The Stock Market Is A Zero-Sum Game

It seems to me that it should be intuitively obvious that the stock market is a zero-sum game, but I guess some people don't think so. Maybe they don't understand what a zero-sum game is. Or maybe they have some other reason for wanting to believe that the market magically creates wealth.

Professor Lawrence Harris is chairman of the Dept of Finance at the University of Southern California and Chief Economist of the Securities and Exchange Commission, so he knows more about the stock market than probably most brokers ever will. Unlike the brokers, Harris has no financial conflict of interest in the question.

His seminal paper "The Winners and Losers of the Zero-Sum Game" (now included as part of his book Trading and Exchanges) carefully nuances the zero-sum question. Considered alone, the market is a zero-sum game, but in a wider context certain types of traders derive non-monetary benefit (such as the thrill of gambling, or the risk management due to time-shifting funds, or just the cost of learning) from their monetary losses, which makes it positive-sum for those people. My concern is only the cash-in/cash-out aspects of market trading, which Prof.Harris assumes to be zero-sum without spending any effort proving it. I guess it is too obvious to a person of his intellectual caliber. The "Winners and Losers" paper discusses the title topic in that context. He's rather brutal about who the losers are, but he admits that they are necessary for the market to function efficiently, which seems to me a curious way to look at it.

For those with less financial sophistication than Prof.Harris, I offer the following analysis.

Zero Sum

A zero-sum game is any set of operations with two or more players, which when it is over, there are winners and losers, and the total points awarded to the winners exactly matches the total points the losers lost by.

The NASDAQ glossary defines the term thus:

Zero-Sum Game
  A situation in which one participant's gains result only from another participant's equivalent losses. The net change in total wealth among participants is zero; the wealth is just shifted from one to another.

Checkers is the simplest form of zero sum game, because there is exactly one winner and one loser, and the winner "won" (the only point is winning, not by how much), and the loser "lost" by exactly the same score. Or else it is a draw with no winner or loser.

Poker is another zero sum game. Some players come away from an evening at poker with more money than they went in, and for every dollar they won, some other player lost a dollar. Poker illustrates another important property of zero-sum games, namely that the sum of any number of zero-sum games is still a zero-sum game. Each poker hand is a zero-sum game with exactly one winner; everybody else lost, winner takes all. However, after the evening is over, you can add up every player's winnings and losses, and the net result is still a zero-sum game: some players won and other players lost, and the total of winnings and losses is zero. Exactly all the money that came to the game left the game.

There is another property of zero-sum games that the poker game illustrates, which is that the winnings and the losses are all there is to the game. It doesn't matter how much money any one player has in his bank account -- or even in his wallet on game night -- his winnings at the game came from some other player's losses (or his losses went to some other player's winnings.

There is a third property of zero-sum games that we can learn from poker games, which is that the bottom line is the bottom line. You can win some hands and lose some hands, but when the evening is over, the sum of your winnings and losses is your score for the evening. If one player starts early in the evening, but gets tired and goes home, and then some other player comes in later and plays until they turn the lights out, it's still a zero-sum game, with the total winnings of all the players exactly matched by the total losses. If the early quitter left $100 richer than he came, you can be sure that among the rest of the players there were losses adding up to $100. Maybe the latecomer lost it all, or maybe the players who stuck it out the whole evening lost some of it, but the total is still zero; no money was left on the table, and none magically came into the game from some other source than the players themselves.

A Ponzi scheme is another form of zero-sum game. Each player pays in a fixed amount, which is given to the player who recruited him. That new player then goes out and recruits more players, and thus profits from their buy-in payment. Every dollar that the early players take away from the scheme is paid into the scheme by some other player. Who are the losers? All the last people to enter the game, when there are no more people to recruit, they lost their entry fee. Their losses exactly match the profits of the early adopters. Social Security is an example of a Ponzi scheme, and people are starting to recognize that we are running out of players to ante up the premiums which pay out in benefits to the older people. Except that Social Security is not strictly a zero-sum game because Uncle Sam will come riding in on his white horse in 2040 and collect some other kind of taxes to pay out the outstanding benefits -- or maybe Uncle Sam won't come riding in, and the latecomers really will be losers. Most everybody younger than 50 sort of expects that.

Stock Market

The stock market is a zero-sum game like a Ponzi scheme. There is no Uncle Sam to come riding in and bail out the losers. Every dollar that some investor wins in a stock market investment, some other investor lost -- or will lose. The stock market is also a zero-sum game like an evening of poker. There are many hands (many listed companies), many opportunities for individual wins and losses, but the bottom line is the bottom line: every dollar of profit that any investor earns on the sale of stock was put into the market by another investor hoping to win. Maybe that investor won also, but sooner or later the sum adds up to zero. Like the poker hand, every dollar that goes in, comes immediately back out. Unlike poker, people can't tell if they are winning or losing until they cash out. Unlike poker, the hands overlap, so it's hard to see that each corporate stock is a single zero-sum game: when the company is finally delisted, every dollar earned in profit is matched by another dollar in losses. Except for brokerage fees, which are pure losses.


Strictly speaking, the stock brokerage fees make the sum non-zero (negative). However, the fees are quite small compared to the average transaction, and can be neglected. Furthermore, most of the people arguing that the stock market is not a zero-sum game want you to believe the sum is positive; brokerage fees actually make it worse than zero, not better. Unless you are the broker. The broker is like the house in a casino. The house always wins.

There is another form of leakage in the stocks game that, like the brokerage fees, is usually so small compared to the total trades (profits and losses) as to be negligible, and that is the liquidation value when the company is delisted. Many companies get bought out by other companies in a stock swap. When that happens, the stockholder's investment is still in play, but it's like interrupting a poker hand to merge two games: everything is still in play, but the chances of winning or losing changed.

Many -- probably most, if published figures are to be believed -- companies just go bankrupt and close their doors. The investors holding stock in those companies are the losers, the final round of Ponzi buy-ins who gave profit to the other players from their own losses.

Sometimes a company is delisted by going private. That is no different than a single investor buying up all the stock. That's exactly what it is: that player put in all the money that any other outstanding players profited from (if at all). The buyer then can attempt to liquidate the assets, or otherwise try to recover his investment, but it's off the board. The sum has already been zeroed.

The company going private is the exact opposite of the initial product offering (IPO), when a private company takes money out of the system that it did not put in. Somebody else put that money in. When a company goes private again, the final buyer puts in money that it never gets back out. These are both leaks in the game.

Virtually all stock transactions are neither IPO purchases nor buyouts. These normal trades are zero-sum.

There is another form of leakage that is strictly speaking not a part of the stock trading game, so it does not figure in whether it is a zero-sum game, and that is dividends. Dividends are not included in either the purchase or sale price of the stock, so they are essentially irrelevant to whether the sum is zero. However, whoever happens to be the owner of record on the day the dividends are announced gets paid. Like the other leaks in the system, dividends are miniscule compared to the vast majority of stock trades, so their impact on the profits and losses in the market is negligible. Most people are looking for capital gains profits, not dividends. Many companies pay no dividends at all. Stockholders accept that.


There are several false notions about whether the stock market is a zero-sum game or not. I searched for the best arguments against this point, but there really aren't any. Different commentators argue different (sometimes contradictory) versions of these three points. I got these from The Motley Fool (the "fool" part of his name is accurate, judging from his analysis), who presents them with the least fluff.

"Zero-sum requires a fixed sum." This is easily seen to be false in the poker game. The pot that the winner takes can be any size, from slightly more than the players' antes, up to the total wallet of some player plus comparable bets from all the other players still in the game. In a Ponzi scheme the total pot keeps growing until you run out of players.

Some people try to argue that the value of the stocks reflects the net worth of the underlying companies -- which is often correlated -- while ignoring the fact that none of that stock price ever gets back into (nor out of) the company's bottom line. Other commentators agree that there is no connection while still arguing that it is not a zero-sum game. The fact is, the company profitability may go up or down, but the stock is still sold for whatever the next investor is willing to pay for it. The company net worth may figure in the buyer's thinking, but the money comes out of the investor's pocket, not the corporate bank account.

"The stock market creates wealth." This is obviously false. Unlike Social Security, no dollar ever comes out of the market into an investor's pocket that didn't go into the market from another investor's pocket. The underlying companies whose stock is being traded can create wealth, but none of that wealth ever shows up in the stock market -- unless the company buys back its own stock and goes private. As I pointed out above, this is a rare event. All the other transactions just move money from one investor to another. No wealth is created nor destroyed in the process. Except brokerage fees.

"Total market capitalization increases." This may be true, but it has nothing to do with whether it is a zero-sum game or not. That's like saying poker is not a zero-sum game because as the evening wears on there are more tables in the saloon playing poker, and the total of all the pots on all the tables is increasing. True, the slice through one instant of time, across all corporate stocks listed in the market might have a market capitalization greater than the last time you looked, but each company is a zero-sum game, and the sum of many zero-sum games is still a zero-sum game. The size of the pot on the table during one hand is irrelevant to the question of whether the winnings of the winners equals the losses of the losers.


A PricewaterhouseCoopers analyst reports a 1986 to 2000 average of 113 public company bankruptcy filings (up to 200 in 2002), out of 17,000 publicly traded companies. This is about 1% per year, a pretty dismal survival rate in the long run.

Cornell Law School News Service noted that 15 large public companies (out of 300) filed bankruptcy in 1997. At 5% per year, the average lifespan to bankruptcy is 20 years. Since some companies survive much longer, that means many more must fail sooner to attain that average.

Tom Pittman
rev. 2007 February 17