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February 25, 2009

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I think the pons is shaking my asinorum off and into the river (efficiently).

I'm a bit confused. I can understand _some_ of the anti-inductive situations, but not the general principle (other than "stuff bottoms out because there really is a lower bound (zero, obviously (baring items that can become so nasty/wasteful that you'd be willing to pay someone to take them off your hands, but that's not really an issue here...)) And upper bounds because even if someone thinks something is a good investment, sooner or later they simply won't be able to afford it... which means sellers can't sell it, which means it will get cheaper"

Is this what you were going for? because, if not, I find myself a bit confused.

The knowledge about increasing prices would seem to me to itself push prices to increase faster (ie, everyone thinks something is a good investment, so many many buyers, so high demand, etc... up to the above mentioned limit) while if something is sinking and everyone believes it's sinking, the demand will get lower, which means to get it sold will take faster price drops, which will lead to more people believing it's sinking, etc..

I'm probably being stupid here, so can anyone clarify this for me? (Or is it just the bounds that I mentioned making things have to start going the other way eventually?)

Well, now you f***in' tell me.

Seconding Psy-Kosh in being confused & unconvinced.

Psy-Kosh:

You are not confused. You have clearly articulated the structure of a market bubble and its resulting crash.

Psy and John, I think the idea is this: if you want to buy a hundred shares of OB at ten dollars each, because you think it's going to go way up, you have to buy them from someone else who's willing to sell at that price. But clearly that person does not likewise think that the price of OB is going to go way up, because if she did, why would she sell it to you now, at the current price? So in an efficient market, situations where everyone agrees on the future movement of prices simply don't occur. If everyone thought the price of OB was going to go to thirty dollars a share, then said shares would already be trading at thirty (modulo expectations about interest rates, inflation, &c.).

If someone notices that morgage defaults are uncorrelated, and new instruments that exploit that lack of correlation are invented, investors will be more likely to buy securitized morgages, so the rates are bid down and they become cheaper for homeowners. But that in itself should not cause defaults to be more correlated.

In the event, the models for correlation were off, and defaults were more correlated from the start. But that's not a problem with public/private knowledge or anything; they were just bad models. If the prizing had been done correctly to start with, I see nothing paradoxical in assuming that introducing CDOs would lead to persistently lower morgage rates -- the lack of correlation doesn't stop being real just because people believe in it.

the general public being unaware of the fact that stock prices are an equilibrium of beliefs about whether the stock will rise or fall is not a major cause for concern.

Vilhelm S., companies and people who lose money on CDOs have mortgages to pay and employ people who have mortgages to pay... Once the system gets coupled like that, one unlucky bet can start the cascade. I'm not saying this actually happened, but it's a mechanism which could falsify the assertion "the lack of correlation doesn't stop being real just because people believe in it".

Elizer, I accept your general point, but in your coin flipping example, it was unclear to me what your trade would be. Would you bet on heads or tails and in what circumstances? In a real world scenario I suspect its more likely to be the opposite of what I think you suggested but that is not entirely clear to me.

It all depends on where the market price is. There is a theory formed by a relatively respected speculator called "reflexivity," basically that markets tend to perpetuate trends and overshoot fair values http://www.geocities.com/ecocorner/intelarea/gs1.html). And there is some other evidence of this in books such as Bob Schiller’s Irrational Exuberance about information cascades etc. So given there have been 9 heads in a row, maybe your average bear would think its more likely to come up heads than it’s genuine expected value, so I would argue that the market would probably overvalue the true likelihood (which according to you is 10/11ths), and so they would bet on heads and you would want to be short (bet on tails) if their expectation/price is greater than 10/11ths. The difference between their price and your price is called the edge, and you would capture that edge by betting on tails. So it would be a relatively modest profit opportunity. Not the other way round as I think you described, where you seem to be saying that the market would be pricing it at 50/50 and fair value is 10/11ths and you should bet on heads. It all depends on where the market would trade, above fair value or below fair value, I say above, in which scnenario one should bet on tails, and there is a minor profit opportunity, you seem to be saying below, bet on heads, and there is a major profit opportunity. A related question is how much should you actually bet?

Anyway, maybe just a case of my misunderstanding things. Another, perhaps, simpler way to think of markets are as beauty contests, where you are trying to pick the winner of the contest, which is not the girl you think is most beautiful, but the girl that everybody else thinks is the most beautiful: http://en.wikipedia.org/wiki/Keynesian_beauty_contest

Elizer, I accept your general point, but in your coin flipping example, it was unclear to me what your trade would be. Would you bet on heads or tails and in what circumstances? In a real world scenario I suspect its more likely to be the opposite of what I think you suggested but that is not entirely clear to me.

It all depends on where the market price is. There is a theory formed by a relatively respected speculator called "reflexivity," basically that markets tend to perpetuate trends and overshoot fair values http://www.geocities.com/ecocorner/intelarea/gs1.html). And there is some other evidence of this in books such as Bob Schiller’s Irrational Exuberance about information cascades etc. So given there have been 9 heads in a row, maybe your average bear would think its more likely to come up heads than it’s genuine expected value, so I would argue that the market would probably overvalue the true likelihood (which according to you is 10/11ths), and so they would bet on heads and you would want to be short (bet on tails) if their expectation/price is greater than 10/11ths. The difference between their price and your price is called the edge, and you would capture that edge by betting on tails. So it would be a relatively modest profit opportunity. Not the other way round as I think you described, where you seem to be saying that the market would be pricing it at 50/50 and fair value is 10/11ths and you should bet on heads. It all depends on where the market would trade, above fair value or below fair value, I say above, in which scnenario one should bet on tails, and there is a minor profit opportunity, you seem to be saying below, bet on heads, and there is a major profit opportunity. A related question is how much should you actually bet?

Anyway, maybe just a case of my misunderstanding things. Another, perhaps, simpler way to think of markets are as beauty contests, where you are trying to pick the winner of the contest, which is not the girl you think is most beautiful, but the girl that everybody else thinks is the most beautiful: http://en.wikipedia.org/wiki/Keynesian_beauty_contest

But clearly that person does not likewise think that the price of OB is going to go way up, because if she did, why would she sell it to you now, at the current price?

Maybe she needs to increase liquidity for some reason? For example, the IRS wants payment in cash, not stock. Additionally, she might want to use the resources for immediate consumption rather than for investments; she might want to use the cash to take a vacation, or pay medical bills. There are all sorts of reasons why someone might want to sell a stock, even if they think it will go up.

(Myself, I sort of suspect that, if a stock doesn't pay dividends, it's mostly worthless. To quote some guy with a blog:

If you put your Mickey Mantle rookie card on your desk, and a share of your favorite non-dividend paying stock next to it, and let it sit there for 20 years. After 20 years you would still just have two pieces of paper sitting on your desk.)

Eliezer, your main point is correct and interesting, but the coin flip example is definitely wrong. The market's beliefs don't affect the bias of the coin! The map doesn't affect the territory.

The relevant FINANCE question is 'how much would you pay for a contract that pays $1 if the coin comes up heads?'. This is then the classic prediction market type contract.

The price should indeed be ten elevenths. Of course, you don't expect to make money buying this contract, which was exactly your point.

What WILL be true is that the expected change in the price of the contract from one period to the next will be zero. This need not mean that it goes up 50% of the time, but the expected value next period (in this case) is the current price.

The first proof that I know of this was done by Paul Samuelson in 1965, in his paper 'Proof that Properly Anticipated Prices Fluctuate Randomly'.

I think this is why there will always be opportunities for high returns. Quantifiable correlations will always be bid away. But, there will always be unquantifiable uncertainty. Much of investing is earning rents on uncertainty, so that if you're even slightly skilled at picking the right uncertainties, you can make huge returns. It seems to me that finance seems to either quantify uncertainties into risk models or pretends they aren't important. But, for an individual investor they can be the most important thing to consider, and due to the very nature of uncertainty, it's not likely to be anti-inductive. That's why great investors like Buffett & Munger are as skilled at recognizing biases people have in the face of uncertainty as they are at doing finance. If you asked Charlie Munger what it took to be a good investor, I bet he'd be more likely to give you a rundown of biases than to offer anything quantitative.

Doug, I meant ceteris paribus.

Behemouth, i'm not sure the coin flip example is completely wrong, perhaps the fair thing to say would be that its open to interpretation, but Elizer can clarify his thinking for us.

Elizer seems to be saying that the market price will be around 50%, fair value is 91%, and you should bet heads on that basis, and should expect to capture an edge of 41%.

Another alternative is that the market price could be above 91%, say 95%, and in that instance you should bet on tails, and expect to capture only a 4% edge.

We could informally test this ... we could ask/email 20 people if given they know a coin is baised and given that it just landed heads 9 times in a row, how many heads in 100 tosses will the coin produce. Their responses could become the market price, if that number averages out to say 90 heads, then the market price is 90% for example, and then we could see if a bet on heads or tails would be more appropriate. I am not sure of the final answer, but I think its unlikely that the market price will be near 50/50.

See added PS. The coin example is intended as a humorous exaggeration of the way the world would be if most physical systems behaved like market prices, with the coin coming up "heads" being analogous to prices rising.

Once upon a time, I thought I saw some important news that should have affected a company's stock price, as it would have led to significantly decreased demand for one of the company's flagship products.

I looked at the stock price, and after the trade show in which the announcement was made, the value of the stock had, to my great surprise, actually increased.

That company was Sony. The announcement was that Final Fantasy XIII would no longer be a Playstation 3 exclusive; its English version would also be released for the Xbox 360. As a game player, I knew that Final Fantasy was a game series that was popular enough to drive sales of whatever console it was available for, regardless of its other merits. However, this announcement meant that many people who might have bought a Playstation 3 would no longer do so. As the original Playstation and the Playstation 2 were one of Sony's largest revenue sources, further bad news regarding the the Playstation 3's future should have negatively affected its stock price. Why didn't it?

I came up with three guesses:

1) Average stock traders don't know as much as I do about the video game market. This is possible, but "Hey, Sony just lost its exclusive Killer App!" should be something that anyone actually paying attention should notice - stock traders aren't that stupid, are they?
2) Sony is a huge conglomerate. It sells so many other products that bad news in one area either just didn't matter (nobody expected the Playstation 3 to sell as many units as its earlier versions, for the simple reason that it was much more expensive) or it was outweighed by good news about other markets, such as digital cameras.
3) There is some other explanation, which I have not yet thought of.

but still, the market does not leave hundred-dollar-bills on the table if everyone believes in them.

People fail to act on stated beliefs all the time. Why wouldn't this sometimes happen in the market?

Doug: Sony loses money on every PS3, so it would be bad news if people bought them for FF and bought few other games; I don't know how plausible that is.

Russ, I think that if you take the example literally, the price would be 91%, not 50%, and you wouldn't expect to make money.

Eliezer, the PS definitely clarifies matters.

Although I also think the example is actually instructive if taken literally too. In particular, if you see nine heads in a row, each additional head means you expect a higher chance of heads next flip. But you do not expect an increase in the price of the contract that pays $1 if heads comes up. THAT still has an expected price change of zero, even thought we expect more heads going forward.

In other words, future EVENTS can be predictable, but future PRICES cannot.

Eliezer does a good job of explaining a mechanism by which two investments with negatively correlated returns can switch to having positively correlated returns. But he doesn't do a good job of convincing me that a stock's price has a tendency to go down when it has just gone up, and vice versa.

I can think of an argument against this position. It seems plausible that stock traders see the past movement of a stock as an indicator of it's future movement. If a majority of traders share this belief, this will compel them to buy the stock from those who don't, inflating it's value and reinforcing the cycle. This would indicate that markets are inductive, which is the opposite of what the title suggests.

Doug: Sony loses money on every PS3, so it would be bad news if people bought them for FF and bought few other games; I don't know how plausible that is.

Yeah, that would probably be bad, too; a PS3 sold that doesn't generate much additional revenue is just a straight loss. On the other hand, once you've already decided to get the system because of the blockbuster title that you Need To Have, non-blockbuster games for the system become more attractive than they were before, so the pattern of "very few games" over the entire lifetime of the system isn't really all that likely. In the short run, though, it could definitely be an issue. Personally, I currently have only two PS3 games: Disgaea 3, and Metal Gear Solid 4. I expect to get more eventually, but not for a while.

John: I don't think Eliezer's saying that a stock that has recently risen is now more likely to fall. Quite the opposite in fact. Any given stock should be about as likely to fall as to rise, at least if we weight by the amount of the rise. That is, if I hold a share of XYZ, which costs $100, and I anticipate a 99% chance that the stock will rise to $101 tomorrow, then I should also expect a 1% chance that the stock will drop to $1 tomorrow. Were that not true, the share would be worth nearly $101 *right now*, not tomorrow.

See also: Conservation of Expected Evidence

Correlation is not "arbitraged away" because there's no inherent arbitrage in correlation. I think in your first example, you had in mind pairs trading where there is *lagged* correlation, or negative autocorrelation of the spread. In the second example, mortgages, what you're saying's just wrong.

An important aspect that you also omit to mention is that efficient market means the risk free expectation is the risk free rate. That does not mean that up and down are equally likely. A junk bond is much more likely to go up than down, only it'll go up a little and down a lot. Returns can be skewed.

Last point, arbitrages are costly and often risky (the information available is not certain). You may not have more information than other people, but you may be less risk averse or you may be able to arbitrage at a lower cost.

(Myself, I sort of suspect that, if a stock doesn't pay dividends, it's mostly worthless. To quote some guy with a blog:

If you put your Mickey Mantle rookie card on your desk, and a share of your favorite non-dividend paying stock next to it, and let it sit there for 20 years. After 20 years you would still just have two pieces of paper sitting on your desk.)

Maybe it would help to think of a sole proprieter running a small retail business who starts with perhaps $500k in personal equity. He pays himself a relatively meager salary and invests all other net income back into the business to increase inventory, advertise, move to a better location or open another branch etc. After running this business for forty years its expanded successfully and worth $8MM dollars, even though it hasn't paid a single dividend. Did he waste the last forty years of his life? Do you think he'll be able to extract that earned value?

From there you should be able to see that a privately held corporation (only owned by family) could work exactly the same, and from that its not a leap at all to see how a publically held company can increase in value without ever actually extracting the value from it.

3) There is some other explanation, which I have not yet thought of.

Maybe the sales of the game on the other platform will be more profitable than the PS3 sales they miss out on? The margin for games is much higher than for consoles and you definitely can broaden your market by including 360 owners who do not wish to shell out $400 just to play that game. Is it conceivably possible that Sony knows as much or more about the gaming industry as you do?

Jeremy: we're drifting from the topic, but I don't believe the Final Fantasy games are produced, distributed, or sold by Sony. Thus the decision to release FF for multiple platforms was not a decision made by Sony, simply one which affected Sony.

Doug and Jeremy:

Generally, the fundamental value of a stock is determined by one of two things. It can be defined by the net present value of the future dividends of the stock. Alternately, it can be determined by the per-share liquidation value of the company's assets (after creditors are paid). Which one applies or what mix depends on whether and how the company will be liquidated.

The rest is a mix of market psychology and adjustments for risk/uncertainty.

A big wrinkle is that the many investors look for companies with major earnings growth potential. As a result, most traded companies try to give the appearance of major earnings growth potential. One way to signal growth potential is to allocate little or no cash to dividends, because using the cash for expansion (or for activities that superficially resemble expansion) signals that the company has strong growth opportunities. If investors believe this signal, then the stock price rises from its fair value as an existing business to its expected fair value as a much bigger company in the future. The management rewards everyone with bonuses and all is good, until the future arrives disappoints everyone.

I was going for a peacock analogy, but perhaps lemmings would be more appropriate.

It can be defined by the net present value of the future dividends of the stock. Alternately, it can be determined by the per-share liquidation value of the company's assets (after creditors are paid).

So if the stock does not pay dividends, and never will, and the corporation's assets equal its liabilities, and always will, then the appropriate value of the stock is, in fact, zero? (Well, there are voting rights, but still...)

It all depends on where the market price is. There is a theory formed by a relatively respected speculator called "reflexivity," basically that markets tend to perpetuate trends and overshoot fair values

Yes, this is how I make day trading profits. Wait until there is a big crowd on the "wrong side" of the trade, watch for the signs of them starting to panic, and make $$$ when they all go stampeding through the doorway driving the price in your direction. This is a good example.


It can be defined by the net present value of the future dividends of the stock. Alternately, it can be determined by the per-share liquidation value of the company's assets (after creditors are paid).

So if the stock does not pay dividends, and never will, and the corporation's assets equal its liabilities, and always will, then the appropriate value of the stock is, in fact, zero? (Well, there are voting rights, but still...)

No, the value also includes the NPV of future net earnings, even if they are not currently being paid as dividends. When you value a business for the purpose of selling it, revenue, assets and intangibles like brand awareness are all things you look at.

Also if a company's assets = its liabilities then it has not been profitable or its losing money (or its a very new business). Obviously failing businesses are not worth anything and stock prices reflect that; but a business that is earning a net profit has a value regardless of if dividends are paid. If dividends are not paid they are re-invested in the business, which isn't really different from you getting the dividend and investing it in that or some other stock except that you are giving the company's management credit for making wise investments (bonuses are an expense and are sub-tracted from net income and so are not relevant here).

All competitive situations against ideal learning agents are anti inductive in this sense. Because they can note regularities in their actions and avoid them in the future as well as you can note regularities in their actions and exploit them. The usefulness of induction is based on the relative speeds of the induction of the learning agents.

As such anti induction appears in situations like bacterial resistance to antibiotics. We spot a chink in the bacterias armour, and we can predict that that chink will become less prevalent and our strategy less useful.

So I wouldn't mark markets as special, just the most extreme example.

kebko: " Much of investing is earning rents on uncertainty, so that if you're even slightly skilled at picking the right uncertainties, you can make huge returns."

The last year has demonstrated that it is not always trivial to differentiate between earning rent on uncertainty and running a variation on the martingale.

IMO, a fair amount of the profit in the highest flying risk arbitrage schemes is based on leveraging with the bankruptcy put.

If I am allowed to run martingales with an exposure of 5-10 times my actual capital, I will make me and everyone who invests with me some very high and consistent returns *most of the time*. But when the returns go bad, they go devastatingly bad. This is pretty much what happened in large segments of the financial markets over the last 20 years. 20% across the board drops in housing prices was the casino cutting us off before we could double down again.

Jeremy and Doug,

There's less disagreement than you think here. Future net earnings enter the equation as future dividends (appropriately discounted) or share buybacks (driving up farther-future dividends and per-share liquidation value). I didn't specify that assets on liquidation had to be tangible; trademarks and the like are valuable (both because they improve the business as it operates and because they can be sold on liquidation).

If earnings are reinvested in the company, that's fine. The investments will be profitable or not; profitable investments will result in even more earnings. The cycle can continue until either (1) management decides that it has no further opportunity for reinvestment, and returns the now-compounded earnings to shareholders as dividends, or (2) investments are made that are unprofitable, and the money is wasted. Option 2 is a surprisingly popular choice.

In any case, a stock that has no dividends, no liquidation value, and no prospect of either of those facts ever changing is worthless. You may be able to convice a greater fool to buy it, but there's no actual wealth attached to the stock.

What about Moore's Law?

I understand it is a totally different situation. There is no opponent, and plenty of positive feedback. However, I still think that "up so far, so up forever" is just as much of a fallacy with chips as with markets.

Doesn't this mean that once everyone realizes that markets are anti-inductive, markets will become inductive?

As well as a towel, an interstellar hitchhiker should pack a can opener.

This resoning works good if I assume that I have average IQ - and so my predictions are averege and so I should not try to predict the market. But most people think that they are smarter then most people. So do the traders.

Smartest traders can first notice trends in psevdorandom enviroment. But most traders mistakenly think that they are smartest.

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