From the paper, “Illusions of Precision, Completeness and Control: A Case for Simple, Transparent Portfolios” by Bob Maynard,
The traditional mean-variance model treats all volatility equally; excess returns are as risky as poor returns. It also assumes that investment behavior will be similar for a gain and an equivalent loss. Such behavior clearly is not the case. The work of Daniel Kahneman and Amos Tversky shows that losses are at least twice as influential as gains when making an investment decision. Such work has helped spread awareness that assumptions about behavior at the heart of mean-variance models are, at best, incomplete. Some investors, however, remain unconvinced or ignore research results highlighting differences between investment theory and reality.
Whether full variance or semi-variance, models assume log-normal distributions, but actual returns are not normally distributed. Extreme events, like “fat tails,” can skew returns. Plus, the severity and frequency of extreme events can be greater than predicted. Actual monthly U.S. equity returns have been different than forecast by a traditional bell-shaped distribution. The diagram below, shows actual returns (gray line) have been milder and wilder than expectations (tan bars). Note the narrow, higher peak near the median and sharp, upward spikes at the tails.
Also, actual returns tended to have a higher frequency of modest returns, creating periods with a false sense of calm (with a false sense of confidence in skill). While the outliers or fat tail events were far less common, they did great short-term damage—both financially and psychologically. However, volatility fades over time. Exhibit below shows that annualized 5-year rolling stock returns were more consistent with expected returns.
In addition, because mean-variance models are linear, they do not account for discontinuous events. That is, there is no way for those models to adequately account for the long stretches of mild returns interrupted by bursts of dramatic swings in the market.