Why Trading is a Zero-Sum Game

From Investment Intelligencer

I write a series for Slate called "Bad Advice," in which I take common but poor investment advice and explain why it’s bad.  One of my consistent themes is that, in most cases, the more you trade, the worse you do.  The logic behind this is that, unlike investing, trading is a zero-sum game: every dollar "won" by one trader must be "lost" by another.  (When you throw in transaction costs, moreover, trading becomes a negative-sum game: most traders lose.)

One Slate reader argued that this logic was bogus, that trading is NOT a zero-sum game, because if you buy a stock at $5 and it goes to $10, the $5 you make does not come out of someone else’s pocket.  The reader is missing an important distinction, but the response is common, so here’s a longer explanation.

First, you have to draw a clear distinction between "investing" and "trading."  Every market participant defines these terms differently, but, for now, let us say that "investing" means holding a portfolio of stocks for an entire period (any period–a day, month, year, decade, or century).  "Trading," meanwhile, means switching stocks during the period with the aim of exceeding the mere "investment" return. (There is no other reason to trade.)

Investing in a diversified portfolio of stocks is usually a positive-sum game: stocks usually go up, and when they do, "investors" make money. The only way to exceed the "investment return," meanwhile, is to buy good stocks and sell bad ones.  If a trader does this well, he or she will exceed the market (or "investment") return.  Stocks have to be owned by someone, though–even bad stocks–and the trader who bought the bad stocks from the better trader will lag the investment return.  In a case in which there are only two traders, the winning trader will exceed the market return by exactly the amount that the losing trader lags it (before costs).

In an essay called "The Arithmetic of Active Management," professor William Sharpe explains the phenomenon this way: The gross return of all traders in a market must equal the market return.  If the market goes up 10%, in other words, the gross return of all traders must also be 10% (assuming they all remain fully invested and don’t keep some percentage of their portfolio in cash, which is another "market").

To apply this to the reader’s example above, let’s assume that the "investment return" of the stock in question is $5 (the move from $5 to $10).  Assuming the reader held the stock for the entire period, he or she would have made $5.  If instead of holding the stock for the entire period, however, the reader tried to exceed the "investment return" by trading the stock back and forth with another trader, the gross return of both traders would still equal $5.  Depending on the relative skill (or luck) of the traders, however, the return of each particular trader might be very different: One trader might make $3 while the other made $2.  Or one might make $5 while the other made $0.  Or one might make $10 while the other lost $5.

What the Slate reader is missing, in other words, is the distinction between "investing" and "trading."  In the U.S. stock market over the past century or so, the "investing return" has been about 10% a year.  The aggregate "trading" return, meanwhile, has been 10% less the costs of trading.  Because it is impossible for the aggregate "trading" return to exceed the "investing" return, every dollar that has been won by one U.S. stock trader has been lost by another.   

Posted by Henry Blodget on March 08, 2007

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