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"All truth passes through three stages. First it is ridiculed. second, it is violently opposed. Third, it is accepted as being self-evident."
-Arthur Schopenhauer
The perfect investment, as everyone knows, is positively skewed, leptokurtic, and has low semi-variance. But these moments about the mean of an investment's return probability distribution are at least partially incompatible since investment returns are non-Gaussian, and variance/semi-variance obviously loses its utility in non-mesokurtic (that is, non-Gaussian) skewed distributions. Which is exactly the point.
Just in case you're not sure what that first paragraph means, here is a rough translation: people like to make money, not lose it. Making above-average amounts of money frequently is better than a tiny chance at winning the lottery. And when an investment performs poorly, it's best if it doesn't perform too poorly or too often. The problem is that while we have an elegant mathematical model for describing the perfect investment-called modern portfolio theory (MPT)-that model is wrong. Not wrong in the sense that the overall theory is no good, just wrong in the specific sense that it produces inefficient (and sometimes silly') portfolios. And we've known it for decades.
The primary reason MPT produces inefficient portfolios (even though the whole point is supposedly the building of efficient portfolios) is simple: standard deviation is not risk. Risk is something else, and we need a better mathematical framework to describe it. The primary purpose of this paper is to describe that framework and suggest a use for it-the building of better portfolios through downside risk optimization (DRO). We define DRO as optimization of portfolio risk versus return using downside risk as the definition of risk instead of standard deviation. The secondary purpose of the paper is to give definition to the concept of post-modern portfolio theory (PMPT) and how we as financial planners can apply it on our clients' behalf.
Background: The Giants of Portfolio Theory
In 1959, Harry Markowitz, the "father of modern portfolio theory," published Portfolio Selection,' in which he proposed that investors expect to be compensated for taking additional risk, and that an infinite number of "efficient" portfolios exist along a curve defined by three variables: standard deviation, correlation coefficient, and return. The efficient-frontier curve consists of portfolios with the maximum return for...