Zero Sum games

[RedGreenBen]

My thought of the day, which says something about the kind of day it was...

Broadly speaking trading is a zero-sum game (I know that isn't 100% true for all instruments/timescales but it is an approximation I can live with). However, the average intelligence/resources of the players in that game is scarily high. The only way we make money consistently is to be consistently better at the 'game' than the average player.

So does that make this a foolish game to play? There must be other games where the participants are on average much less intelligent/dedicated/disciplined (You only have to look at the online poker rooms to confirm that !).

Thoughts welcome.

RGB.

 

[DC STOXX]

Correct
However many of the elite traders are far from smart...I strongly believe you only need to possess Slightly higher that average intelligence plus the necessary trait to become an consistent trader. I use the phrase "slight above average" because lets me frank, most the population are horrifically naive.

 

[Rhody Trader]

Broadly speaking trading is a zero-sum game (I know that isn't 100% true for all instruments/timescales but it is an approximation I can live with). However, the average intelligence/resources of the players in that game is scarily high. The only way we make money consistently is to be consistently better at the 'game' than the average player.

You could probably say most markets aren't zero sum, depending on how you quantify "markets". Pure asset markets (stocks, physical commodities, etc.) are not. And options sometimes are and sometimes aren't. Anything that is contract based where there's no option (futures, retail forex) is zero some.

But to your wider point, I would most definintely disagree with the idea that the average intelligence/resources among market participants is "scarily high". Do institutions have some bright folks and loads of data, analytics, etc.? Sure they do. Are there loads of folks with little experience and no fancy resources? Absolutely. You trade against them all, so to speak.

Keep in mind too that even the supposedly smart ones can do really stupid things. I wouldn't sweat it.

 

[Directional]

And options sometimes are and sometimes aren't.

I'd be curious to know in what circumstances an option is not zero-sum.

From write to expiry, the gains subracted from losses from the buyer to seller sides will always add up to zero, excluding commissions?

 

[arabianights]

Yep. But luckily many market participants are hedgers, so in theory the average local should make money

(Like an insurance company really, being paid for taking on risk)

 

[0007]

There must be other games where the participants are on average much less intelligent/dedicated/disciplined (You only have to look at the online poker rooms to confirm that !).

Thoughts welcome.

RGB.

50% of people are of below-average intelligence. Are they trading?

 

[Rhody Trader]

I'd be curious to know in what circumstances an option is not zero-sum.

From write to expiry, the gains subracted from losses from the buyer to seller sides will always add up to zero, excluding commissions?

The option premium automatically makes it not zero-sum because the writer will always be better off than the buyer. But lets take the premium out of the picture and just talk about intrinsic value.

You could say that in the money options are zero sum because presumably for each point of movement in price the owner and writer see their sides of the transaction change by roughly the same amount.

An out of the money option isn't the same. Let's say XYZ is at 100 and I sell you a 105 Call for 1. In a couple of days the call rises to 2. You've just doubled your money, but unless the price of XYZ has rising to more than 105, I am not in negative position since I do not have to buy back the option.

Make sense?

 

[Directional]

I was actually thinking of the option as a standalone derivative vehicle, regardless of how its priced on the underlying.

if you buy an option or sell it, you exchange risk with the counterparty. So regardless of whether the option trebles in value, or the relative value of the option in relation to Theta or Gamma vs the underlying - as a risk swap, from the point the option is created (sold) to the point that it expires, the net of all gains or losses from every counterparty will always net to zero, making it zero sum. The only time a trade is not zero-sum, AFAIK, is when new value is created?

At all stages from the moment the option contract is first written, to the moment it expires, the sum total of the money exchanged through out the life of the option will balance to zero:

example (excluding commissions for simplicity's sake):

FIRST SELLER: (Writer) Sell short 1 x call option @ $500 premium collected
FIRST BUYER: Buys 1 call for $500

Market rises & Call Option increases in value to $3000

FIRST BUYER decides to cash in and sells his option -
FIRST BUYER Sells 1 call for $3000 to SECOND BUYER

Market falls & call option decreases in value to $2000

SECOND BUYER decides to eat his loss and sell the option
SECOND BUYER sells the option for $2000 to THIRD BUYER

Market again surges & call option increases in value to $4000

THIRD BUYER takes his profit
THIRD BUYER sells the option to FOURTH BUYER for $4000

Market continues the trend upward & option increases in value to $4500

FOURTH BUYER takes his profit
FOURTH BUYER sells the option to FIFTH BUYER for $4500

market retraces and option expires OTM worthless...

FIFTH BUYER loses entire option value at expiry.

so:
WRITER = net profit of $500
FIRST BUYER = net profit of $2500 ($500 purchase and $3000 sale)
SECOND BUYER = net loss of $1000 ($3000 purchase and $2000 sale)
THIRD BUYER = net profit of $2000 ($2000 purchase and $4000 sale)
FOURTH BUYER = net profit of $500 ($4000 purchase and $4500 sale)
FIFTH BUYER = net loss of $4500 ($4500 purchase with expiry of option worthless)

TOTAL OF ALL GAINS = $5500
TOTAL OF ALL LOSSES = $5500

This example is a simplistic one, and the original writer holds his short for the whole example, but the writer could have joined the chain of buyers at any stage and the net swap of wealth would stay the same amongst all the participating traders.

Am i missing something?

 

[Rhody Trader]

I was actually thinking of the option as a standalone derivative vehicle, regardless of how its priced on the underlying.

if you buy an option or sell it, you exchange risk with the counterparty. So regardless of whether the option trebles in value, or the relative value of the option in relation to Theta or Gamma vs the underlying - as a risk swap, from the point the option is created (sold) to the point that it expires, the net of all gains or losses from every counterparty will always net to zero, making it zero sum. The only time a trade is not zero-sum, AFAIK, is when new value is created?

At all stages from the moment the option contract is first written, to the moment it expires, the sum total of the money exchanged through out the life of the option will balance to zero:...

OK. I get what you're saying. You're looking at it kind of like if a company's shares ever expired, so to speak, or the case of a company going bankrupt. I'm looking at it a bit more immediately.

In futures, which are clearly zero sum, on the other side of every long is a short, so by definition if you're long and prices are rising, someone is short and losing exactly as much as you're making. In stocks, if you're long there isn't necessarily (and probably isn't) a short on the other side, so you can't say someone is losing if you're gaining.

In options there is a short on the other side of every long, but it doesn't operate the way futures do. If prices rise the longs do gain, but not necessarily to the detriment of the short. Like my earlier example, if I sell a call to you at 1 and it then rises to 2, you gain that point, but I don't lose it - unless we're talking an in-the-money situation, but that's not necessarily a direct 1-to-1 depending on what the underlying is doing.

 

[arabianights]

OK. I get what you're saying. You're looking at it kind of like if a company's shares ever expired, so to speak, or the case of a company going bankrupt. I'm looking at it a bit more immediately.

In futures, which are clearly zero sum, on the other side of every long is a short, so by definition if you're long and prices are rising, someone is short and losing exactly as much as you're making. In stocks, if you're long there isn't necessarily (and probably isn't) a short on the other side, so you can't say someone is losing if you're gaining.

In options there is a short on the other side of every long, but it doesn't operate the way futures do. If prices rise the longs do gain, but not necessarily to the detriment of the short. Like my earlier example, if I sell a call to you at 1 and it then rises to 2, you gain that point, but I don't lose it - unless we're talking an in-the-money situation, but that's not necessarily a direct 1-to-1 depending on what the underlying is doing.

But if the option isn't exercised in the money then the holder will eventually lose the full value of the option so it remains zero-sum.

 

[intradaybill]

In stocks, if you're long there isn't necessarily (and probably isn't) a short on the other side, so you can't say someone is losing if you're gaining.

I think you are making a very fundamental mistake. There are no gains in long stock positions unless a buyer is found. If no buyer is found, you make nothing. When a buyer is found, the game becomes automatically zero sum because your winnings are now the charges to his account to buy the stock less what you paid if he is not also able to find another buyer and so on ad infinitum

You supposed to be an experience trader and so you must know better than a rookie like me that gains can only be realized if a counterparty exists and is willing to pay the price.

Bill

 

[arabianights]

I think you are making a very fundamental mistake. There are no gains in long stock positions unless a buyer is found. If no buyer is found, you make nothing. When a buyer is found, the game becomes automatically zero sum because your winnings are now the charges to his account to buy the stock less what you paid if he is not also able to find another buyer and so on ad infinitum

You supposed to be an experience trader and so you must know better than a rookie like me that gains can only be realized if a counterparty exists and is willing to pay the price.

Bill

Equities are not zero sum in the long run... Need to take into account cash flows from the value added by the company (be they share buybacks, dividends, eventual sale, or otherwise).

 

[intradaybill]

Equities are not zero sum in the long run... Need to take into account cash flows from the value added by the company (be they share buybacks, dividends, eventual sale, or otherwise).

I don't think that anyone spoke about equities being zero-sum. That would be silly. But equity trading is zero-sum. Unless you can prove that trading equities adds money some way.

Bill

 

[RedGreenBen]

50% of people are of below-average intelligence. Are they trading?

The wider discussion illustrates why I was pragmatic/lazy enough to just accept my zero-sum assumption.

However, to go back to the above quote, I think what concerns me is (again simplifying, but I just can't help myself) ....

1. Those below average intelligence (/aptitude/endurance etc) will lose money and when they reach in their pockets to find nothing but a fluffy-polo will cease trading and raise the average.

2. It isn't just a case of their being sufficient sub-optimum people out there. We need to weight the particpants by the volumes they are trading. Mr 'gut feel innit' may not be that succesful but his effect on the market is very much less than the Oxford-educated, supercomputer-backed institutional fund manager.

RGB.

(impressively educated, psychologically balanced, now breaking even after 9 expensive months )

 

[arabianights]

Bill: if you think of it like this: any decent company makes profits which in the end are distributed to the shareholders by some means or other. Or it makes losses which ultimately come from the shareholders. It therefore follows that equity trading cannot be zero sum in terms of expectancy. On an intraday basis of course it might as well be but only to the first approximation. As zero sum is a mathematical term (whether Nash's, von Neumann's or whoever I don't really care) I think it's pretty important to be precise about it as it has great implications for traders.

 

[arabianights]

Ben: I wouldn't assume anyone educated at Oxford has a clue what they're talking about to be honest...

 

[Rhody Trader]

But if the option isn't exercised in the money then the holder will eventually lose the full value of the option so it remains zero-sum.

I don't disagree with that. When talking about expiration, options are indeed zero sum.

 

[Rhody Trader]

I think you are making a very fundamental mistake. There are no gains in long stock positions unless a buyer is found. If no buyer is found, you make nothing. When a buyer is found, the game becomes automatically zero sum because your winnings are now the charges to his account to buy the stock less what you paid if he is not also able to find another buyer and so on ad infinitum

You supposed to be an experience trader and so you must know better than a rookie like me that gains can only be realized if a counterparty exists and is willing to pay the price.

Of course there are no gains if no one is willing to buy the stock from you at a higher price. But while lack of buyers may be a problem in real estate (especially right now in certain markets) that's generally not a problem in stocks, unless you're trading the most obscure, illiquid one out there. And even then there's probably a market maker somewhere willing to make you a price, so it's hardly relevant to the discussion.

 

[arabianights]

When are they ever non zero sum then? On a mark to market basis.

 

[timm]

RGB,
Not every market participant is a speculator. Take the stock market. It exists to match investors with corporations needing investment. In the middle of this process a speculator might make a profit. It doesn't mean another speculator has necessarily lost out. It might just mean a slightly higher price for the investors.

The same principal applies to other markets like futures and forex. As a small time speculator, you don't need to worry about who is counterparty to your trades. There is plenty of liquidity provided by other speculators and 'non-speculators' alike.