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As I mentioned somewhere above, I gave the new edition of Poor Charlie’s Almanack to my sons for Christmas.

Between that and his centenary tomorrow, Mr Munger has recently been on my mind.

In particular, late last week I was thinking of his advice to have multiple models:

"If the facts don't hang together on a latticework of theory, you don't have them in a usable form…. the first rule is that you've got to have multiple models - because if you just have one or two that you're using, the nature of human psychology is such that you'll torture reality so that it fits your models, or at least you'll think it does. …And the models have to come from multiple disciplines - because all the wisdom of the world is not to be found in one little academic department. (1)

…which had been prompted by my musing on albatross flight, and mungofitch.

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Until recently, the biophysics of the domestic economy of the albatross didn’t add up. In particular, the wandering albatross, Diomedea exulans, lives for decades (2) while maintaining a twelve-foot wingspan and traveling up to 75,000 km/year (not a typo). Its realm is the great Southern Ocean, where icy temperatures, perpetual high winds and giant waves are the norm. The wandering albatross spends almost all of its time in flight, rarely touching the ground (there is no ground), but despite all of this somehow gets by principally on a diet of small squid and fish, and dead stuff, that can be scooped up mid-flight on or near the surface. That’s an energy budget associated with a small and/or sedentary bird, not a perpetual flying machine with a wingspan half again as great as an NBA guard.

In 1883, Lord Rayleigh published a hypothesis in Nature, but one problem was that his dynamic soaring model (while presumably on the right track) didn’t, uh, correspond well to how the albatrosses were actually observed to fly. But six years ago, a group from MIT did a much more detailed and accurate analysis (3), which was paraphrased elsewhere by the senior author as “it turns out that the important metric is the ratio between gains and losses. So it is more efficient to gain a little, often, as is the case with small turns, rather than a lot, but rarely, such as with half turns” (4) (bolding mine)

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…which brings me to mungo (5): “I just pump some money out of the portfolio as the strikes I'm using gradually ratchet higher, though they're all "in the money" by around the same percentage. This fun will all end when I no longer find calls that are available at implied interest rates that seem attractive relative to my expectations for the stock price trajectory. Then it will be back to simple stock again. But while it lasts, it's great. One interesting thought is that, to the extent that I'm making a living from the option market rather than actually being an owner of Berkshire Hathaway the company, I am playing in the zero-sum part of the markets: it's just a side bet on how Berkshire stock is doing.” (bolding again mine)

So, the trick seems to be: from a complex dynamic system extract a little, frequently, while at the same time not appearing to work at it very hard. And you can go on for decades that way, while the feared and maligned Southern Ocean howls and churns around you. (6)

-- sutton

(1) OID May 5, 1995
(2) There’s a crank theory that their natural lifespan is unknown, and may in fact be a century or more. But injuries to wild birds can be unforgiving – hollow-boned wings are delicate – and with no port in a storm, a 2-3% annual chance of a crippling misjudgment make survival past fifty or so unlikely.
(3) Optimal dynamic soaring consists of successive shallow arcs. Bousquet GD, et al. J R Soc Interface. 2017. PMID: 28978747
(4) https://news.mit.edu/2017/engineers-identify-key-a...
(5) https://www.shrewdm.com/MB?pid=790103941
(6) Also, it's handy to have pitot tubes in your beak. AFAIK, this has nothing to do with my point (we could check with Jim), but just another cool albatross fact ("The tubes of all albatrosses are along the sides of the bill...(t)hese tubes allow the albatrosses to measure the exact airspeed in flight; the nostrils are analogous to the pitot tubes in modern aircraft. The albatross needs accurate airspeed measurement to perform dynamic soaring. https://en.wikipedia.org/wiki/Albatross

The wandering albatross spends almost all of its time in flight, rarely touching the ground (there is no ground)

Water, water, every where, Nor any drop to drink...

Jim

The wandering albatross spends almost all of its time in flight, rarely touching the ground (there is no ground)
...
Water, water, every where, Nor any drop to drink...

For those who might not get the obscure reference, that's a quote from the The Rime of the Ancyent Marinere (poem from 1798 by Mr Coleridge), who gets into big trouble by killing an albatross.
Moral of the poem: don't kill magical albatrosses?

Jim

One interesting thought is that, to the extent that I'm making a living from the option market rather than actually being an owner of Berkshire Hathaway the company, I am playing in the zero-sum part of the markets: it's just a side bet on how Berkshire stock is doing.” (bolding again mine)

In real life, I do not believe that the options market is zero sum. The reason is that market makers hedge their options positions with actual stock. This means that when

1) Options traders buy more calls than they sell, and/or sell more puts than they buy, market makers on the other side of the trades buy and hold more BRK stock to hedge their long-calls and short-puts positions
2) Options traders sell more calls than they buy and/or buy more puts than they sell, market makers on the other side of the trades sell BRK stock short to hedge thir short-calls and long-puts positions.

Indeed, there are special rules for options market makers that allow them to more easily and with fewer restrictions make short sales to hedge their options positions.

The upshot of all of this is that an options trader taking a long position (buying calls or shorting puts) she can quantitatively be assigned an equivalent number of shares she has purchased through her impact on the net positions of market makers. And vice versa when she goes short (shorts calls or buys puts).

Sorry to break the clean, but false, distinction between side-bets and bets. Even bookies lay off large bet positions by betting at the track.

R:

In real life, I do not believe that the options market is zero sum. The reason is that market makers hedge their options positions with actual stock. This means that when
1) Options traders buy more calls than they sell, and/or sell more puts than they buy, market makers on the other side of the trades buy and hold more BRK stock to hedge their long-calls and short-puts positions
2) Options traders sell more calls than they buy and/or buy more puts than they sell, market makers on the other side of the trades sell BRK stock short to hedge thir short-calls and long-puts positions.
Indeed, there are special rules for options market makers that allow them to more easily and with fewer restrictions make short sales to hedge their options positions...


The things you say are true, but it doesn't mean the options market isn't a zero sum game.

If you consider every security trade by people who are participants in the the options market (as you seem to), including their trades in shares, then no, it's not zero sum, because share ownership isn't a zero sum game. But I don't think that's a useful way to delineate "the options market"...you're including non-options in the discussion.

If you consider only the set of all standard traded option contracts, that is in aggregate a zero sum game. An option contract can't ever create or destroy the underlying shares, nor ever affect the value of the underlying shares in any way.

None of the ways that an option contract can be bought, or sold, or come into existence, or cease to exist, or expire, or be exercised, can change the number of shares in existence or their value. So there is an absolute perimeter that you can draw around the options market that is nothing but the option contracts themselves, and the money passing between the people writing them, buying them, selling them, or seeing them expire. An option assignment doesn't create a share, it just obliges someone to move some already existing shares from one place to another.

Ultimately, all of the money received from selling options exactly equals the amount of money paid to buy options. It's an identity, true in every sub-period and over time.

What is more interesting to me is that there is no reason to believe that subsets of option trading are zero sum. I suspect that there is a long run net transfer of funds from buyers of options to sellers of options, though it may be modest. The amount gained by one group would have to equal the amount lost by the other group, however, as the boundary around all option contracts is a zero sum game.

Jim

Hi Jim,

In this reply I reach the conclusion that in real life, buying and selling options does social good comparable to the social good done by buying and selling stock in the secondary market. The only transactions int he stock+options markets that are NOT zero sum are transactions done by the issuer of the stock: paying dividends, buying back stock, or issuing new shares for public offerings or to fill exercise of warrants and options the issuer has previously written. Otherwise, all the stock trading that comprises 99.9..% of stock transactions are just as zero-sum as are options transactions: every share sold for N$ necessarily is matched by a share bought for N$.

You (Mungofitch) write:
What is more interesting to me is that there is no reason to believe that subsets of option trading are zero sum. I suspect that there is a long run net transfer of funds from buyers of options to sellers of options, though it may be modest. The amount gained by one group would have to equal the amount lost by the other group, however, as the boundary around all option contracts is a zero sum game.

I like that you get to the "what is more interesting to me" part. Unless there is something interesting about zero-sum-game vs not-zero-sum-game, then I am just playing word games, or being overly pedantic along the "words matter" axis.

My own "interest" is in determining whether options trading is particularly more-or-less zero-sum compared to stock trading. My interest is driven by the idea that trading stocks on a public market has, ultimately, the fantastic contribution to the public good that it funds productive enterprises which make everybody richer, even non-investors. As opposed to, say, gambling in casinos, which is a "zero-sum game" and doesn't do nobody no good except of course the owners of the casinos.

You write: "If you consider only the set of all standard traded option contracts, that is in aggregate a zero sum game. An option contract can't ever create or destroy the underlying shares, nor ever affect the value of the underlying shares in any way."

If by value you mean Market Value, then this is pretty clearly NOT true. Presumably we agree that Market Value is increased as demand for a stock is increased and decreased as demand for a stock is decreased. Is there a similar causal connection between buying or selling options and the market values of the underlying shares? Absolutely! Market makers hedge the long-ness or short-ness of their options book by buying and selling shares in the underlying. There are actually greek letters that will tell you for a simple valuation model how many shares a given strike price and expiry contract need to be hedged with, it is likely that to first order the connection of options transactions to purchases of shares in the underlying is actually automated.

The implication of this is, that in terms of social good, going long using options is "within a constant" of the same social good as directly buying stock.

If by value you mean Intrinsic Value, then options are no more or less zero-sum than are transactions in the secondary stock market. The only transactions that impact Intrinsic Value involve the underlying company issuing new shares in a public offering or to service the exercise of options/warrants it issued, or buying back shares and putting them in the shredder.

So the thing that was interesting to me about this is: trading in options in the presence of market makers has entirely similar social good to trading in stock. Whether you call one, or the other, or both "zero-sum" doesn't change that in the real world.

****

The other thing to consider is how would the options market be different if there were no market makers? Well market makers make their transactions to ENFORCE a model like Black-Scholes or one of its more complicated descendants on the price spread of options. Without market makers, prices on each options contract would reflect the demand of people who are not primarily trying to push prices towards their BS or other model values. This means there would be wild deviations in the spread of prices of differnt options contracts, and there would be wildly profitable arbitrage opportunities generated. That is, without market makers it would behoove me or you to write some code that would spit out the BlackScholes predicted prices based on the price history of the underlying stock, and would build hedged books of approximately balanced long and short options, buying the cheap ones and selling an selling/writing and offsetting number of expensive ones. And when the customer's options trended long, my algorithm would tell me to lay on some number of shares to hedge by options book, just like it tells the market makers now.

Hi Jim,

In this post I challenge the claim that options are any more or less a zero-sum game that is stock trading. The thing that makes options trading seem zero sum is implicitly excluding the options (and warrant) trades which include the issuer of the underlying stock as a counterparty. The thing that makes stock trading seem NOT-zero-sum is implicitly including transactions engaged in by the issuer of the underlying stock (including dividend payments, public offerings, exercise of warrants and options they issued and share buybacks).

So including the issuer of the underlying makes the market non-zero sum whether it is options or stock. Excluding the issuer of the underlying makes the market zero-sum whether it is option or stock.

You wrote:
Ultimately, all of the money received from selling options exactly equals the amount of money paid to buy options. It's an identity, true in every sub-period and over time.

This is true but it isn't the whole story. It *is* the whole story for options that expire worthless, but for options that are exercised, there is a further transfer of value. Further, the exercise involves the exchange of cash for shares, exactly the same kind of transaction that characterizes stock trading.

This is still zero sum. Just as any trade of shares for cash in the secondary market is zero-sum.

Ultimately, options contracts are just a funny way to organize exchanging shares for cash, but statistically aggregated, that is what they are.

R:

Hi Jim,

One last thing on the options. I have a feeling that I've asked you this before but didn't save the answer. Do you have any guidance on writing covered calls on BRKB? Sweet spots in expiry dates and/or distance out of the money?

Maybe more to the point, how much extra can one get reliably?

You wrote:
What is more interesting to me is that there is no reason to believe that subsets of option trading are zero sum. I suspect that there is a long run net transfer of funds from buyers of options to sellers of options, though it may be modest.

I think it is a safe bet that there is a net transfer of money from non-market-makers to market-makers. Wannabee Market-Makers for whom this is not true would not last long.

Do market makers write more contracts than they buy? This seems likely and would seem likely to produce a better return to people coat-tailing the market makers by writing contracts instead of buying them. IF their inferior access to the right side of the bid-ask spread doesn't negate the advantage, which at my level of ignorance is a big IF.

Of course, it is conceivable that on something like BRK, call contracts are dominated by retail investors writing covered calls, in which case coat-tailing the market makers would tell you to buy calls.

Who knows.

"If you consider only the set of all standard traded option contracts, that is in aggregate a zero sum game."

Technically it would be a negative sum game after the rake (fees) by all participants is taken into account. Sure the fees are generally small and not everyone pays them, but they do exist.

"Excluding the issuer of the underlying makes the market zero-sum whether it is option or stock."

I know this is a semantic argument, but I am still bothered a bit by this. I know this isn't going to come out right, but I will try and explain.

Buying or selling actual stock shares on the secondary market may net to zero financially, but there are also non-financial effects to companies of stock transactions on the secondary markets that do not exist in options markets.

Buying shares on the secondary market give a person a say (no matter how small) in the future of the company. Selling those shares, terminates any future say in the company.

I know that is a quaint view in this day and age where stock transactions are often looked at as more of a casino bet then as actual ownership of a company. But I still think the ownership matters. To take an extreme example, Warren Buffett has amassed stakes in companies by buying stock on the secondary market. It is hard to argue that his ownership of those secondary shares didn't have at least some influence on many of those companies.

To bring it back to Jim's original point. The trading of stock options (as he defines it) is not only zero sum financially, but zero sum non-financially as well. They are literal casino bets. Sure there are casino bets that are positive expectation and some (most) that are negative expectation, but a person making those bets is not adding anything productive to the world where a capitalist buying and selling stock shares (even on the secondary markets) is still doing something productive.

Technically it would be a negative sum game after the rake (fees) by all participants is taken into account. Sure the fees are generally small and not everyone pays them, but they do exist.

Well, sure, but that's true for almost every human activity : )
The options contracts per se are zero sum.


Unlike, say, common stocks.

One possible demonstration:
Imagine that every stock in the world were trading at fair value tomorrow, and we all agreed on that fair value.
The sum total of the market cap is vastly more than the aggregate amount paid for the shares by their current holders.

Another possible demonstration:
Again, let's assume that all stocks always trade at fair value all the time.
I buy a stock from you for $100.
A year later there have been retained earnings of $4 and dividends of $2 sent to me, and the share price is up a bit because the value is up a bit. That "extra" did not come from your pocket.

Jim

" To bring it back to Jim's original point. The trading of stock options (as he defines it) is not only zero sum financially, but zero sum non-financially as well. They are literal casino bets. Sure there are casino bets that are positive expectation and some (most) that are negative expectation, but a person making those bets is not adding anything productive to the world where a capitalist buying and selling stock shares (even on the secondary markets) is still doing something productive." Good morning bud, not sure what you are getting at? When capitalists sell and promote smoking, worldwide, is that productive to the world? When capitalists finance sports betting companies to promote sports betting apps on 100 million cell phones, including those under 21, is that productive worldwide? If I sell 30 brkb calls to generate 60K in proceeds and use that cash to buy cars for grandkids or add to their 529s, why isn't that,productive? How many hours of labor go into producing a car? Has my 30 years of ownership in Brkb common allowed me to convince Buffett that buybacks at, material discounts to IV, are accretive to IV, and to forget the BV hurdle? Could I convince him to authorize a buyback in 2006 along with the Gift letter he disclosed at that time? Real world 101, our common ownership in almost all shares we own have almost zero power. Have a grand day, your pal, Harold, which has never been my name that I know of.

Jim

Your first demonstration confuses me. It seems wrong.

You write:
Imagine that every stock in the world were trading at fair value tomorrow, and we all agreed on that fair value.
The sum total of the market cap is vastly more than the aggregate amount paid for the shares by their current holders.

The vast majority of the stock's current holders bought their stock sometime in the last few years. A quick google turns up about 36 days to turn over the entire market cap in daily trading volume, and an estimate of 5.5 months for the average (probably median) time a stock is held in a portfolio. So it seems virtually certain that when the Market is overvalued for a few years at a time, the aggregate paid by the current holders of the shares will be on average higher than the current fair market value of the shares, and that therefore, in the aggregate, larger than fair market value.

Am I missing something here?

Jim: Imagine that every stock in the world were trading at fair value tomorrow, and we all agreed on that fair value.

You: So it seems virtually certain that when the Market is overvalued for a few years at a time, the aggregate paid by the current holders of the shares will be on average higher than the current fair market value of the shares, and that therefore, in the aggregate, larger than fair market value.

Am I missing something here?

You were asked to imagine that all stocks were fairly valued. Instead, your premise is that the market is overvalued

"Good morning bud, not sure what you are getting at?"

You should have stopped there.

The rest was just a bunch of loaded questions demonstrating you didnt have a clue what was being said.

Good luck Harold.

Engr27,

Thanks for helping me out. To be fair to me, though:

You wrote:
You were asked to imagine that all stocks were fairly valued.

Actually, Jim asked me to Imagine that every stock in the world were trading at fair value tomorrow

You wrote:
Instead, your premise is that the market is overvalued

Actually my "premise" was noting a fact with which I think Jim would agree, that in the past the stock market has been overvalued for years at a time.

****

But I think after reading your note I did figure out what Jim was getting at, and that is that the stock market rises in value due to retained earnings of companies, and that is an example of its non-zero-sumness, which is true and I agree with.

And what I wanted Jim or others to recognize was that:
1) The entire non-zero component of the stock market arises form transactions in which the issuer of the stock participates.
2) If the issuers of stock that write or redeem warrants and options were included as part of the options market, the options market would also be non-zero sum.

****

In one of the posts, Jim hypothesized that there may be a net transfer of cash from the buyers of options to the sellers (or writers) of options. A very interesting thing to contemplate and something that would NOT be true in a frictionless market with "properly priced" options. It would not be true because the definition of "properly priced" is a set of prices which statistically average to equal amounts won and lost by people on both sides of the options transactions. If buyers are systematically overpaying for options, it is either because they are on the wrong side of the bid-ask spread more often than sellers, or because the options are mispriced and us retail guys should be writing options more often than we are buying.


I will hypothesize that there should be a net transfer of cash to the buyers of calls from their sellers, and to the sellers of puts from their buyers. My reasoning is that stock prices rise over time, so "properly" priced options will win on the long side over time and lose on the short side over time. That to zeroth and first orders, "investing" in options is just a funny way to invest in stock and eliminating arbitrage opportunities means the long side has to make more money than the short side since the stock hedge of long options books is rising in value, on average, while the short stock positions that hedge short options books are falling in value over time. In fact, if I am right, there should be a systematically higher advantage to being on the long side of options trades when markets are rising and a systematic advantage to being on the short side of options trades when the markets are falling.

I hope at least someone besides me has been entertained by these considerations. Whether that is true or not, I will go back to thinking about more useful things like how many angels can dance on the head of a pin and whether the devil is real.

R:)

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