There are two extreme schools of thought when it comes to investing. On one side are the proponents of active investing, while on the other are the proponents of low-cost passive investing. In the middle lies a method that uses a bit of both, known as the core and explore approach.

Let's take a closer look at the debate between passive and active investing, and then examine the case for using some of each. Finally, I'll offer a new solution I call the core and casino approach.

Passive Vs. Active

Most often, fans of passive investing rely on the efficient market hypothesis (EMH). According to a strict view of the EMH, it's impossible to beat the market over long periods of time because all available information is already priced into it. Thus the investor is better off with the buy-and-hold approach of passive investing.

Critics of passive investing typically point out the track record of such investors as Warren Buffett. Statistically speaking, Buffett's results are more than random luck. But as a counterargument, allow me to point out one day in the stock market: April 1, 2008. Stephen Dubner noted on his Freakonomics website that the news for the day read something like this:

• "Celent: 200,000 U.S. Banking Jobs at Risk"
• "Manufacturing, Construction Sectors Weaken"
• "Ford, Toyota U.S. Sales Down in March"
• "Congress Has Big Questions for Big Oil"
• "UBS Writes Down $19 Billion"

The investors digested this new, bleak drumbeat of information and promptly caused the stock market to rise 3.6%. I guess they don't call it April Fool's Day for nothing. The Associated Press rationalized the market's rise as "optimism that the worst of the credit crisis has passed and that the economy is faring better than expected."

In truth, Dubner's headline explanation made more sense to me: "Stocks Surge, Reasons Unknown; May Be Nothing More Than the Random Fluctuation of a Complex System."

Active investors, on the other hand, argue that ongoing buying and selling is superior to the passive approach. With ongoing monitoring of market conditions and individual firms, investors can exploit the market by seizing profitable conditions. These proponents also argue that to settle for market returns is to settle for mediocrity.

And the Winner Is...

We all know that, over long periods, the track record of mutual funds versus the index they try to beat is rather dismal. While an award-winning paper in the Journal of Financial Planning entitled "Passive Investing: The Emperor Exposed" claimed that these studies were flawed, it was actually this study that was eventually retracted.

Irrespective of where you fall in the EMH debate, there is no debating what I call the Second Grader Hypothesis. That hypothesis says that 10 - 2 = 8, meaning that if the market earns 10%, and we pay 2% in fees and other costs, then the average dollar invested must earn 8%. And if the market loses 10% and we pay 2% in fees and costs, then the average dollar invested must lose 12%. It's that simple to prove that the average active investor can only match the market before fees and costs, and must underperform after those fees and costs. In other words, active investing is a zero-sum game before costs and a negative game after costs.

One final argument for active investing is that the professional investor can do better than the individual investor. Even with the zero-sum nature of the stock market, the professional investor can extract profits from the individual investor who consistently makes mistakes explained by behavioral finance. For example, individuals consistently chase performance by buying what's hot and selling what's not.

So perhaps separately managed accounts or other professionals do provide enough alpha to offset their fees. Right now, at least 80% of stock market ownership is managed by professionals, and this proportion is constantly growing. Thus, while it is possible that this argument was valid 20 years ago, it is virtually mathematically impossible now. Even if every individual is below average, the rest of the professionals cannot all be above average.

Finally, a recent study entitled "Assessing the Costs and Benefits of Brokers in the Mutual Fund Industry" showed that, as a whole, financial planners do no better in providing disciplined asset allocation strategies than individuals doing it themselves. This study, forthcoming in The Review of Financial Studies by Daniel Bergstresser and Peter Tufano of the Harvard Business School and Johan Chalmers of the University of Oregon, found "no evidence that, in aggregate, brokers provide superior asset allocation advice that helps their investors time the market." If financial planners aren't providing this discipline with mutual funds, there is no reason to believe we are doing it with separately managed accounts.