Academics took on a similar liking to statistics, and when Markowitz first suggested a portfolio could be optimally diversified, finance professors across the land agreed risk should be measured by the volatility of returns. This, in turn, in the language of statistics, translates to variance or, more commonly, standard deviation.

But, while standard deviation became the foundation of portfolio optimization models, including asset allocation, its proper use depends on two facts that don't exist in the real world. First, returns are not normally distributed. Second, it's assumed return volatility remains constant over time, but real world data shows this is not the case.

Let's be charitable, however, and ignore these facts. Still, standard deviation proves inadequate. Why? Because it fails to address our original definition of risk – failure to prevent a downside loss. In the case of investing, this means failure to meet the objective.

Harking back again to WWII, albeit a fictionalized account of it, do you remember this scene from the movie "Catch 22″ – the story of a bomber squadron based off the coast of Italy? After each bombing run, the general would give an award for the crew with the tightest bombing pattern. A "tight" bombing pattern means one where the bombs hit in a straight line. Usually the line is jagged, reflecting a volatility or variance in the bombing pattern.

This volatility occurs because the plane is usually dodging flack while it's dropping its bombs. In the scene I'm referring to, the winning crew had a perfectly straight. They was great, except for one thing – the bombs fell in the ocean! They totally missed their target.

For those who prefer a non-militaristic analogy, here's a great (and entertaining) explanation using the game of darts. The truth of the matter is standard deviation does not address the true concern of 401(k) investors – their ability to meet their investment objective. Whether trying to determine an appropriate asset class or an appropriate mutual fund option within an asset class, too often 401(k) plan sponsors rely, in some way, on statistical models that fail to address the true concern of 401(k) investors.

Worse, with this dependence on stochastics, the entire concept of risk has moved away from its common sense origins. In fact, some fiduciaries assume they need to measure the risk-aversion of a beneficiary before selecting investment option. In reality, risk-aversion doesn't matter to the fiduciary. Let's say you're the trustee of an IRA for a 25-year who's extremely risk-averse. Should you abide by the beneficiary's risk aversion? No. As a trustee, you have to do what's best for the beneficiary, and for an 25 year-old, that means placing his IRA in equities, which, while displaying greater short term volatility, tend to yield higher returns over the long term.

But wait! Isn't the client always right? Maybe, but, as a fiduciary, in this case, the client isn't the 25 year-old of today, but the 59 ½ year-old of tomorrow. Whew! Who knew this whole fiduciary thing involved time travel!

Using this knowledge, 401(k) plan sponsors can help their employees in two ways. First, they can avoid falling for the false siren of risk as defined by the various statistics derived from Modern Portfolio Theory (i.e., basically, any term derived from the variance or standard deviation of returns).

Second, 401(k) plan sponsors can discourage employees from looking at their 401(k) plan assets too frequently. This advice only tangentially comes from incorrect definitions of risk, but connects directly to research in behavioral finance.