In terms of risk, a prior positive demand flow (+ve standard deviation) has more impact on liability risk in an out of equilibrium world, so that arguments that suggest that a statistic that fails to focus only on the downside is meaningless are incorrect.
Way back when the world was more enamoured than today about standard deviation I openly discussed its weakness in terms of managing liability risks. This was primarily to do with the fact that mean variance optimisers did not incorporate liabilities into the portfolio construction (optimisation process) and ignored relative and absolute valuation issues.
My criticism centred on the fact that the model assumed (implicitly) a general equilibrium and (explicitly) random independent price movements (itself a necessary characteristic of general equilibrium) which meant there was no need for a valuation risk input. The risk to the ability of a portfolio to meet liabilities is held in the uncertainty over future random independent price movements, and structure is a function of optimising the fundamental nature of assets via their combination to manage this uncertainty.
In a world where prices are to a material extent price dependent, valuations and time frames become important. Standard deviations ignored this and the risks that mispricing pose to the ability of assets and structure to meet liabilities as and when they arise. In other words liability risk was in the price and optimisation ignored this risk.
However, to say that a standard deviation is a meaningless dimension misses the point. Indeed, since standard deviation is is a reflection of how the price moves in reaction to point in time news this also means it reflects demand flows, which are key to valuation issues.
In terms of risk, a prior positive demand flow (+ve standard deviation) has more impact on risk in an out of equilibrium world, so that arguments that suggest that a statistic that fails to focus only on the downside is meaningless are incorrect. Note the following excerpt from a March 2012 blog sent to me by Ken Kivenko.
For one, standard deviation measures risk as dispersion around a mean value, therefore any value above the mean is risk, and carries exactly the same weight as a value below the mean (downside risk). I don’t personally know too many investors that actually believe that upside deviation is an important risk factor to consider.