Mean-variance analysis is standard practice in many business schools and financial planning programs. You know the drill: take a pool of randomly selected data points such as stock returns measured over a period of time, plot them on a graph, and you find they create the so-called normal distribution, a bell-shaped curve around the axis that marks their average. Among other things, it’s considered a model for assessing stock market risk over the long term.

Like a lot of other fondly-held beliefs, however, its value has come into question since the financial crash in the fall of 2008. As Kent Smetters, as associate professor of insurance and risk management at The Wharton School at the University of Pennsylvania puts it, no theory guarantees that the probability of an investment risk will be normally distributed. “The reason why we teach that in business school,” Smetters said wryly, “is primarily because it’s easier to teach.”

Smetters spoke this week at “Challenging the Traditional Advice Model,” a program in New York sponsored by Advisor Partners LLC. Mean-variance analysis is actually of limited value in assessing investment risk, he said, and people who thought otherwise got into trouble in 2008. It’s extreme events that drive investment results over time.

He offers, by way of example, a $100 investment in the S&P 500 in 1928 that, through the magic of compounding and reinvested returns, grows to nearly $113,000 in 2008. Removing just the two worst-performing years of that 80-year period would nearly triple the final value of the investment, while removing the two best performing years of the period would hammer the outcome by two-thirds. And it’s a rare investor who can stand pat amid such ascents and plunges over the long term. “This is why 2009 is called one of the most hated bull years ever, because when people got hit in 2008 they took risk off the table, and they missed the bull run of 2009,” Smetters said.

The fact that an event has a low probability of occurring doesn’t mean it can’t happen. The likelihood of the great Black Monday fall in October 1987 stood at 3 in 100,000. The market collapse in October 2008 had odds of just 7 in 10,000. “Either our model is not quite right, or we just got really, really, really unlucky during the past eight years,” Smetters said.

Diversifying portfolios can also be of limited use in reducing risk, he added. The fortunes of domestic corporations have become more closely aligned to economic conditions abroad as globalization advances. In 2008, the percentage of foreign revenue as a share of total revenue among companies in the S&P 500 stood at about 48 percent; 25 years ago, that figure was in the teens, Smetters said. The correlation between the S&P 500 and the MSCI’s Europe, Australia and Far East Index recently stood at 84.5 percent (Indexes with 100 percent correlation move exactly in the same direction.)

Diversification “is not providing nearly as much bang for the buck as it once did,” he said. “Should you diversify? Of course. That’s lesson one, there’s some value to diversification. But that alone is no longer a silver bullet.”

Is there another way? Smetters likes the concept advanced by Advisor Partners that investor goals ought to be matched to their assets. Building a household balance sheet is an important first step in determining how much risk the household can afford in its investments. Short-term goals call for more conservative investments, while long-term goals can absorb riskier bets. And be careful when clients tell you the amount of risk they can stomach, Smetters advised. Many investors, particularly men, often overstate their tolerance for the ups and downs of markets.