Volatility represents the tug of war between greed and fear, and it has been on the rise for months now. Even normally stable blue-chip stocks have been bouncing up and down, spooking investors along the way.

Do stocks with high historical volatility produce correspondingly higher returns as a reward for the extra risk? Frequently, the answer is no, says Pim van Vliet, a professor at Rotterdam’s Erasmus University. In his paper, The Volatility Effect: Lower risk without lower return, van Vliet examined the relationship between historical volatility and risk-adjusted return for stocks worldwide. His conclusion: equities investors regularly overpay for risky stocks.

Looking at large-cap stocks over the 20-year period ending in 2006, he found that on a risk-adjusted basis, the least volatile tenth of stocks worldwide outperformed the most volatile tenth by an average of 12% annually. Low-volatility stocks generally underperform the market during “up” months, but their underperformance during these positive months is considerably smaller than their outperformance during “down” months, he says. High-volatility stocks exhibit the opposite behaviour. This volatility effect is separate from, and comparable in magnitude to, the widely accepted size, value and momentum effects, van Vliet says.

The maximum peak-to-trough decline for the least volatile decile of stocks over the period he studied was 26%, compared with more than 38% for the overall market and more than 80% for the most volatile decile of stocks, according to his research.

Can explosive moves such as these be put to use? Definitely, says Mark Kritzman, CEO of Cambridge, Mass.-based Windham Capital Management LLC. He believes that the recent economic crisis in the U.S. and other markets has increased the volatility of many stocks. This, he says, means that conventional approaches to risk management may not be sufficient right now.

During periods of financial stress like these, advisors trying to navigate the efficient frontier using estimates of risk and return by asset class may need to vary their approach, depending on whether markets are in quiet or turbulent periods, he says.

Turbulence occurs when these two variables behave in ways that are significantly different from their historical patterns — which is certainly what we are seeing now.

Kritzman, in following up on his paper, Risk, Regimes and Over-confidence, proposes splitting historical returns into two subsamples, one associated with quiet periods and one with times of turbulence, and then computing risk measures and correlations that are specific to these regimes.

He uses statistical anomalies as a proxy for market turbulence, and characterizes a set of returns as noteworthy when either one or more of them is significantly above or below average or when they interact in an uncharacteristic fashion.

These statistically unusual returns tend to coincide with easily recognizable events, Kritzman says, such as the 1987 stock market crash and the Persian Gulf War.

Looking at these watersheds, Kritzman tried to determine whether volatility and correlation differ from the levels that prevail during quiet times. If, for example, correlations across a set of assets rise during turbulent periods, then, as a result, portfolios may be less diversified during periods when that diversification is most essential.

Looking at monthly returns of U.S. stocks, it is no surprise that October 1987 was the most turbulent month in the past, when the U.S. stock market dropped by more than 20% in a single day. The turbulence index peaked that month, which, until recently, marked the all-time high. Recently, however, daily turbulence scores for U.S. equities and global assets have spiked to multiples of their long-run averages, Kritzman says.

Is such turbulence predictable? Quite often, says Kritzman. For the most part, the market is positively correlated with itself, which means turbulence today is likely to be followed by turbulence tomorrow. IE