Ask a person on the street (Main Street or Wall Street) and they will tell you a closer description of risk than the average quant. Why? Because we (and I will throw myself into the quant catergory) generally use normality (and hence symmmetry) for any number of solid reasons, to describing risk, somewhere deep inside we realize that there has to be a better risk measure.
In the FPA Journal--The Journal of Financial Planning-- Swisher and Kasten analyze this problem in their paper entitled Post-Modern Portfolio Theory. While I am not convinced they have the solution, their paper does offer important thoughts on the topic of risk and risk management. Undoubtedly a recommended read!
A few sneak peeks:
* "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."
* "Downside risk (DR) is a definition of risk derived from three sub-measures: downside frequency, mean downside deviation, and downside magnitude. Each of these measures is defined with reference to an investor-specific minimal acceptable return (MAR)."
* "Portfolios created using MVO and DRO are often similar and the differences in absolute risk and return values small—diversification works regardless of how you measure it. Yet DRO seems to avoid the known errors of MVO and provide a more reliable tool for choosing the "best" portfolio."
For the quants here today:
"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."*"Risk is the potential for a bad outcome. Losing money, underperforming, failing to meet financial goals—those are real-life human concerns. Yet this risk definition—potential for an undesirable outcome—is fuzzy. Hard to quantify mathematically. But just because a concept has no clear mathematical equivalent does not mean that we cannot create mathematical models to describe it."
* Possibly my favorite quote of the paper is the following:
"As Brian Rom and Kathleen Ferguson report: "It has long been recognized that investors do not view as risky those returns above the minimum they must earn in order to achieve their investment objectives. They believe that risk has to do with the bad outcomes...and that losses weigh more heavily than gains." Investors are worried about downside deviation, not upside deviation.Read the rest for yourself. You will be glad you did--do not shy away from it just because you fear math. The paper has the enviable quality of being both quantitative and readable!
Markowitz himself said that "downside semi-variance"would build better portfolios than standard deviation. But as Sharpe notes, "in light of the formidable computational problems...he bases his analysis on the variance and standard deviation." Markowitz did not have a Dell laptop with a 60 Gb hard drive and Microsoft Excel in 1959."
Swisher, Pete and Gregory W. Kasten. Post-Modern Portfolio Theory. FPA Journal, September 2005.
Interesting trivia: Kasten is an MD!