Michael Nairne. Financial Post · Jun. 9, 2011 | Last Updated: Jun. 12, 2011 11:02 AM ET

If your investment manager beat the market over the past three years, you may want this question answered before congratulations are in order: Was this outperformance due to serendipity or skill? Unfortunately, the answer is — it’s virtually impossible to tell.

Lurking behind any set of return numbers is the role of chance. The world of stocks is incredibly noisy. Prices change almost randomly in response to a constant stream of new information. In this environment, chance and not skill can explain superior stock picking.

Let me illustrate. If you had 1000 monkeys throwing darts at a stock page to form portfolios, at the end of the first year you would have a range of performance among your monkeys’ portfolios. The lucky monkeys would have outstanding numbers while the unlucky would have dismal results. Given the almost random movement of stock prices, you would expect approximately one-half to beat the market.

Now, repeat the exercise with the 500 outperforming monkeys. At the end of year two, you would expect to have 250 or so outperformers. Repeat the exercise in year three and you still expect to have 125 outperformers – about one in eight monkeys is a star stock picker.

Now, don’t get me wrong. I am not suggesting investment managers aren’t smart and capable. In fact, the investment business is filled with exceedingly bright and ferociously competitive people — it’s why I enjoy it so much. It is the sum total of all their research, analysis and insights that ultimately determines the prices of securities.

Chance aside, the market is difficult to beat because the intense competition among managers prices stocks efficiently, leaving mispriced opportunities the exception.

This begs the question then — how long a track record of outperformance is needed before one can have a high level of confidence that a manager is skillful as opposed to lucky? Statistically speaking, it depends on the amount of outperformance by the manager and its volatility. Because the “typically skillful” manager has only a modest and volatile pattern of outperformance, it usually takes about 17 to 25 years to separate skill from good luck.

Here is the real catch. By the time you know with any certainty that your manager is skillful, his or her outperformance may have attracted so many assets that there is a real question of whether he or she can deliver superior results going forward. As assets swell, the opportunity to fully capitalize on the mispriced stocks of small and mid-size companies declines.

Academics have studied the issue of luck versus skill among mutual fund managers. In one study of 3,156 U.S. fund managers from 1984 to 2006, professors Eugene Fama and Ken French found strong evidence of skill, but only for a small proportion of managers.

Management skill, however, cuts both ways; they found some managers are unskilled and deliver results worse than one would expect by chance as well as evidence of “true winners” who did deliver returns superior to those expected by chance.

Here is the final bit of bad news though. Once fees and expenses are deducted from the excess returns of “true winners,” the evidence of outperformance vanishes. Where skill exists, managers and not the investors appear to be the prime beneficiaries.

Many investors are tiring of the quest for skillful active managers in favour of indexed solutions. In the U.S. assets in low cost index mutual funds and exchange traded funds have exploded to over $2-trillion. Even in Canada, assets in exchange traded funds are now in excess of $45-billion.

Napoleon Bonaparte is reputed to have asked the question, “Is he lucky?” before promoting officers. Maybe, investors should be asking the same question about their managers.