See also:In Mel Brooks's classic 1974 comedy, Young Frankenstein, the grandson of the original Dr Frankenstein (Gene Wilder) dispatches his faithful assistant Igor (brilliantly played by Marty Feldman) to steal a brain for his creation from a nearby laboratory. In his usual fashion Igor bungles it and brings back the wrong brain. When it becomes apparent that all is not well with the monster, Dr Frankenstein confronts Igor and asks whose brain he has just installed. Igor's response "Aby..something...Aby-normal."
The parallel to finance is that the assumption of normality is deeply ingrained in classical finance and in particular in the application of Modern Portfolio Theory (MPT) to portfolio construction in the form of Mean Variance Optimisation (MVO). In this process the 'optimal' weights to hold in each security or asset in your portfolio are determined based on the Mean, average or expected return, and the variance or more commonly the variance squared or standard deviation of the overall portfolio. The linking of return to 'risk' through this ratio of reward to variability, later simplified by William Sharpe, was one of the key insights of Harry Markowitz's seminal 1953 paper on Portfolio Selection and was good enough to earn him his Phd. and eventually a Nobel Prize. Although Markowitz's theory does not require returns to be normally distributed ( Gaussian or Bell Shaped ), in practice most people still do make that assumption.
Why does this matter to you ?
The answer is simple. We now know that returns are not always Normally distributed about their means and that things can get if not completely abnormal at least a little skewed. Quite often returns are skewed either to the left (negative) or right (positive) of the center or mean and can also have excess Kurtosis or peakedness relative to the Normal distribution. Sometimes when they have both excess peakedness and left skew they are said to be 'leptokurtotic' which sounds like a form of leporosy but is in fact Greek for 'Thin Arches' and describes the more peaked nature of the distribution.
The more common recent term in Finance is Fat Tailed because the consequence of the excess peakedness and negative (left) skewness is that both the frequency (probability) and magnitude of large losses is higher than Normal under these circumstances. So in a nutshell ignoring these effects by assuming Normality can underestimate the potential for losses in your portfolio.
Similarly ignoring positive skewness can underestimate the potential for one or more assets to out-perform relative to the Normal distribution. A portfolio construction process that ignores these higher moments ( Skewness and Kurtosis ) will thus underweight or hold less in that asset than it arguably should. Fortunately there are now a number of methods to take higher moments or differently shaped return distributions into consideration, however they are far from widely used. The simplest of these methods is the so called Modified distribution method which utilises a formula developed by E.A.Cornish in the 1930's known as the Cornish Fisher expansion to take the impact of skewness and excess kurtosis into account.
When there is no skewness or excess kurtosis these terms simply cancel out in the formula which then gives the same result as the Normal method. Due to the relative computational complexity of these methods computers have only really become powerful enough to utilise them in the past decade or so. This is one reason for the slow uptake the other of course being institutional inertia. However there is no longer really any excuse for ignoring these methods many of which can now even be implemented in a spreadsheet.
The key question here I guess is, is it worth the extra effort ?...MORE
iShares Four Moment Optimal Portfolio
