Foreword
There are some who think that stocks are gambling, that trading stocks is, essentially, a zero sum game. In some sense, they are right, but the truth is more nuanced than that.
How do we reconcile the idea that trading stocks are a zero sum game, with the very real fact that a non-trivial number of financial fiduciaries encourage their clients to invest in stocks?
Can you even “invest” in something that is a zero sum game?
As usual, a reminder that I am not a financial professional by training — I am a software engineer by training, and by trade. The following is based on my personal understanding, which is gained through self-study and working in finance for a few years.
If you find anything that you feel is incorrect, please feel free to leave a comment, and discuss your thoughts.
Flip flopping
Let’s say we have 2 buddies, Alex and Blair. They each have $1,000 as they begin their journey:
| Total Cash (dollars) | Total Assets (units) | Asset value (dollars) | Debt (dollars) | Net Worth (dollars) | |
| Alex | $1,000 | 0 | $0 | $0 | $1,000 |
| Blair | $1,000 | 0 | $0 | $0 | $1,000 |
Now, let’s say they have a brilliant idea(1) — they’ll create a brand new asset, let’s call it Kelpie, and they have a brilliant, fool-proof way to get rich, together. First, Alex starts with 100 Kelpies, conjured out of thin air, and they will value it at $1 each.
| Total Cash (dollars) | Total Assets (units) | Asset value (dollars) | Debt (dollars) | Net Worth (dollars) | |
| Alex | $1,000 | 100 | $100 | $0 | $1,100 |
| Blair | $1,000 | 0 | $0 | $0 | $1,000 |
Voila, our two friends, combined, are now $100 richer. But they have grander plans than that! Alex next sells 50 Kelpies to Blair at $1.10 each. The “market value” of each Kelpie is now $1.10.
| Total Cash (dollars) | Total Assets (units) | Asset value (dollars) | Debt (dollars) | Net Worth (dollars) | |
| Alex | $1,055 | 50 | $55 | $0 | $1,110 |
| Blair | $945 | 50 | $55 | $0 | $1,000 |
Now, our two friends are, combined, $10 richer — Blair is still worth $1,000, but Alex made another $10. Well, this is a mutually beneficial relationship, and so far, only Alex is making hay. To make it up to Blair, Blair now sells 10 Kelpies to Alex, at the princely price of $2 each.
| Total Cash (dollars) | Total Assets (units) | Asset value (dollars) | Debt (dollars) | Net Worth (dollars) | |
| Alex | $1,035 | 60 | $120 | $0 | $1,155 |
| Blair | $965 | 40 | $80 | $0 | $1,045 |
Notice how both Blair and Alex are now worth more than their initial $1,000. More interestingly, even though Alex bought Kelpies from Blair at a much higher price than when they sold it to Blair, Alex actually “made” $45! I think we have a winner here!
Alex and Blair continue trading between themselves, with Kelpies trading at higher and higher prices. Eventually, we hit this state, where Kelpies are $100 each:
| Total Cash (dollars) | Total Assets (units) | Asset value (dollars) | Debt (dollars) | Net Worth (dollars) | |
| Alex | $2,000 | 20 | $2,000 | $0 | $4,000 |
| Blair | $0 | 80 | $8,000 | $0 | $8,000 |
Now, we have a problem. Blair is supposed to buy Kelpies from Alex this round, but they are out of cash! That’s fine, Blair takes out a loan of $1,000 against their “assets” of $8,000 — that’s only a 12.5% loan-to-value (LTV), which is generally considered “safe” by most banks. Blair then use the newly acquired cash to buy more Kelpies from Alex at $200 each.
| Total Cash (dollars) | Total Assets (units) | Asset value (dollars) | Debt (dollars) | Net Worth (dollars) | |
| Alex | $3,000 | 15 | $3,000 | $0 | $6,000 |
| Blair | $0 | 85 | $17,000 | $1,000 | $16,000 |
Notice how Blair’s net worth doubled, despite taking out a loan, and spending cash to buy Kelpies.
Our two friends continues trading Kelpies between themselves, taking out loans if needed if one of them runs out of cash when it’s their turn to buy. By trading Kelpies back and forth, both of them managed to greatly improve upon their net worth. Their last trade has Kelpies valued at $1,000 each. Houston, we have liftoff!
| Total Cash (dollars) | Total Assets (units) | Asset value | Debt (dollars) | Net Worth (dollars) | |
| Alex | $10,000 | 40 | $40,000 | $5,000 | $45,000 |
| Blair | $2,000 | 60 | $60,000 | $5,000 | $57,000 |
Car shopping
At some point, Blair decides they want to buy a new car. And since they are rich now, only a fancy car will do — a fancy car that costs $50,000. It’s going to hit their net worth hard, but what the hell, you only live once! Besides, Blair has found the secret infinite money cheat to life!
Unfortunately, the car dealership won’t take Kelpies (they simply do not see the transformative nature of Kelpies), and they want cash instead. So Blair went to Alex, and asks (nicely) if Alex would buy some Kelpies from Blair at, say, $1,100 each, so that Blair can raise $50,000 for the new car. However, Alex does not have the cash, and is unwilling to take out such a huge loan.
That’s OK — they have on their hands a transformative asset, that is rising in price faster than inflation. Everybody trading this asset has agreed that it can only go higher, and will never sell at a lower price. So it seems only natural that they should spread this gospel to the world, and lift millions out of poverty!
Alex and Blair approach Cameron, their mutual friend, and fortunately, someone already rather wealthy. They persuaded Cameron to buy some Kelpies from Blair, at $1,500 each:
| Total Cash (dollars) | Total Assets (units) | Asset value | Debt (dollars) | Net Worth (dollars) | |
| Alex | $10,000 | 40 | $60,000 | $5,000 | $65,000 |
| Blair | $54,500 | 25 | $37,500 | $5,000 | $87,000 |
| Cameron | $0 | 35 | $52,500 | $0 | $52,500 |
Blair then takes $50,000 and buys the new car.
| | Total Cash (dollars) | Total Assets (units) | Asset value | Debt (dollars) | Net Worth (dollars) |
| Alex | $10,000 | 40 | $60,000 | $5,000 | $65,000 |
| Blair | $4,500 | 25 | $37,500 | $5,000 | $37,000 |
| Cameron | $0 | 35 | $52,500 | $0 | $52,500 |
Reality bites
To celebrate their new found wealth, the 3 friends decide to take a road trip in Blair’s fancy new car. Unfortunately, they got into an accident, and were all seriously injured. The medical bill came out to $12,000 for each of the friends.
No problem, they thought — all 3 friends are much richer than that, and can easily afford it.
The friends offered Kelpies to the hospital for their bills, but the hospital politely declined. As with the car dealership, the hospital simply did not have the foresight to see the transformative nature of Kelpies, and instead, demanded cash. Well, now we have a problem — our friends are asset rich, but cash poor.
Alex quickly realized that they really only need another $2,000 to cover the bills. So with deep regret, Alex offers to sell 2 of their Kelpies at the previous price of $1,500 to Blair. Alex was previously planning to sell only when Kelpies hit $3,000, so Blair is really getting a good deal here!
Blair looked at their holdings, and at the medical bill, and came up with another idea. How about, Blair sells Alex 8 of their Kelpies, at the unbelievably great deal of $1,200? This will give Blair enough cash to pay their bills, and still have $2,100 left over. And Alex got to buy Kelpies at the fantastic price of $1,200!
Cameron, too, looked at their holdings, and at the medical bill and came up with another even better idea. How about Cameron sells Alex 8 Kelpies for only $1,000 each ($200 cheaper than Blair!), and then another 4 Kelpies to Blair at the same price? That’ll give Cameron enough cash to pay the bill, and both Alex and Blair will get a GREAT DEAL!
This goes on for a while, until eventually, the friends realize, that between the 3 of them, there really is only enough cash to cover one person’s medical bills, and no amount of trading or discounting will change that fact. Also, collectively, they are now $10,000 in debt.
Stock vs flow
As alluded to in Investing vs Speculating, purely trading/speculating is a zero sum game. In our little story, the entire “market” only ever had the actual value that the friends themselves put in. Before Cameron joined the game, there was only ever $2,000 (net of debt), which was why despite their lofty “net worth”, Blair was not able to buy the car without the cash infusion from Cameron.
There never was the grandiose “value” that our friends made up in their minds, it was only ever “paper gains”, and our friends committed the sin of confusing stock with flow.
Flow – The transactions at the margin of the market
Stock – The totality of all assets in the market
Our friends thought that just because there was flow, and that the flow was consistently valuing Kelpies at a higher price, that, therefore, their stock of existing Kelpie was worth as much. This quickly breaks down, when the liquidity needs of the market participants exceeds the available flow in the market. And when that need for liquidity emerges, the phrase “prices are set at the margins” quickly became apparent.
Zero sum game?
Kelpie was just a analog for a stock, right? So, are stocks a zero sum game?
No, and no.
Kelpie is an analog for any asset that can be traded, not just stocks. This means, stocks, gold, bonds, houses, cars, bread, art, etc. Everything that can be traded. But no, that does not mean stocks (or any of the other assets listed) are zero sum games.
Remember that stocks represent fractional ownership of actual businesses. Assuming the business is performing well, it will generate profits. Even if the profits are not distributed to the shareholders, the profits exist somewhere. Unless there is fraud, that somewhere is generally “the books of the company”. This means that if Kelpie was a business, then the 3 friends could have just found another entity to buy the business from them. If the business is run well, and is profitable, it shouldn’t be hard to find some entity willing to pay for the business, although possibly at a discount — the 3 friends are desperately in need of liquidity, and thus have less leverage in making the deal with the buying entity.
In effect, a productive asset, like a stock (or bond) periodically injects the value of their production into the system, which means the entire system is a positive sum game.
For other assets, like cars and bread, which have intrinsic values (people want the car/bread, because both have attributes that are desirable), there is a natural floor to how low the prices of the assets will go. Yes, in a firesale, where the seller is desperate for liquidity, they may sell the asset for less than intrinsic value. But if the seller has enough time to shop around for buyers, they will likely be able to get fairly close to intrinsic value at least. This also means that if someone bought an asset with intrinsic value at a price higher than its intrinsic value, they stand a higher chance of losing money — unless they can find a greater fool to pay an even higher price, they will be forced to sell at intrinsic value, at a loss.
In effect, for non-productive assets, trading is basically a zero sum game — without the constant injection of value from production, the net of all trading will be $0. That said, assets with intrinsic value at least have a price floor. Assets with no intrinsic value, like our original Kelpie, will likely go to nothing eventually (technically, they revert to their intrinsic value of $0).
Productive assets at any price?
Let’s consider a stock that represents fractional ownership of a business.
At an instance in time, where the business already has some amount of assets on its books, and also has the potential to generate future profits, we are able to value the assets currently on its books, and as well as to provide an approximate value for the future profits (see the How To Value A Company series for discussions on how to value a company).
In some sense, at a specific moment in time, we can say that a business has a fixed intrinsic value, and we can treat the business as essentially non-productive, at that instance in time.
Which means that yes, like with regular non-productive assets, it is possible to overpay for a business (i.e.: stock).
To paraphrase Investing vs Speculating —
The net amount of gains and losses, from all investors of [a business], across all time, based only on [the business], will be exactly equal in dollar value to the sum of all earnings of [the business].
So, you can consider trading stocks as both investing and speculating. Part of the profits from trading stocks will come from the productive part of the business (i.e.: investing), and part of the profits will come from just selling to a greater fool (i.e.: speculating).
Now, consider the P/E ratio of a company — it is the price of the company, divided by its earnings (i.e.: profits (2)). In effect, the P/E ratio is how much you pay for each dollar of profits from that company.
Remember how profits are injected into the system for productive assets, leading to positive sum games?
Let’s say we have a company with a P/E ratio of 1, i.e.: investors pay $1 for each $1 of earnings.
Every year, an equal amount of value is injected into the system as the value of the stocks. In this extreme case, the productive nature of the asset is very significant to the trading — it represents 100% of the stock value of the asset every year! In effect, if we have $1m of stock value, then every year another $1m of productive value is injected by the business, pushing our zero sum game to a sum of +100% per year.
Now, let’s consider a company with a P/E ratio of 1,000, i.e.: investors pay $1,000 for each $1 of earnings.
Every year, only 0.1% (1/1000) of stock value is injected into the system by the production of the business. In this extreme case, the productive nature of the asset is almost a rounding error — it pushes the trading from zero sum to sum of +0.1% every year.
So, the larger the P/E ratio(3), the most speculative, and more “zero sum game”y the asset.
Final words
As with our 3 friends, in the heat of the moment, when our paper net worth is rising quickly for what seems like doing nothing, it is easy to convince ourselves that we are geniuses, that we have discovered “the secret to wealth”, or that the asset(s) we are investing in has intrinsic value — who wouldn’t want to own an asset whose price is going to the moon?
But remember that unless the asset has productive value, in an emergency, when you desperately need liquidity, it may be hard to sell the asset for anything more than intrinsic value. And intrinsic value may be a lot lower than whatever price you personally paid.
It may help to think of “the asset” as “a $1 bill”. Yes, if you have a $1 bill that, for whatever reason, is desirable (maybe it was handled by some famous celebrity), you may be able to sell it to a speculator for more than $1. But the universe of people who are wiling to pay more than $1 for a $1 bill is relatively small — not everyone cares about the provenance of their cash. So the latest owner of that $1 bill, may find that in an emergency, they can really only use that $1 bill as… a $1 bill — even if they paid $100 for its provenance. In effect, that $100 “intrinsic value” applies only to a niche market, and the broader market simply does not care, and unless you can find someone else from that niche market, you are stuck with the broader market’s intrinsic value of $1.
Footnotes
- For the purposes of this illustration, we are going to ignore the legality of the things discussed. Some of the things discussed here are in the legal gray area (some may be outright illegal!), so please, do not try this at home.
- Earnings/profits mean something very specific in finance/accounting. Technically, the usage here is not quite correct, but it’s close enough. See How to value a company – income statement for details.
- This is an oversimplified explanation. In reality, businesses grow — just because a business generates $100 in profits this year, doesn’t mean it’ll only generate $100 in profits the next year. A company with growing profits and static stock price, will naturally see a P/E ratio that shrinks with time. In effect, P/E ratio is a static, snapshot in time, valuation metric, that does not capture the dynamic nature of businesses over time.


