Is the Stock Market a Zero-Sum Game?

The Basics The initial way to view the stock market is as a zero-sum game. With any stock trade, one side wins, because it buys a security that increases in price, or because it sells one that declines. The other side loses, by the same amount. In aggregate, then, the stock market's collective trades amount to nothing at all.

However, this approach ignores costs. The two traders will lose the difference between the stock's bid and ask price, which accrues instead to the stock's market maker. (The trade will also generate a brokerage commission.) In addition, if the traders are professional investment managers, they will charge a fee for their services. In aggregate, then, the game does not sum to zero--it is negative because of expenses.

That might seem like common sense, but it was uncommon knowledge until fairly recently. In 1991, freshly minted Nobel laureate William Sharpe outlined the negative-sum case in "The Arithmetic of Active Management," in response to such flimsy claims as "Any graduate of a top business school should be able to beat an index fund through a full market cycle," or "The case for passive management rests only on complex and unrealistic theories of equilibrium in capital markets." (What?) The fruit was hanging low, and Sharpe plucked it.

The professor was careful to note that although all trades summed to zero, the subset of mutual fund trades might not. Perhaps, the average mutual fund manager enjoys above-average results because he is more skilled than other market participants. This counterargument was plausible when Sharpe published because institutional investors held fewer stock-market dollars than did individuals, and because many actively run funds had consistently strong records. It is implausible today, with institutions controlling three fourths of the U.S. stock market's assets.

Sharpe's article remains highly relevant. That the stock market is zero-sum overall, and negative-sum after expenses are paid, is a somewhat depressing but accurate defense of index investing. However, there are two additional, more optimistic, considerations.

An Open System One is that the stock market is not a closed system. As Lasse Heje Pedersen points out in the forthcoming "Sharpening the Arithmetic of Active Management," (Ph.D.s love puns), Sharpe's article assumes that the market's contents are fixed. No security enters, no security exits. In reality, of course, companies increase supply by issuing stock and withdraw supply through share repurchases, by buying other companies, or (sadly) by declaring bankruptcy.

In other words, the stock market has two players: 1) corporations, who reside outside the system; and 2) everybody else, who trade within the system. If the corporations are foolish, in aggregate, they will issue stock at a low price, when securities are undervalued, and they will retire stock when it is relatively costly. In such a case, that would make them negative-sum investors, with rest of the marketplace moving from zero-sum to positive-sum, even before expenses are considered.

I would be delighted to write that is what occurs, even if that report might further diminish my reputation with Morningstar's brass. However, from what I gather, corporations collectively are neither foolish nor bright. They, too, are neutral investors, which means that moving the analysis from one player (noncorporate investors, as assumed by Sharpe) to two players (noncorporate plus corporate) does not improve the math.

Perhaps it will sometime in the future. Admittedly, that is just a possibility. Nonetheless, at least in theory, active mutual fund managers could participate in a positive-sum market (before costs), if corporations were obliging. Whether the effect would large enough so that active managers could be "worth positive fees in aggregate," as Pedersen postulates, seems unlikely to me. But I cannot rule that out, either.

Winning Ugly The second path for making investing in the stock market a positive-sum game is personal, not public. It concerns individual decisions. While we cannot predict future market returns, either for single securities or for groups of securities, we know from both experience and logic that stocks with certain features are likely, over time, to record higher gains than the overall stock market. One way of describing these stocks is to say that they carry undesirable attributes, such that investors must be induced to own them by the promise of higher returns.

Another way is to view the matter in reverse, by stating that stocks that have attractive features will have lower returns, because of their popularity. That's how the discussion is framed in "Dimensions of Popularity," by Roger Ibbotson and Morningstar's Thomas Idzorek. Stocks that have pleasing characteristics, such as excellent liquidity, name-brand recognition, and the comforting stability of being a reliable growth company, will appeal to every investor. In contrast, not everybody will desire their unsightly siblings, which might make them bargains.

Ibbotson and Idzorek cite value stocks (that is, securities that trade at low price/earnings or price/sales multiples, generally because the company's business prospects are uncertain), securities that have low trading volume, and smaller companies as being areas of unloveliness. There are many other possibilities. For example, stocks that are not held by the major indexes might become somewhat orphaned, as might low-volatility issues (as performance-chasing investors seek racier fare).

None of these strategies are guarantees. They are amply supported by history and reasonably supported by theory. But that is as far as the matter goes; the investment odds can only be improved, not eliminated. In addition, cost remains critically important. Just as expenses turn zero-sum investments into negative-sum outcomes, so can they reverse the fortunes of positive-sum decisions. Costs go only in a single direction.

In summary, describing the U.S. stock market as zero-sum before costs, then negative-sum after costs, is a fine approximation of the truth. Investors who know no further than that understand enough to succeed. It is, however, not the complete truth. The full story is somewhat more complex.

Reality Bite In the early 1990s, during the height of the mutual fund mania, I switched dentists. My new practitioner asked what I did for living. Investment research, I replied. He became animated: What sort of research, and where? Sure enough, he was an enthusiastic Morningstar subscriber, buying our monthly floppy-disk program (I kid you not) and spending hours combing through the research.

I was reminded of this experience by a coworker, who overheard a woman at a holiday party exclaiming how she had just invested in a company that was booming because of bitcoin prices. How had she heard about the firm? Her cousin's dentist, of course.

Well, mutual funds didn't crash, even if they no longer are glamorous. Perhaps that will hold true for bitcoin prices as well.

John Rekenthaler has been researching the fund industry since 1988. He is now a columnist for Morningstar.com and a member of Morningstar's investment research department. John is quick to point out that while Morningstar typically agrees with the views of the Rekenthaler Report, his views are his own.