Are there times you shouldn't be passive? (MoneyWatch) One of the more persistent investment myths is that while passive investing/indexing works well in efficient asset classes such as large U.S. stocks and government and investment grade bonds, active investing is the way to go in so-called "inefficient" markets, such as U.S. small stocks and emerging markets stocks. That's the argument made by a recent Motley Fool article: "Active managers and individual investors willing to conduct a deep-dive analysis have a great opportunity to outperform in less-efficient asset classes, like international, mid-cap, and small-cap equities. If you're a do-it-for-me investor, consider going with actively managed funds for these asset classes. If you've been reading my material for a while, you probably know that I'm a big proponent of William Sharpe's paper The Arithmetic of Active Management. At its simplest level, it states that, in aggregate, active funds and passive funds must earn the same gross returns. Once you add fees, passive funds must trump active funds, since active funds are more expensive. Vanguard founder John Bogle noted the same thing about costs in his Cost Matters Hypothesis. One could argue that Sharpe and Bogle are talking only theory, so let's take a look at real world results. We'll begin by looking at Standard & Poor's most recent active versus indices scorecard. In the supposedly inefficient asset class of small stocks, for the latest five-year period, 78 percent of actively managed small-cap mutual funds underperformed S&P's SmallCap 600 Index -- an even worse performance than the 65 percent of actively managed large-cap funds that underperformed the S&P 500 Index. It gets even worse. While the S&P 600 Growth Index returned 3.4 percent, the average active fund returned 0.6 percent, underperforming by 2.8 percent. While the S&P 600 Core Index returned 1.8 percent, the average actively managed fund lost 0.1 percent, underperforming by 1.9 percent. And while the S&P 600 Value Index returned 0.3 percent, the average actively managed fund lost 0.3 percent, underperforming by 0.6 percent. We'll now turn our attention to what many consider the least efficient market: emerging markets. Unfortunately, the data is even worse, as 84 percent of actively managed funds underperformed the S&P/IFCI Composite Index over the prior five years. While the benchmark index returned 0.2 percent, the average actively managed fund lost 1.9 percent, an underperformance of 2.1 percent. The Motley Fool article also stated that passive investing might be the way to go with investment-grade bonds -- the implication being that active would be the way to go in less efficient markets like high-yield bonds. Once again, the data says otherwise. For the latest five-year period, the Barclay's High Yield Index outperformed 95 percent of all active funds. My favorite example is the long-term performance of active and passive funds in the emerging markets. The emerging markets sector is supposedly the least efficient of asset classes. Thus, it should be easy for active managers to outperform. Using Morningstar's percentile ranking score, we'll take a look at both Vanguard's Emerging Markets Index Fund and the passively managed emerging market funds of Dimensional Fund Advisors. When considering the ranking, keep in mind that Morningstar's rankings aren't free of survivorship bias -- they don't include funds that no longer exist. Since it's the poorly performing managed funds that tend to disappear, the percentile rankings of surviving funds will be understated. Vanguard's Emerging Markets Index Fund (VEIEX) had a percentile ranking of 32 over the 15-year period ending February 27, 2013 -- meaning that just 31 percent of the actively managed funds survived the full period outperformed. The DFA Emerging Markets Fund (DFEMX) had a percentile ranking of 19 over the 15-year period ending Feb. 27. The DFA Emerging Markets Small Cap Fund (DEMSX) had a percentile ranking of 2 over the 10-year period ending Feb. 27. The DFA Emerging Markets Value Fund (DFEVX) had a percentile ranking of 3 over the 10-year period ending Feb. 27. There are two takeaways for you. The first is that perhaps the so-called inefficient markets of small stocks, high-yield bonds and emerging markets aren't so inefficient after all. The second is that even if they're inefficient, that doesn't mean that active management is likely to prove to be the winning strategy. In fact, instead of the Motley Fool stating that active management provided a great opportunity to outperform in less efficient asset classes, they should have said that active management in these asset classes is fraught with opportunity.