How Risk is Measured

When I think about risk I think about the chance I'll lose money. This is how most people think about it and this being the case, why do so many investment texts teach standard deviation as the primary measurement of risk? Standard deviation incorporates both upside and downside variation and most people would agree they have no problem with an above average return or a slightly below average return given the average is positive. What we hate to do is lose money, i.e. negative return. This brings up two points: should the average be used in the calculation of standard deviation or some other benchmark (I might would suggest zero, the S&P or NASDAQ or some other minimum hurdle rate) rather than the average, which is used in standard deviation.

Secondly, does incorporating the full spectrum of deviation (positive and negative) into the calculation make as much sense as only incorporating the variation below your benchmark or hurdle? Since investors are typically more concerned about losing money, it makes sense to separate the negative and positive deviation. This calculation is referred to as semi-deviation (upside and/or downside).

Using a benchmark or minimum hurdle instead of the average in the deviation calculation makes more sense because you are then framing the deviation around the return "tipping point" you actually care about. Calculating the semi-deviations instead of the general standard deviation makes more sense because you then understand which way your deviation is coming from, upside which most people are happy with or downside which is the real deviation people are trying to avoid.