Have Index Funds Become Too Popular?

 |  Includes: SPY, VTI
by: Larry Swedroe

It's the big lie. Active management wins in inefficient markets (such as small or emerging market stocks). Active management wins in bear markets. And now, thanks to Yahoo Finance's Aaron Task, we can add to that list active management wins because indexing has become too popular.

In a discussion on active versus passive investing Task noted that index funds may be outperforming the returns posted by active managers ... for now. "Ten years from today, active fund managers have a good shot at beating the indexes. The pendulum has swung way too far where everyone thinks all you have to do is index and you're going to do better. When everyone is on the same side as the boat there is a reversion to the mean." As is the case with most big lies, it's easy to expose them. Let's see why Task is wrong.

It's Not Theory, It's Simple Arithmetic

In 1991 William Sharpe wrote a 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 it also holds true whether it is a bull or bear market, and it also must hold true for subsectors of the market (e.g, small stocks or emerging market stocks). The reason is simple: All stocks must be owned by someone.

The Mathematics of Investing

A simple example will demonstrate conclusively that active investing, despite claims to the contrary, must, in aggregate, be a loser's game. The market is made up of only two types of investors, active and passive. For the purpose of this example, let's assume that 70 percent of investors are active and that 30 percent of investors are passive. (It doesn't matter what percentages are used, the outcome will be the same.) Let us assume that the market returns 15 percent per annum for the period in question. We know that on a pre-expense basis a passive strategy (like owning Vanguard's total stock market fund (NYSEARCA:VTI)) must earn 15 percent. What rate of return, before expenses, must the active managers have earned? The answer must also be 15 percent. The following equations show the math:

A=Total Stock Market, B=Active Investors, C=Passive Investors

A= B + C

X=Rate of return earned by active investors

15% (100%) = x% (70%) + 15% (30%)

X must equal 15%

If one active investor outperforms because he overweighted the top-performing stocks, another active investor must have underperformed by underweighting those very same stocks. The investor that outperformed had to buy those winning securities from someone. Since passive investors simply buy and hold, the stock must have been sold by another active investor. In aggregate, on a pre-expense basis, active investors earn the same market rate of return as do passive investors. Note that if we substituted the S&P 500 Index (or small-value stocks or REITs or emerging-market stocks) for the total stock market, we would come to exactly the same conclusion. It doesn't matter which asset class we are discussing, the math is exactly the same. The same thing is true for bull and bear markets. The math doesn't change if the bull is rampaging or the bear comes out of hibernation - active management must earn the same pre-expense gross return as passive management, regardless of asset class or market condition. However, because active managers also bear the burden of the greater costs they incur in the pursuit of outperformance (operating expenses, transactions costs, market impact costs, the drag of low returns on cash holdings, and for taxable accounts, taxes) their net returns - the only kind you get to spend - must, in aggregate be lower.

Task was right about one thing - indexing is becoming more and more popular, with more than $3 trillion investing in index funds. And what's more interesting is that Task himself noted the irrefutable math in the discussion. Yet, he then ignored the irrefutable math with his forecast that active managers would win in the future because of the trend to indexing.

With this trend to indexing, I'm often asked: What would happen if everyone indexed?

What if Everyone Indexed?

To begin to answer the question, it's important to understand that we're a long way from that happening with perhaps 40 percent of institutional assets and 15 percent of individual assets invested in passive strategies. In addition, there will always be some trading activity from the exercise of stock options, estates, mergers and acquisitions, etc. With that in mind let's address the issue of the likelihood of active managers either gaining or losing an advantage as the trend toward passive management marches on.

We begin by addressing the issue of information efficiency. The proponents of active management argue that with less active management activity there will be fewer professionals researching and recommending securities, making it easier to gain a competitive advantage. This is the same argument they currently make about those "inefficient" small-cap and emerging markets. Unfortunately, their underperformance against proper benchmarks has been just as great in these asset classes. The reason is that less efficient markets are characterized by lower trading volumes, resulting in less liquidity and greater trading costs. As more investors move to passive strategies it may have been logical to conclude that trading activity would decline. Yet, despite the shift to passive management by both individuals and institutions, trading volumes have not declined and in fact have set new records as the remaining active participants became become more active - think of all those high frequency traders. However, if as investors shifted to passive management trading activity fell, liquidity would decline and trading costs would rise. The increase in trading costs would raise the already substantial hurdle that active managers have to overcome. Based on the evidence we have from the "inefficient" small-cap and emerging markets, any information advantage gained by a lessening of competition would be offset by an increase in trading costs. Remember that the costs of implementing an active strategy must be small enough that market inefficiencies can be exploited, after expenses.

In other words, the math is irrefutable. Passive investing doesn't win because active managers are dumb. And as John Bogle points out with his Costs Matters Hypothesis, you don't need the markets to be efficient for passive investing to be the winning strategy. It's simple math. It's their greater costs that is the cause of their underperformance.

There is another interesting conclusion that can be drawn about the trend toward passive investing. Remember that for active managers to win, they must exploit the mistakes of others. It seems likely that those abandoning active management in favor of passive strategies are investors who have had poor experience with active investing. The reason this seems logical is that it doesn't seem likely that an individual would abandon a winning strategy? The only other logical explanation I can come up with is that an individual simply recognized that they were lucky. That conclusion would be inconsistent with behavioral studies that all show individuals tend to take credit for their success as skill based and attribute failures to bad luck. Thus, it seems logical to conclude that the remaining players are likely to be the ones with the most skill. Therefore we can conclude that as the "less skilled" investors abandon active strategies, the remaining competition, on average, is likely to get tougher and tougher. To take Aaron Task to task, "Who exactly are going to be the victims that the active managers are going to exploit in their quest for Alpha? As the trend to passive investing marches on there will be fewer and fewer victims to exploit, leaving the remaining active managers to trade against themselves. And that's a game that in aggregate they cannot win.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.