Is the stock market zero-sum?

Suppose I buy a share in Microsoft from you at $400. Microsoft do well, and it increases in value to $500. At that point, I don’t want to push my luck any further, and sell my share for $500. It just so happens thatyou are the buyer.

In this scenario I have made $100 by “playing the markets”. But you have lost $100: you received $400 and paid $500, and ended up holding the same share that you started with. In effect, I have taken $100 from you. (Thanks!)

That was a zero-sum transaction, because your loss exactly cancelled out my win.

My question: is the whole stock-market zero-sum?

27 responses to “Is the stock market zero-sum?

  1. No, because while you own the share you also receive dividends from the company. Otherwise it would be.

  2. Why are you buying shares in Microsoft?

  3. I know a young man with a grasp of economics, put the question.

  4. Also, I didn’t “buy $400” for $500. I could turn around and sell that item immediately for $500. It’s a victimless crime! :D

  5. Otherwise you could also argue that any market surrounding items which accrue in value (eg housing) are also zero-sum — unless that’s also where you’re going with this? I’m not arguing one way or another — just that it’s the same thing: supply and demand drives the price of both scenarios.

  6. John Mark Ockerbloom

    “My question: is the whole stock-market zero-sum?”

    I don’t think it is, assuming that the stock prices reflect real value. (They don’t always perfectly do so, but neither are they completely arbitrary prices in most cases. The dividends mentioned by Andrew Hickey above reflect one manifestation of that value, but I think the point still holds when a company is applying its profits to growth rather than to dividends.)

    In particular, if we assume that MS when I bought it at $500 really is worth more (due to productivity, profits, etc.) than it was when I sold it at $400, then I sold a less valuable asset to you at one time, and bought a more valuable asset from you later. Moreover, during the time you owned the share, I had $400 in cash to invest that I otherwise wouldn’t have had, which might made me more money than if I had simply held onto the share. (If I invested the $400 in something else that returned over 25% over that time period, for instance, then I came out ahead overall.)

    I’m hand-waving a bit here over what constitutes “real” value, but I think a market in stocks, which invest in companies that actually produce goods and services at a profit, is different from a market in, say, options, which are pretty much betting on what’s going to happen as opposed to infusing money into a productive operation. I’m comfortable calling option markets zero-sum (or negative sum from the option-holders’ point of view, once broker fees and other transaction costs are taken into account), while stock markets in productive economies are not. But an actual economic expert could probably explain this better.

  7. Otherwise you could also argue that any market surrounding items which accrue in value (eg housing) are also zero-sum — unless that’s also where you’re going with this?

    Believe it or not, I’m not going anywhere with it — or at least, I’m going wherever it takes me. I’m not asking the question as a rhetorical device to lead up to a point that I want to make, I genuinely want to know what the answer is.

  8. John (or do you prefer John Mark?),

    Thanks for that thought-provoking comment. I think that even if we leave out the complication of you investing the $400 in between the two transactions, you’ve put your finger on something I missed: that the share in Microsoft really is worth $100 at the end of the story than it was at the beginning. So you started with a share worth $400, plus $100 in cash; and finished with a share worth $500. You’re neither better or worse off. I still make my $100 profit. SO it looks like this has not been a zero-sum game for us after all.

    (Of course, the share might “really” be worth only $400, with a temporary spike in its price due to, I don’t know, a particularly exciting Windows 11 announcement or something. In that case, either you will indeed have turned out to come out of this whole thing a hundred dollars down on the deal, or you’ll dump the stock on some other poor sucker who will then have funded my $100 while you’ve come out of it even.)

  9. In some sense, every transaction is zero-sum: together, we both possess at the end what we possessed at the start. Say I buy a loaf of bread for a quid at the supermarket; we start and end owning a quid and a loaf of bread, in some combination. But, presumably, we are both happy we engaged in the transaction; in some sense, we must have both gained. We can model this abstractly with “utility functions”, or more concretely by looking at the overall profit the supermarket made over the the lifetime of the bread, and the fact I want to eat a sandwich. In the end, we model a net gain.

    The stock market is more abstract, but John Mark explained neatly some of the inputs to individuals’ utility functions we’d need to consider. Sure, you won this bet, but everyone involved traded voluntarily, so they must have felt personally better off after the transactions than before.

    Still, that’s only one layer of the onion here. It’s not very surprising that the game looks net-positive when we have only considered a simplified example with a myopic utility function.

  10. Okay, consider that you want to expand your small business. You obtain one million in investment from a venture capitalist. He gets half the new, larger company in exchange.

    Why does he invest? Because he’s hoping you will grow and go public. Suppose you do and the new market value of the company starts at twenty million. You take ten million of that as new investment. Your share is five million, the VC has five million worth, and the new public investors have ten million worth of shares.

    So each time someone invests, the company has capital to grow. If the company does grow, the value of the investment rises. The social benefit is a prosperous business and the private benefit is the rising value of the investments. Nothing so far is zero sum.

    You pay an occasional dividend or you reinvest profits in the company and promise that once it gets even bigger and more profitable you’ll pay dividends then. The dividends are what make the shares worth keeping, but the value is the payback for the initial investment.

    Now there’s a lot of effort being wasted in the market trading back and forth all the shares as your company prospers and faces setbacks. Probably lots of your shares are being traded at various prices all the time. The benefit is that a reasonable estimate of your future value is being maintained for pension funds and investors so they can make good decisions and a liquid market is maintained so that your investors can get cash out when they need it.

    There’s another benefit to all the activity of a public stock market, too. Sometimes even a big company needs investment capital. You could go to those markets and issue more stock. That doesn’t happen often, though. What does happen is that you can offer stock to employees and your top managers can be paid largely in stock. Your employees are being paid less cash and more stock so that they’ll be especially invested in the fortunes of the company. The company can afford more investment because the employees are taking less cash each which means the employees have become investors. In effect, your own employees are your new stockholders and new capital investors.

    So the supply of stock shares is not fixed — companies raise investment by issuing more and that is positive sum if the investment works. Each trade in the public market is zero sum but maintaining the market benefits investors and the company. The net result is that stock markets provide people with value worth paying for.

    Remember that just getting a loan is also possible. You don’t have to take equity (shares) investment. In fact, getting a loan is much cheaper because of extensive bank subsidies in the tax code. Here in the USA, the banks and other debt investors get roughly a 33% tax break over shares investors which is a lot of money. It’s similar in Britain. (No wonder the bankers are so rich.) Yet the benefits of equity in public markets mean that shares investing is still very popular so there must be a lot of value in the system for investors.

  11. cjp39 posits “In some sense, every transaction is zero-sum: together, we both possess at the end what we possessed at the start.”

    I don’t think so. There are plenty of processes that create value — for example, growing the wheat that the bread is made from. So if you consider farming as a game where someone invests in land, seed, tractors, etc., and eventually gets bread out of it, you’d hope that the sum is greater than zero.

  12. behiker57w, I think that all the non-zero-sumness you’re referring to follows directly from the growth of the entire market — is that right? In other words, if no-one traded any shares at all, the total growth would be the same. (Obviously it’s not that simple in practice, because the market would notice the odd trading patterns, and respond in some way that affected its growth, but let’s ignore that effect for now.)

  13. “There are plenty of processes that create value.”

    I was intending to unambiguously exclude these processes when I used the word “transaction”. Sorry for the confusion, Mike!

  14. How do you define “zero-sum”? To some extent, the fact that the stock sale happened at $500 indicates that not only do both parties expect an increase in their personal welfare from the sale, but that $500 is a better point for that exchange than is $450 or $550.

    The seller could have several motivations for selling the stock — he wants the cash for some other purpose, he thinks the stock is overvalued, he thinks there is a better investment out there, he wants to diversify his investments, or something else. The buyer usually has only one motivation: He thinks the stock (at the price being asked) will be worth more in the future than it is now.

    I would argue that only an unduly narrow definition of “zero-sum” (looking only at cash exchanges) would conclude the stock market is zero-sum. Beyond the subjective values and possibly-wrong expectations of the parties, the price they settle on communicates information to others, helping to form a consensus on what the stock is worth.

    Closely related to this zero-sum question is Arnold S. Kling on how economists cannot measure the value created by financial intermediaries.

  15. You have constructed an artificially simple model to tackle a very interesting but very complicated question about multi party stock markets. Such markets are not zero-sum, as explained, for example, in the book “The Theory of Gambling and Statistical Logic”, by Richard Epstein. But what they are, exactly, is extremely complicated and IMO (I am not an economist) not well understood. Interestingly, other markets, like those for options and futures, are thought to be ‘almost’ zero-sum. Alas, I’ve forgotten why that is the case.

  16. If you think about this from an accounting point of view, it has to be zero sum. Have you ever studied double entry bookkeeping? Every positive addition to an account has to be balanced by a negative subtraction from another account. The idea is that the books balance when the grand total is zero. So, if you sell an item from stock, the money goes into cash on hand while money flows out of stock on hand. At this level, you can set yourself up as the accountant for the whole world and expect that the final sum will be zero.
    If you look at that example, you wonder where the profit comes from. In this case I carried stock at expected sale value, so when the item was readied for sale and added to stock on hand, various other accounts were debited, for example, materials, available labor and so on. One of them would be or be linked to expected profit. If this awfully roundabout, blame the Florentines. Are you old enough to remember when two shillings were a florin? That was those Florentines.

  17. There are plenty of processes that create value — for example, growing the wheat that the bread is made from. So if you consider farming as a game where someone invests in land, seed, tractors, etc., and eventually gets bread out of it, you’d hope that the sum is greater than zero.

    No, this is not true.

    Or at least, it’s not always true.

    Specifically, there are no processes that always, unambiguously, create value. Because ‘value’ means demand, so if the global demand for something is already satisfied, then creating more of it adds no value to anybody, because it will just go to waste.

    Consider, for example, steel. There are plenty of processes involved in creating steel, from the extraction of the raw metals from ore, to the alloying. And if there is demand for steel, then at the end, what you have is worth more than what you had at the beginning: the process has added value.

    And the steel you have just made can do on to make bridges and buildings, and create even more value.

    But if there is already enough steel in the world to make all the buildings and bridges that people want to make, then your creating more it hasn’t created any value whatsoever. Worse, in fact: you have used energy that could have been used to make something that is needed, to instead increase a useless supply of something that is surplus to requirements. So the process of creating the steel has, in that circumstance, caused a net loss.

    And that in a nutshell is what your stock exchange point is missing: the idea that ‘value’ is a fixed commodity, that is added to raw materials in fixed amounts by processes. It’s called the ‘labour theory of value’, Marx was big on it, and it is utterly wrong.

    What something is worth, its value, demands on how many people want it, how much they want it, what alternatives there are, and indeed their personal circumstances at the time. The ‘value’ of something is not a quality of it, like its mass.

    To take your exact example: say at the time I sold may share to you it was just before payday so my liquid-cash reserves were low (everything else being tied up in high-yield investments with large penalties for early withdrawal) and I had a loan payment of $400 due that, if I paid it late, would have given rise to a $200 penalty charge. I sell the share to you, get $400, pay the bill. Then a week later I get paid and buy the share back for $500.

    Result? You have made $100 and I have saved $100.

    Doesn’t look so zero-sum now, does it? Looks, in fact, a lot like +$200 sum (plus whatever the interest was the person who lent me the loan made on my payment).

  18. Interesting stuff, X. It all seems right to me, but I think it contradicts the point I was aiming to make. I wasn’t arguing that all farming is always positive sum, but that the existence of positive-sum outcomes in farming contradicts the idea that perhaps all transactions are zero-sum.

    Meanwhile, in your final example, hasn’t the payday lender lost out on $200?

  19. the existence of positive-sum outcomes in farming contradicts the idea that perhaps all transactions are zero-sum.

    The side-point is that all (non-forced) transactions are positive-sum or the parties involved in the transaction wouldn’t make them.

    But the main point was that you are wrong about why they are positive-sum. It’s not because there is some process that ‘adds value’ to things, as if ‘value’ were a property of something, like, I don’t know, its melting point (still stuck on the steel example) and you could change that by putting it through a process like alloying.

    Transactions are positive-sum because value is not a property of the thing, it is a property of the person. If I am cold, then a warm coat has value to me, so I might buy one — swapping something which won’t keep me warm (money) for something which will. However if I am already toasty warm, the coat is of no value to me, and the money is worth more (because I could use it to buy some ice cream instead) so I keep the money.

    That’s the fundamental thing you seem to have misunderstood: you seem to think of value as an intrinsic property of the thing, so that, for example, a nice warm cost is in some way ‘worth’ $200.

    But value isn’t like that. There is not, contra Marx, some mysterious quality that resides in things called ‘value’. Marx thought that because commodities exchanged for each other at fixed rates — a pound of steel for a gramme of gold for ten gallons of milk, say — then there must be some quality they all share, intrinsic to them, that those things all possess in equal amounts, like how a tonne of steel and a tonne of feathers and a tonne of water all possess the same amount of the quality ‘mass’. But this is utter nonsense, as can be seen my, for example, how the price of a commodity can fall relative to others once a substitute becomes available, or once the market is flooded.

    Basically: you seem to think there is some inherent value in a loaf of bread. There isn’t. Any value a loaf of bread has depends entirely on who it has value to, and the circumstances in which the transaction takes place (in the middle of a famine, say, or in the middle of a bumper harvest).

    Meanwhile, in your final example, hasn’t the payday lender lost out on $200?

    You could see it like that; but on the other hand they have gained the amount of the $400 payment that was interest, as well as now having the amount that was capital back so they can lend it out to someone else. So they are better off than they were (if maybe not quite as much better off as they might have been).

  20. X, this is all really interesting. We seem to be verging on philosophy as much as economics. Nearly everything you say here makes sense to me — certainly the example of a warm coat having different value in different climates works. And yet the example we started with was one of financial transactions — specifically, the stock market. It seems clear to me that, however much the value of a warm coat may vary, the value of $100 is still $100. So perhaps what’s going on here is that the stock market really is exchanging value rather than things that have value — and that’s why it’s not really a market.

  21. We seem to be verging on philosophy as much as economics

    Well, my brother keeps telling me Marx is far more interesting as a philosopher of the German Romantic school than as an economist. Not sure I see it myself.

    It seems clear to me that, however much the value of a warm coat may vary, the value of $100 is still $100

    But it very much isn’t. For example, the value of $100 in ready money, to me, today, might be very different to the value of $100 to you today, or to me a year, or even a week, from now.

    For instance if I have no expenses coming up that might require me to spend that $100, then having it available and ready to use in my current account might be of no value to me — I would get more value from putting it in a high-interest account, which would mean I had no access to it for a year, but at the end of the year I’d get it back with interest.

    On the other hand if I might have to pay out $100 for something in the next week, then the value of having that $100 instantly on hand to spend might outweigh the value I could have got from the interest.

    So liquidity is one way in which money is not ‘just money’: a liquid asset, ie, one I can easily use to settle a bill, might in some circumstances be worth more to me, and in some less, than a non-liquid asset, even though both might nominally be priced at $100.

    Another way money is not just money is temporally: in an inflationary economy, $100 today is worth more than $100 tomorrow. So things that allow me to shift money about in time might be useful, and the stock market allows that. That, for instance, is what takes us back to my building on your example: the reason you say it was zero-sum is that, nominally, I ‘paid’ $500 and ‘got’ $400.

    But the reason it’s not zero-sum, and the reason I did it, was that today, that $100 was worth $200 to me (because it helped me avoid the penalty clause), whereas in the future it was worth less (worth less to me, that is: presumably it was worth more to you, which is why you sold the share then). So I ‘paid’ $100 in order to shift $400 from the future to now, and so save myself $200: a net gain of $100.

    See? Value is a circumstantial thing, not an intrinsic thing, and that applies just as much to the bits of paper, or electronic balances, we call ‘money’, as it does to everything else.

  22. So I ‘paid’ $100 in order to shift $400 from the future to now, and so save myself $200: a net gain of $100

    I mean, another way you could see the same transaction is that you loaned me the $400, charged me $100 interest, and I gave you the share as surety.

    Looked at it that way, which is a perfectly valid way to look at it, it doesn’t look so weird, does it? It looks like a perfectly normal loan arrangement.

    I think you’re getting confused by the involvement of the stock market, but really, that’s all that’s gone on: I’ve paid you $100 interest for a loan of $400, and once the loan is paid off we’re both back where we started.

  23. (What the stock market makes easier, is the fact that I don’t have to find a single person willing to make me the loan I need; as long as the market is liquid, I can sell the shares to one lot of people, and buy them back from another lot. This is obviously much more convenient all around, and takes out a lot of the transaction costs which might otherwise make getting the loan uneconomical (on either side), and is part of why economies with functioning stock markets work much better than those without, where every loan must be individually arranged.

    That’s part of why the Anglo-Dutch financial model conquered the world (both metaphorically and literally): it’s just so much more efficient. It’s also why the loss of liquidity in markets, as in 2008, is so scary and devastating a thought.)

  24. Really interesting insights, X, many thanks!

  25. “Basically: you seem to think there is some inherent value in a loaf of bread. There isn’t. Any value a loaf of bread has depends entirely on who it has value to, and the circumstances in which the transaction takes place (in the middle of a famine, say, or in the middle of a bumper harvest).”

    Only if the cost or benefit of those events is passed on to purchasers of bread, which needn’t happen. I agree that as a matter of practicality value is assigned by purchasers. But that’s a political and psychological process, not something physical and inviolable like the second law of thermodynamics, nor universally uniform.

    As the earlier poster pointed out, transactions sum to zero in terms of money unless they somehow involve money being created or destroyed. Their perceived value depends on the models the participants have, so the value of the transaction can appear different to each, as X says. However, I can’t see why there is not an actual (if inaccessible) value that can be assigned to a transaction, given sufficient knowledge of the state of the world, in terms of actual utility. It may not be directly accessible, but as with scientific knowledge it can be approached asymptotically or ignored, and the difference in approach matters a great deal.

  26. Currency is just a proxy that makes trading things easier. “The value of $100 is still $100” is a meaningless statement. If I’m the only person left in the world, what is the value of $100? If I’m visiting some tribe in the Amazon, what is the value of $100? The only “value” it has is as an expectation of being able to exchange it for something else.

    If I want a car, it is difficult for me to exchange anything I have directly for the car. I could perhaps offer the dealer 1,000 hours of labor, but how much use does a car dealer really have for 1,000 hours of labor from a computer engineer? With currency as a proxy, though, I can find someone (eg. a company) that actually wants 1,000 hours of labor from me, and instead of giving me a car in exchange they give me currency as a proxy for my labor, which I can then take to the dealer and exchange for the car, and the dealer can take that currency and exchange it for something he wants, etc.

    It’s a level of abstraction/indirection/whatever that allows us to efficiently figure out a way for me to exchange what I want to give up for something that I want to have, without needing to find a bunch of people to route the exchanges through in a way that satisfies a bunch of different parties. In other words, $100 doesn’t have value, it is the way (the unit, if you will) that the value of something else is measured.

    If I have a dirty kitchen and I value a clean kitchen at $80, I have several options (leave it as is, clean it myself, hire someone to clean it). If I estimate that it would take me 2 hours to clean, but I value 2 hours of my time at $50/hour, then it doesn’t make sense for me to clean it myself (I’d be worse off by $20). But if I can find someone who values their own time at $30/hour, and hire that person to clean my kitchen for $70, and I end up at least $10 better off than before (I paid $70 for something that I valued at $80 and which would have cost me $100) and they end up $10 better off than before (they got $70 for something they valued at $60). In that case we’ve evenly split the $20 of surplus that that trading generated (only $60 of time was consumed, but $80 of clean kitchen was produced), but of course the people I hire would try to get all $20 of the surplus by charging more if they knew what I valued a clean kitchen at, and I would try to get all $20 of the surplus by offering less if I knew what they valued their time at. Having better information about the other party’s value system, or having a monopoly, allows you to grab more of the surplus for yourself.

    When you buy stock in a company, you are basically buying N% of that company. You do it because you expect that having N% of the company in the future, plus the dividends the company will pay in the future, is worth more than the money (or really the other things you could buy with the money) you pay for the stock now. When you eventually sell the stock, you do so because you expect that N% of the company in the future, plus the dividends the company will pay in the future, is worth less than the value of having the money (or really the other things you could buy with the money) now.

    When you keep money instead of immediately spending it for something (eg. an investment that is expected or even guaranteed to grow in value), you are basically “spending” it on the flexibility to easily spend it on something in the future (or perhaps you’re just valuing laziness over the opportunity cost of not investing).

  27. Thanks, Jeshua, that all makes sense. I’d agree with almost of it, except that I’d rewrite the end of paragraph three to say “The only reason $100 has value is because it is the way (the unit, if you will) that the value of something else is measured.”

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