About half the actively managed U.S. stock mutual funds beat the market over the past 10 years, or so the headline goes. Does this mean index funds are dead and we should all go active? It depends on whom you ask.

The active fund managers have many reasons why active should outperform: "It's a stock picker's market" or "You need sector rotation to win" or "Buy and hold is dead." If you ask an academic or an unbiased analyst, however, he or she will say that the headlines do not tell the whole story. Active managers did not beat the market when performance was adjusted for risk.

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The market as measured by the S&P 500 has become the favorite benchmark for active managers over the past decade. This is because the S&P 500 was an easy target. Large cap U.S. stocks underperformed all other size deciles. In addition, at the beginning of the decade, the S&P 500 had a large position in tech stocks, while most mutual funds were not as tech heavy. So, while small stocks beat both large stocks and tech stocks last decade, the active managers basked in the glory of "beating the market." I suppose these managers deserve some recognition after their truly dismal performance in the 1990s. (For more insight, see Active Management: Is It Working For You?)

The swings back and forth between active managers performing OK and then performing poorly does not mean managers are smart and then become dumb; it means the methods for measuring performance need fixing. There shouldn't be these swings. I am happy to report that measurement analysis has changed since the days when everything was measured against the S&P 500. Mutual fund analysis has become more precise; and this is not good news for active managers.

Two companies now publish bi-annual mutual fund "style" analysis reports that do apples-to-apples style comparisons. The McGraw-Hill's (NYSE:MHP) S&P unit publishes the SPIVA, which compares active managers to appropriate S&P style benchmarks. Morningstar, Inc. (Nasdaq:MORN) publishes the Box Score, which compares active managers to their appropriate popular Morningstar Style Boxes. Both reports are interesting reads. Not surprisingly, both the SPIVA and the Box Score show that the average active manager has not kept pace with the appropriate indexes.

In every SPIVA and Box Score update, there appeared to be a few styles where active managers did better than their benchmarks, and that caught my interest. Ironically, active managers seemed to perform very well in styles that did poorly relative to all other styles and performed poorly in the styles that had the best returns. In other words, managers performed well when a style did poorly and vice versa.

This strange phenomenon has a name. It is called "Dunn's Law" after Steve Dunn, a friend and cohort of William Bernstein. Dunn's Law is as follows: "When an asset class does relatively well, an index fund in that class does even better." In 1999 Bernstein immortalized Dunn's Law in his insightful Efficient Frontier.

William Thatcher of Hammond Associates built on Dunn's Law and published an article titled "The Purity Hypothesis" in the Journal of Investing in the fall of 2009. Thatcher explained the reason why more active managers beat their benchmark in underperforming styles was because the benchmarks were pure plays on a style while active managers often selected at least some securities outside that style. This created better performance for the active funds.

Mutual fund analysts have started making adjustments for the 'impurities' to better measure active fund performance. By filtering out the impurities in active funds, a clearer picture emerges. For example, suppose a fund classified as large cap growth actually held a few mid cap value companies over the past decade, but not so many as to push the fund out of the large cap growth style category. This fund would have beaten the large-cap growth index over the past 10 years because large-cap growth was the worst performing style while mid-cap value performed very well. An adjustment to the fund's performance based on style impurity reveals that that fund actually did not beat the large-cap growth index.

You can learn more about the academic foundation for size and style impurity adjustments by reading the research of Eugene Fama and Ken French. They are pioneers in factor analysis and the creators of the three-factor model.

Morningstar's Box Score Report began publishing three-factor adjustments to active funds starting in 2009, and the results were eye-opening. After U.S. equity funds were adjusted for impurities relative to their benchmarks, the number of funds that beat the benchmark in poorly performing styles dropped considerably. For example, over the past decade, and before style adjustment, 89% of large-cap growth funds beat the Morningstar Large Cap Growth Index. However, after style adjustment, only 27% outperformed. That is a huge difference. To be fair, in the styles that performed well, the managers picked up points from the three-factor adjustment. For example, active managers in the mid-cap value style increased their standing from 19% beating the index to 56% doing so.

Three-factor analysis removes style impurities in active funds and smooths out the returns across all styles, ending in underperformance for active funds by about the fees they charge. The result should have been expected. Stanford emeritus professor and Noble Laureate William F. Sharpe wrote in 1991: "Properly measured, the average actively managed dollar must underperform the average passively managed dollar, net of costs. Empirical analyses that appear to refute this principle are guilty of improper measurement."

When active managers as a group make the headlines because they "beat the market," it is not a triumph of skill, it is an error in measurement. New methods that properly adjust for style bias show that, as a group, active management is still underperforming passive management in all categories and over nearly all time periods.

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