Stock Picking and the Zero-Sum Game

Most stock fund managers fail to outperform their benchmarks. This is a widely discussed and repeatedly corroborated phenomenon. There are studies showing abysmal rates of outperformance among active U.S. equity managers in recent years. Warren Buffett made a famous bet against hedge funds that looks better every day. The flow of funds from active to passive (index) investing is one of the most popular discussion topics in modern investing.

All this raises the question: is it even possible for actively managed funds, as a group, to outperform passive funds?

When index funds gained popularity in the ‘80s and ‘90s, many professional investors dismissed them, believing that any decent business school graduate could outperform the market. Now, some commentators dismiss outperformance as an impossible challenge, arguing that market “efficiency” has wiped out the possibility of achieving excess returns.

Amid this discussion, a well-worn maxim is the idea that stock picking—and therefore active management—is a zero-sum game. The idea holds that market participants, as a whole, cannot outperform the market, and therefore active participants, as a whole, cannot outperform passive participants. The zero-sum game concept is often touted as an argument for passive management or for the futility of active management.

By rephrasing an assertion from William Sharpe, we can define the zero-sum game concept of markets in the following way:

The Zero-Sum Game Rule of Markets: Before costs, for any distinct set of securities, the collective return of all active participants must equal the collective return of all passive participants.

This is simple enough logic. For a distinct set of securities, any excess return achieved by one active participant comes at the expense of another.

This logic can be misused in common discourse by suggesting that actively managed funds as a group cannot, by some immutable law of finance, outperform the market. Although there is ample evidence that most actively managed stock funds have performed poorly in recent years, the zero-sum game concept does not suffice as an explanation. It is theoretically possible for active funds, as a group, to outperform passive funds, as we will see below.

Actively-Held Stocks vs. Passively-Held Stocks: a True Zero-Sum Game 

Let’s imagine the universe of equity shares split into two buckets: passive and active. The passive bucket represents all shares held by those who can only hold stocks at the market weight. The active bucket represents all shares owned by those who can hold and trade shares at any other weight. The active participants determine the market weights of all equity shares, while the passive participants must accept the market weights. Combined, the two buckets represent all publically traded equity shares. For simplicity, we will exclude fees and assume that the passive investors can invest perfectly with zero tracking error. The two buckets look like this:

Given these assumptions, the passive bucket and active bucket will always have the same return. The returns of individual active participants may differ widely, but as a group, their stocks cannot outperform the stocks held by passive participants. This is a true zero-sum game.

But, as William Sharpe also points out, there are a number of ways that active equity funds could outperform the market.

Active Funds vs. Passively-Held Stocks 

Remember that the zero-sum game rule holds true for a distinct set of securities (i.e., the set of all stocks). But active equity funds are not bound by this set; they can choose to substitute some amount of cash, bonds, or other securities outside of the set held by the passive funds, as illustrated below:

In theory, one advantage held by active equity managers is that they have a broader investable universe than index funds. And because they can reach beyond the set of securities held by the market, they could collectively outperform it. In theory, they could hold more cash in falling markets and less cash during rising markets. They could short equity futures in falling markets or sell covered calls in flat markets. This is the crucial distinction: while the returns of active stocks must equal the returns of passive stocks, the returns of active funds do not necessarily equal the returns of passive funds.

Consider the following example in a hypothetical stock market. Imagine there is one passive fund, one active fund, and other active participants who trade stocks at a variety of weights. For the first half of the year, the stock market returns -5.00%. For the second half, the market returns +10.53%. To exclude the effect of stock-picking, imagine the active fund invests all of its stocks at market weights and only adjusts the size of its cash position.

For the full year, the return of the passive fund equals the market return. But imagine that the active fund held 15% in cash for the first half of the year and 1% in cash for the second half. Assuming cash returns 0%, the results are summarized below:

The active fund outperformed the passive fund simply by modifying its cash position. Because active funds can reach outside of stocks into a broader investable universe, the zero-sum game rule does not prevent them from outperforming the market.

Active Funds vs. Other Active Participants 

Of course, there is a second (and perhaps more obvious) source of potential outperformance. Excess returns for active funds could simply come at the expense of other active investors. Anyone else who trades stocks at non-market weights including individual investors, corporations, and employee stock-plan participants (the supposed “dumb” money) could underperform, effectively transferring excess returns to professional fund managers (“smart” money).


This exploration is simply a reminder that actively managed equity funds could, in theory, outperform the market, and that the zero-sum game rule does not prevent them from doing so. None of this is intended as an argument for, or against, active management.

The interesting thing is that most active funds don’t outperform the market. The reasons for this deserve further exploration. Structural causes of underperformance, along with thoughts on how to tackle them, will be the subject of future pieces.