There's nothing Standard about these Deviations

Reading most financial publications, we are quick to see that investment rates of return are usually compared with each other relative to the volatility of those returns.  This seems sensible, because if all we had to go by were rates of return, we would all be fully invested in products with high returns and, likely, high volatility.  Scaling returns based on a statistic that helps to normalize unlike investments is a fundamental element of modern portfolio theory, and a critical element to the ubiquitous Sharpe Ratio. 

Unfortunately, volatility is regularly defined as the standard deviation of the return distribution of an investment.  This is unfortunate because the well-known implications of the statistic (e.g. 95% of occurrences fall within 2 standard deviations) are only relevant to data that are normally distributed, while the vast majority of investment products are decidedly not.  Moreover, practically, standard deviation is only relevant to investors who are equally concerned with upside and downside volatility – one of these people, I have never met.

On the technical side, equities have historically offered a negatively skewed return distribution, meaning there are more profound moves to the downside, though more rare, and smaller, more consistent moves to the upside.  The Implication that the typical difference between an investment’s mean return and observed return is the same during periods of outperformance and underperformance is misleading, and complicates the responsibilities of managing client expectations. 

More importantly, from a practical standpoint, investors in aggregate are risk-averse.  This means that the utility they derive from a gain is lower than the utility they lose from a loss of equal magnitude.  More simply, losing a dollar hurts more than winning a dollar feels good.  So how can it be, then, that the vast majority of analysis of investment products focuses on standard deviation, rather than breaking out upside volatility and downside volatility.  Investors obviously seek to maximize returns, but they do so with an eye on intermittent losses, not deviations from the average.

One way that the alternative investment universe has led the way is by addressing upside and downside volatility separately, as well as looking at ‘maximum drawdown’, or the biggest percentage loss an investor would have suffered from peak-to-trough (e.g. in the period from 2007-2009, an investor in the S&P 500 would have had to endure a drawdown of 55.3%).  Furthermore, identifying investments with positively skewed return distributions (bigger right-tails than left-tails) is a great way to diversify and capitalize on upside volatility.

Risk-weighting investments by downside deviation will go a long way in narrowing the gap between client expectations and outcomes.  The implications of a standard deviation in normal distributions are not applicable to the investments we own, and they are not important to that subset of investors who worry more about losses than gains – everyone.


Dave Donnelly is the Founder and CEO of Strategic Alpha, a rebalancing service dedicated to helping financial advisors improve client outcomes.