Fund managers who actively pick stocks rather than passively follow an index of companies have long taken a beating. A long line of studies has shown that the majority of active mutual funds—weighed down by high charges and expenses— yield low returns relative to comparable passive funds. For instance, a study finds that in the past 23 years an aggregate portfolio of active equity mutual funds in the United States underperformed various benchmarks by about one percent a year. Most active fund managers who succeed in beating the market in one year tend to fail in the next, dashing investors' hopes that there is more to a manager's stellar performance than just good luck. Altogether, the evidence firmly suggests that for most investors it does not pay to seek the skills of an active manager.

Yet the active funds industry remains large, with investors choosing to put far more of their financial assets in active rather than passive funds. Despite the robust growth in index-style mutual funds, the Investment Company Institute notes that, at the end of 2008, about 87 percent of all assets in equity mutual funds were actively managed. Even institutional investors, who seem more inclined than retail investors to invest passively, put at least half of their US equity investments in active funds.

A number of explanations have been offered for this puzzling result, many of which suggest that investors are not very smart. Investors may be fooled by slick fund management firms that manipulate past performance numbers to make their funds look like winners, or investors may stubbornly believe that they know which active managers have real, sustained skills in stock picking.

But a recent study titled, "On the Size of the Active Management Industry," by Chicago Booth professor Lubos Pastor and Robert F. Stambaugh of the University of Pennsylvania, finds that the large size of the active management industry could result from sensible actions of smart investors. In particular, investors understand that a manager's ability to outperform passive funds increases as the active management industry becomes smaller and decreases as the industry grows. This inverse relationship between size and performance has prevented the industry from disappearing decades ago, as its poor record would have predicted.

Why the Active Management Industry Is Large

What is unique about Pastor and Stambaugh's paper is that it assumes that the active management industry exhibits decreasing returns to scale; that is, as the industry grows, more money chases opportunities to outperform the market, which makes it harder for active managers to find bargain-priced stocks for their clients. If the industry shrinks, on the other hand, then less competition among the remaining managers gives them a better chance of finding mispriced stocks and offering clients higher returns.

This view implies that the industry's alpha, which is the expected return from investing in active funds in excess of the return on benchmark index funds, is not constant. Instead, alpha decreases as the active management industry grows and increases as the industry shrinks. The inverse relationship between industry size and alpha, say Pastor and Stambaugh, is the key to understanding the immense popularity of active management.

Investors think about alpha when deciding how much money to invest in active funds. They do not know what alpha exactly is, but they can learn about it by observing the returns of active fund managers. If these returns turn out to be disappointing, for instance, then investors update their views about alpha downward and reduce their investment in active funds.

However, they will not pull out all of their money. The belief that future returns are inversely related to the size of the industry cushions the fall in the share of financial assets that goes into active funds. Rational investors know that if other people withdraw their money, too, then it will be easier for active managers who represent the remaining investors to find good deals and generate higher returns. Because a reduction in the size of this industry implies a higher alpha, investors will take out some of their money but keep a substantial amount invested in active funds to take advantage of higher expected returns. If all investors think the same way, then it is easy to see how the industry may gradually become smaller over time but still remain a formidable presence.

In fact, the authors find that the share of active funds in total financial assets can exceed 70 percent even if the industry's alpha is significantly negative. Given the observed history of active mutual fund returns, the smart investor's allocation to active funds drops very slowly over time, from about 90 percent in 1962 to 70 percent in 2006. This striking result shows that, although the active management industry should be smaller—due to its weak past performance—it can still remain large.

Investors would have withdrawn more money from active funds had they believed that the size of the industry had no impact on alpha. Under this more traditional assumption of constant returns to scale, the authors find that the active industry's poor record would have led to its quick demise, disappearing altogether in 1969.

Rational but Slow

Although investors know that future returns tend to rise and fall with the size of the active management industry, they do not know the exact correlation between these two variables. This is because the industry's size varies little from one period to the next. "The size of the industry doesn't fluctuate wildly, and when a variable changes slowly, it's very hard for investors to figure out its impact on alpha," says Pastor.

Investors learn slowly about the precise relationship between industry size and returns, and that uncertainty affects their decision regarding how much of their financial assets will go into active funds. For instance, if investors see that the actual return on active funds is lower than expected, they will reduce their active fund allocation; however, because investors do not know exactly how their actions and those of other investors will affect alpha, they will be reluctant to make large changes. Investors will proceed more cautiously by not taking as much money out of active funds as they would if they fully understood the correlation between industry size and return. As a result, the active management industry becomes smaller but not by very much.

Small changes in the size of the active management industry, in turn, make learning about decreasing returns to scale more difficult than if investors made large changes to their active funds allocations. The result is a vicious cycle—investors tweak their allocations to active funds slowly because they are uncertain about how steep returns to scale are, but they learn about the returns to scale slowly because the industry hardly changes in size.

The result is an active funds industry that is smaller over time, but remains enormous even after many years of underperformance. "Of course, investors are not perfectly rational," Pastor says. "But even if they were, they would still find it optimal to keep a chunk of their money in active funds."

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