more worried about negative returns;and therefore;the deviation in negative returns is more important to investors. Since returns have been shown historically to not follow the normal distribution;with fatter tails and higher downside risk;the extension of the meanvariance model to incorporate mixed higher moments (i.e. coskewness and cokurtosis) in the allocation of assets has allowed investors to investigate downside risk of assets;particularly for assets that have a larger departure from normality. To evaluate negative risk;mixed higher moments (i.e. coskewness and cokurtosis) are used to optimize asset allocation. The optimization of asset allocation using higher moments is a complex problem which can be solved fairly easily through optimization software or algorithms. We use Quadratic Programming (QP) through R Optimization Infrastructure (ROI) to solve for the quadratic optimization of incorporating four moments into a asset allocation for a portfolio. Adding to the evidence of other studies;our results show that the optimization using higher moments results in drastically different weights for assets;particularly in a manner that minimizes risk. We compare the results between several optimization methods using lower and higher moments.