# Is making alpha zero sum?

I know that the stock market isn't zero sum but I was wondering if alpha is. If I beat the market by \$200 in returns doesn't that mean that someone lagged the market by \$200 in returns?

Suppose the market is simplified into \$1000 which returns 10% overall. At the end of the year, the market is at \$1100 total. If I turned my \$300 into \$400 that means that the other \$700 initially didn't have any gains and had negative alpha.

Is alpha zero sum in terms of dollars (I know its not in terms of %). Thanks.

• I think yo uare using the "coinfusing" term "alpha" basically in the wrong way. Note that the question "is the stock market a zero sum game" is almost unanswerable. Nobody really knows what money is (what is it? nobody knows), and issues around the growth of money supply, credit money, etc, make this a hugely complex topic with no answers, only discussion. – Fattie Jul 9 '20 at 12:00

## 2 Answers

It depends on how you define alpha. Because benchmarks generally take some time to include newly issued securities, it is theoretically possible for active managers in aggregate to beat their benchmarks. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2849071

However, you are correct that for every \$1 an investor is overweight a security relative to a float weighted portfolio, other investor(s) are underweight \$1. This argument was made by Sharpe. https://web.stanford.edu/~wfsharpe/art/active/active.htm

You mentioned beating the market by \$200 in returns. If you cash out then that \$200 gain comes from someone else (or whatever your profit is based on your cost basis).

OTOH, if you have a paper gain in account value, that's not actual money. For example, a stock IPOs at \$20. When it opens for trading, the first trade is \$25. No one makes \$5 of real money until they sell their stock, at which time there's that pesky transfer of money again. This is no different than one realtor telling you that you house is worth \$450k and another telling you that it's worth \$500k. It's only really worth what someone pays you for it.

Alpha measures the amount that an investment has returned when compared to a benchmark. AFAIC, this has nothing to do with zero sum. You asked:

If I beat the market by \$200 in returns doesn't that mean that someone lagged the market by \$200 in returns?

That would be true only if someone else was short exactly what you were long.