# Swedroe: Active Arguments Disproved

May 15, 2015

A reader asked me to comment on a recent Forbes article titled “Active Versus Passive Management: Which Is Better?” The author, contributor Peter Andersen, asks this question while observing that, in 2014, the vast majority of active fund managers underperformed the S&P 500 Index.

However, he also notes that there have been periods “where active management of large-cap equity funds stunningly outperformed simple indexing.”

Andersen, who is the chief investment officer at Congress Wealth Management, presents a graph in which he demonstrates “evidence” showing the percentage of active managers who outperformed the passive S&P 500 index investor each year. His graph shows various periods since 1989 when active managers outperform the S&P 500. I thought I’d share my response.

William Sharpe & Basic Math

We’ll begin by noting there are several problems with Andersen’s graph. It’s a good example of how investors can easily be misled by manipulation of the data. There are, however, further issues with the arguments he offers. The first is one of basic math.

In 1991, William Sharpe wrote a seminal paper, “The Arithmetic of Active Management.” Using simple arithmetic, he demonstrated that active management, in aggregate, must be a loser’s game. On average, active managers must underperform proper benchmarks.

Sharpe’s “proof” demonstrated that this holds true not only for the broad market, but also when the market is in a bull or bear phase. It also must hold true for subsectors of the market, such as small stocks or emerging market stocks. The reason is simple: All stocks must be owned by someone.

If one group of active investors outperforms because they overweighted the top-performing stocks, another group of active investors must have underperformed because they underweighted those very same stocks. In aggregate, on a pre-expense basis, active investors earn the same market rate of return as passive investors. But because they have higher expenses, they earn lower net returns, which are the only kind you get to spend.

Sharpe concluded: “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.” And that leads us to the next problem.

Dunn’s Law Of Style Purity

The second problem with Andersen’s position is related to what’s often referred to as Dunn’s law, or what we can call the law of “style purity.” Dunn’s law states that when an asset class does well, index funds will outperform active managers in that asset class. However, when an asset class does poorly, active managers have a greater chance to outperform their benchmark index.

The logic is simple. Index funds generally achieve the greatest exposure to the relevant risk factors responsible for the vast majority of the returns. Active fund managers, on the other hand, often style-drift. They lose exposure to the targeted asset class, whether it’s the winning or the losing performer.

In other words, when large-cap stocks are the leading asset class (as they were in 2014), index funds will likely outperform large-cap active managers. And we see results similar to those in 2014 in years like 1995 through 1998, when the S&P 500 outperformed the vast majority of active managers each year.

The reverse is also true. From 1977 through 1982, small-caps outperformed large-caps by about 16 percentage points per year. Except for one year during that period, at least 60 percent of active managers outperformed the S&P 500.

Again, the reason for this is simple. Active managers, even the active managers of large-cap mutual funds, tend to own smaller-cap stocks than those in the S&P 500. Thus, they held some of the “outperformers,” unlike in 2014, when they held some of the “underperformers.”