misconceptions about zero-sum games

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There are a lot of misconceptions about zero-sum games being bandied about.

A futures contract (commodities, wheat, currency, etc) is a zero-sum game. This means when a contract is opened one person takes the long side and another takes the short side. Of every contract! If the price goes up (or down) one person loses exactly as much as the other person gains. If the contract changes hands along the way, it makes no difference. All the gains on that contract exactly match all the losses. That’s what makes it “zero-sum”, when you add up all the gains and losses you get zero. And you are competing against professionals, experts, who have direct lines to the wheat exchanges and weather stations in the wheat growing areas etc. They will make money. That means you will lose money.

An options contract (put or call, etc) is a zero-sum game. This means when a contract is opened one person takes the long side and another takes the short side. If you sell a call, someone else is buying it. When it finally expires or is closed the whatever one side has gained the other side has lost, and vice versa. And again, you are competing against professionals. (That doesn’t mean you can’t use options for other purposes, like hedging or insurance, but don’t kid yourself that you are going to make money in the long term (unless you are an expert yourself)).

Playing roulette or betting on sports events are definitely not zero sum games. The house gets a cut and in the long run bettors, on average, lose money.

The stock market is not a zero-sum game. When the price of a stock goes up, everyone invested in the stock makes money. When it goes down, everyone invested in the stock loses money. BUT, on average, the stock market goes up, so, on average, people who invest in the stock market make money. Note how this is different than a futures contract, for instance. When you buy a stock, in general the person selling it isn’t short it, they are out of it. They no longer care if it goes up or down. If it goes up, they don’t lose money as they would if they had sold a futures contract that was going up. A stock is not zero sum because there is no balancing short side of every long contract.

Hope this helps.

Saul

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Saul, in case you are referring to my post, I was talking about markets in general, not the stock market in particular.

If a cook and a farmer meet and the first buys a dozen carrots for a dollar from the latter, is that a zero sum game? Absent commissions, fees and taxes it would be zero sum. Ten dollars passed from the cook to the farmer and a dozen carrots the other way around. I maintain that the only real measurable value is exchange value and therefore the dozen carrots were worth exactly a dollar. Zero sum game.

QED

Denny Schlesinger

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But, what if you extend the analogy so that the farmer buys carrot seeds from the store, plants and grows the carrots, and then sells the carrots to the cook? While the farmer may have some expenditures (and effort) related to growing the carrots, value has been added from the seed to the transaction with the cook.

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But, what if you extend the analogy so that the farmer buys carrot seeds from the store, plants and grows the carrots, and then sells the carrots to the cook?

I think it is instructive to take this one step further.

Suppose the farmer buys seeds from the store, but on the way home a robber stops him and demands his wallet, saying:

“Give me your wallet!”

Well, the farmer is a brawny guy, so he responds, “No way, José. You can have these stupid little seeds, but I am keeping my wallet.”

So the robber thinks it over, and says, “OK.”

Here, as in prior examples, we have an exchange, implicitly, seeds for wallet.

Now, suppose the robber goes home and shows his wife the seeds, saying, “See what I did honey? I brought us some seeds!”

“You brought home WHAT???”

“Uh. . . seeds”

“You blithering idiot, didn’t I tell you I needed cold hard cash for the new horizontal loom you have been promising me since I made the inexplicable and unfathomable decision to marry you?”

“Uh . . . Yes, my little petunia, but the farmer was pretty sturdy, and . . .”

“You go back to that farmer and you take his money!”

“OK, sweetness.”

So the robber runs real fast and catches up to the farmer, who has just lost all of his money playing canasta with a bunch of itinerant circus workers.

The robber says, “Avast there, chum!”

The farmer replies, “What?”

Robber: “Here, I will give you these seeds back, just give me all the money in your wallet.”

Farmer [thinking fast]: “OK, you have a deal, but on one condition. If my wife asks, you confirm that you did indeed rob me, right?”

Robber: “Sure, why not?”

So the farmer gives the robber his wallet, and returns home with the seeds and an acceptable explanation for having no cash, the robber returns home with an empty wallet but having completed his mission – he can hardly be blamed for finding an impecunious victim – and both wives – well, they always have tomorrow to re-launch their respective agendas.

Was this a zero sum game? I rest my case.*

Rich

AB

*I would appreciate it if someone would tell me what my case was; I sort of lost track . . . .

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If the farmer was able to get back the seeds and his name was Jack I would say that it wasn’t a zero sum game.

Andy
Who knows how that story ends.

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Zero sum game or not, in the stock market there is a buyer for ever seller, and vice versa.

The main difference with futures or options is that they expire at some point. The contract has a definitive start and end, and between those points in time one person gain will be another person’s loss on that instrument only. This is important because many use these instruments to hedge their own production or business needs, so to them, whatever part of the zero sum they capture is part of their bigger picture.

Stocks theoretically can go on forever, and any intrinsic value creation is really just a result of potential sellers refusing to sell until buyers will pay more. The open ended time nature is why it isn’t a zero sum game.

Hypothetical scenario - If you tracked a stock price from IPO at $1B to to a take private deal for cash at $3B, that would be a zero sum game. Net $2B of profits you may say, so it’s not a zero sum game, but the company sold the IPO shares, so they essentially missed out on those $2B of gains which were captured by all net investor activity before it went private.

However, it’s also likely that they needed the $1B from the IPO to grow the business and create value so that buyers and seller would agree that $B is a fair price for the business instead of $1B. So they company themselves is the one trying to leverage their expertise and capital to create the value.

Riding the waves of the stock movement can create or destroy value for your own portfolio Every time you sell, someone buys at that price and every time you buy, someone sells at that price.

So, is it a zero sum game? I guess the answer depends on the time frame you look at and how far you zoom out on the bigger picture of markets and all options people can do with their money.
Does it matter either way? Probably not. Just some fun circular thought experiment for Sunday morning coffee.
What should we do with this info? Don’t overthink it. Find good companies to watch. Buy the ones that are going up and sell the ones that are going down. Stack the deck in your favor by buying the stocks that will give people more reasons to be buyers than sellers, and be open to the fact that your thesis may be wrong and change your mind appropriately if that happens :slight_smile:

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If a cook and a farmer meet and the first buys a dozen carrots for a dollar from the latter, is that a zero sum game? Absent commissions, fees and taxes it would be zero sum. Ten dollars passed from the cook to the farmer and a dozen carrots the other way around. I maintain that the only real measurable value is exchange value and therefore the dozen carrots were worth exactly a dollar. Zero sum game.

It’s not a zero sum, because (like the stock market) there is “value added” all the time. The tiny episode you define may be “zero sum”, but then any finite transaction in the stock market is also zero sum.

What Saul has pointed out is that overall and over time the stock market rises (grows), therefore investing in stocks in not zero sum. Likewise you can look at the individual transaction of carrots and say “see? zero sum”, but that doesn’t make Saul’s essay wrong, because you have chosen to focus on the micro, where he is talking about the macro.

“Carrots” grow. They “add value” just by being, and growing bigger tomorrow. Think Carrot.corp (stock ticker: ORNG) and you’ll have a better analogy. I sell you a share, you buy a share: zero sum. Carrotcorp carrots grow bigger (size and number): not zero sum.

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I maintain that the only real measurable value is exchange value and therefore the dozen carrots were worth exactly a dollar. Zero sum game.

Call it what you like, but both parties entered into the transaction for purposes of acheiving something better.

The farmer valued a dollar more than he valued a dozen carrots. He left the exchange with a gain.

The cook valued the carrots more than he valued a dollar. He left the exchange with a gain.

This is free market capitalism. Not a zero sum game. Each party gained/profited through their voluntary exchange with the other.

Bob

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I wrote replies to several objections to my post but I did not and will not post them. On closer examination we are agreed in principle (markets create value) but differ in definitions.

If we take a market as a “blob” then, yes, the blob creates value. If you break down markets into their functional parts, then trades are zero sum: the cook got a dollar’s worth of carrots and the farmer got a dollar’s worth of money. That both valued the outcome as positive is a given as otherwise the trade would not have happened. Seen in that light the trade was a win-win transaction but we have no way of measuring either win without knowing the previous pre-trade state. If we could trace the previous trades (for the carrots and the money) then we would know the value of each win. We can extend this logic back to square one. To me one thing becomes clear, that value is created between trades and realized by the trade. Or put differently, the trades themselves are zero sum but the interval between them are not zero sum, that’s where value is created.

Famed market operator Jesse Livermore agrees!

Nine Surprising Things Jesse Livermore Said

1. “Money is made by sitting, not trading.”
2. “It takes time to make money.”
3. “It was never my thinking that made the big money for me, it always was sitting.”

http://thereformedbroker.com/2013/08/03/nine-surprising-thin…

In a practical sense this might be seen as hair splitting. I’m trying to discover why and how markets work. If you just join the dots in Newtonian physics style, you won’t find the answer. Markets don’t grind out value like a factory grinds out sausages. Markets grind out trades. Where then does value come? It’s an emergent property of markets. By being able to trade something less useful for something more useful at par, both sides have gained in value. But it wan’t the trade that created the value, the trade only realized the value. Here is my proof, suppose the cook and the farmer were to meet every five minutes for an hour, 12 times, they would trade only once. While the farmer would love to sell more carrots, the cook needs no more so there are no more trades. Demand disappeared. If it were the trade that created the value they would trade every time they met! Twelve dollars worth of carrots would have changed hands. It didn’t happen. The first trade realized the value. There was no value to realize in subsequent trades so they didn’t happen.

Denny Schlesinger

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Saul,
I was tempted to write a post similar to yours but then thought better of it. I anticipated that the outcome of such a post would most likely be a friendly argument wherein most folks with an opposing perspective would fail to understand what appears to be a very straight forward clarification.

There is a difference between an at-market trade and a one-on-one bet on a future outcome. Selling carrots for a dollar is inherently different from betting a dollar on the outcome of a coin toss.

I guess I’ll leave it at that.

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folks with an opposing perspective would fail to understand what appears to be a very straight forward clarification. There is a difference between an at-market trade and a one-on-one bet on a future outcome. Selling carrots for a dollar is inherently different from betting a dollar on the outcome of a coin toss.

Hi Brittlerock, I couldn’t say it clearer myself. thanks
Saul

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folks with an opposing perspective would fail to understand what appears to be a very straight forward clarification.

Some of us are more stupid than others and fail to understand, sorry about that.

Some of us don’t realize we should trust authority emitting clarification from on high. Sorry about that too.

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An options contract (put or call, etc) is a zero-sum game. This means when a contract is opened one person takes the long side and another takes the short side. If you sell a call, someone else is buying it. When it finally expires or is closed the whatever one side has gained the other side has lost, and vice versa. And again, you are competing against professionals. (That doesn’t mean you can’t use options for other purposes, like hedging or insurance, but don’t kid yourself that you are going to make money in the long term (unless you are an expert yourself)).

I disagree, just because a professional is on the other side of the trade, that does not mean that he is betting the opposite side. When you buy a call in the belief that the stock will go up, the other side not necessarily sells you the call in the belief that the stock will go down. Most likely, the professional on the other side will use the put-call parity and hedge their short call with a combination of puts and shares (or he may use other calls to become delta neutral).

In addition, if one were to buy a deep-in-the-money LEAP with the intention of rolling it over into the next LEAP close to expiration, that would be a variation of buying stocks, some of it partially on margin.

I am not saying options are safe or for everybody, but I disagree that you cannot make money in the long term (unless you are an expert yourself).

M

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Cap,
Some of us don’t realize we should trust authority emitting clarification from on high. Sorry about that too.

Do I detect some sarcasm? This is not a matter of “authority” form “on high”. It is a matter of definition. You are entitled to your own beliefs. You are entitled to your opinions. But you are not entitled to your own facts.

Saul and I were both simply trying (apparently quite unsuccessfully) to provide a clarification of the definition of “zero-sum game.” If you don’t like, or disagree with our explanation, I suggest you Google it. I’ll save you the trouble:

In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant’s gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s).

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4bears,
Yeah, you’re probably right about that, and Saul made a mistake by making that assertion. Whoever makes money trading options has nothing to do with whether or not it’s a zero-sum game.

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Cap,This is not a matter of “authority” form “on high”. It is a matter of definition…Saul and I were both simply trying (apparently quite unsuccessfully) to provide a clarification of the definition of “zero-sum game.” If you don’t like, or disagree with our explanation, I suggest you Google it. I’ll save you the trouble:

In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant’s gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s).

Hi Cap,
And here is the definition from my dictionary:
zero-sum (of a game or situation) - in which whatever is gained by one side is lost by the other.

It was just a question of clarifying a definition, not authority.
Saul

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It was just a question of clarifying a definition, not authority.
Saul

I didn’t have a problem with your post and I still don’t.

Denny Schlesinger

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Here is an essay that makes a convincing argument that the stock market is indeed a zero-sum game:

http://www.ittybittycomputers.com/Essays/0SumGame.htm

Interestingly, the author of this essay references the Motley Fool as a source of myths and misconceptions about whether the market is a zero sum game.

One quote from the article regarding a widely held myth:

“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.

Actually, as an investor, I don’t really care if it is zero-sum or not. I believe that it really is just a matter of timing. If an investor buys stocks when they are being undervalued by Mr. Market, and sells them when the market is overvaluing them he’ll do fine. Another way to say “Fear and Greed”.

DT

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“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.

While it is literally the case that a dollar coming out originates with someone paying a dollar to make the other side of the purchase, all of the other outstanding shares acquire the value based on the price of this transaction, whether or not they are immediately sold or not. If there is an IPO and some fraction of shares trade on opening, doubling price, all of those who did not sell doubled that portion of their wealth … not permanently, since it can fall again, but at that point in time the wealth is there. Since the long term pattern is for the total wealth in the market to increase, wealth is obviously being created and created for the investors, not the companies.

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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.

The author is very close to the truth but he fails to consider markets as complex systems.

The trading itself is a zero sum game or a negative sum game if you consider commissions, fees and taxes. But if you consider the market to be not just the trading but the valuation of all the tradable stocks, it is not a zero sum game at all because the value of stocks rises and falls all the time. All shares are valued at the last traded price (mark to market).

So far, so good, but does the market “magically create wealth?” If you believe in intrinsic value, then wealth cannot be created by the market but by the people working in the companies creating products and services. To believe that the market creates wealth you have to throw out the idea of intrinsic value and replace it with exchange value*. All shares automagically rise and fall in value based on the last share traded, the last share exchanging hands!

I explained how the magic works in a previous post but let me repeat. The trading itself does not create wealth, it’s a zero sum game. But because people can exchange something of less value (less utility) to them for something of more value to them, and both buyer and seller think they are doing so, the total utility of society rises. Wealth creation is an emergent property of free trade. Things are moved from where they are less useful to another place where they are more useful. A fish in the sea is less useful to me than one on my dinning plate. It’s the same fish, a bit older…

Denny Schlesinger

  • There is a link between exchange value and intrinsic value best described by Ben Graham with his voting machine, weighing machine metaphor. Exchange value loosely tracks intrinsic value.
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