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The Zero Sum Game

The topic of the zero sum game came up recently in a forum discussion in which I was taking part. I thought the subject would be something worth posting on, so here goes.

The point about zero sum game is that there are position holders on both sides of the trade and that the gain on one side represents a loss on the other side. This is true of forex and futures and some other types of markets, but it is not true of a market like stocks and other actual assets.

In the stock market when you go long you are simply buying something, just as if you were buying some gold, or oil, or anything else where you are just acquiring something out of an inventory of supply. No one has to go short in order for you to go long. While it is true that stock is a liability on the books of the company that issues them, that liability does not rise or fall with stock price, and the company is not required to ever buy the stock back, so it’s not the same as being short the stock. Shorting stock means that you actually have to borrow the stock from someone who is long in order to sell them. You can’t just sell something you have no possession of as you can in other markets. That’s why stock trading is not considered zero sum. If you buy Google at $10 and it runs to $10,000 then it represents a growth in your assets, but not a growth in someone else’s liability.

The same is not the case in forex and futures. I’ll start with the latter and address the former more specifically in a second.

In futures, because you are exchanging agreements and not actual assets when doing the trade, in order for you to go long, there must be someone on the other side of the trade willing to go short. That is the definition of the futures contract – I agree to buy something from you at a certain price and you agree to sell to me. Yes, it is true that the original buyers and sellers can close out their positions by making offsetting trades, but it comes down to the fact that for each long position there is a matching short position. That means for each point of profit by one of them, the other must lose a point. That’s the definition of a zero sum game.

Now as to forex, the speculative market acts the same as the futures market. Yes, it is true that you can actually acquire physical currency, but that’s not what you’re doing when you trade spot forex. Technically, spot forex trading operates the same as futures, though on a very short duration basis. If you buy USD/JPY you are technically making an agreement to exchange JPY for USD in two business day’s time at an agreed upon price. Of course you won’t actually do that, just like most futures traders will never take or make delivery on the positions they run. That’s where the rollover comes in to forex trading. Your broker essentially offsets your open position, closing it out, and enters a new position – all done at the current market rate. In some brokers this is very clearly done, especially when you’re talking about interbank trading.

Most retail brokers don’t really work that way, though. Instead, when you buy USD/JPY you actually borrow JPY, convert it to USD and deposit the USD, with the guy on the other side of the trade doing the inverse. That’s where the interest rate differential comes in. Again, you have a situation where any gain you make is a loss for the other guy, and vice versa because you both have a requirement to repay the respective loans you have taken out. It’s not as if you could actually take the USD you bought and walk away.

One way or another, there is always someone with an opposite position to you matching your trade. If your broker cannot directly offset your position against another internal account, it will do so in the market.

That is why forex is a zero sum game, like futures.

By John

Author of The Essentials of Trading

4 replies on “The Zero Sum Game”

you stated : ” If you buy Google at $10 and it runs to $10,000 then it represents a growth in your assets, but not a growth in someone else’s liability”

But you failed to reach the conclusion of selling the stock at 10,000 and taking 10k out of the pot…thus resulting in a decrease in the pot size, which means that if all the investors want to cash out…the pot will be given to them minus the 10,000 dollars you took out..which means it IS a zero sum game because the last to get out gets what’s left over after you’ve taken the 10 k out.

It is a growth in YOUR asset, but a decrease in someone else’s ONLY if no other investor comes in to replenish that 10k you took out of the pot.

example: 10 thousand investors put in 1 dollar in the pot…thus the pot is $10,000….now, the stock is worth 2 dollars…so 10 thousand more investors put in 2 dollars each…putting in $20,000 in the pot…the pot is now worth $30,000 and you have a stock that’s worth 2 dollars. So you take your profit of 1 dollar..meaning you take out 2 dollars…doubling your investment…only you did not take out 1 dollar..you took out 2..meaning that dollar had to come out of somewhere..and it did…it came from the new investors buying the stock at 2 dollars…now unless new investors come in, the stock will be worth what it is..minus the 2 dollars you took out…therefore, one of the new investors has just lost 1 dollar.

But you failed to reach the conclusion of selling the stock at 10,000 and taking 10k out of the pot – thus resulting in a decrease in the pot size….

Cristian,

Think about what you’ve outlined here. If I sell the stock someone else must be buying it from me for that 10k. As such, there is no decrease in pot size, as you put it.

Using your example of 10,000 shareholders, how are the 10,000 new investors acquiring their shares? From whom are they buying? And to whom am I selling my share? The shares of a stock are fixed (excluding company issuance and buyback) so for one investor to sell his shares another must buy them and vice versa. That transaction only changes the value of the pot to the extent that it alter the price of the stock at that point (if it even does so).

John

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