It is very hard, if not impossible," he wrote in his study, "to justify active management for most individual, taxable investors, if their goal is to grow wealth." And he said that those who still insist on an actively managed fund are almost certainly "deluding themselves.

These results add up to perhaps the most important investment lesson of all that can be drawn from this week's market anniversaries: Predicting turns in the market is incredibly difficult to do consistently well. That means that, if your investment strategy going forward is dependent on your anticipating major market turning points, your chances of success are extremely low.

It is very hard, if not impossible," he wrote in his study, "to justify active management for most individual, taxable investors, if their goal is to grow wealth." And he said that those who still insist on an actively managed fund are almost certainly "deluding themselves.

Assuming that the future is like the past, you can outperform 80 percent of your fellow investors over the next several decades by investing in an index fund-and doing nothing else. But acquire the discipline to do something even better: become a long-term index fund investor.

Index funds are the only rational alternative for almost all mutual fund investors.