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Thursday, March 11, 2010

Rational Efficiency

Yesterday, as this graph from Yahoo Finance shows, Radio Shack (RSH) stock was up over 6% on take-over rumors.  The price continued to rise in after hours trading

This is typical behavior when a company is a real or imagined take over target.

Consider the efficient market hypothesis: everything that can be known about a company is known, and baked into the stock price at any time.

Consider rational expectations theory: any investor makes investment decisions in the light of cold logic and a desire to maximize returns, consistent with individual risk tolerance.

So, as a result of these perfectly efficient and rational decisions, at 1:00 p.m., RSH was worth more than it had been at noon, or would be at 2:00 p.m.

The rational expectation is that the acquiring company will pay a premium, and that drives up the price.   But if the noon price was correct, then why would the acquiring company pay more than market value?

Maybe they know something the rest of us don't . . .

No -- wait . . .

And why was it down at 2:00 p.m.?

Er . . . ah -- wha . . . ?


BadTux said...

I'm not a fan of the efficient market theories, but one thing you're missing is that they predict that prices will trend towards the true value of the company over time. That is, at any given time, the price will be above or below the true value of the company, but the average of the prices in the long run will trend towards the true value of the company.

Of course, in the long run we're all dead (i.e., the timeframe where it takes markets to settle on a new price may be longer than the timeframe in which the company's fundamentals change), in which case the entire efficient markets theory involved is useless because the company's fundamentals will change quicker than the markets can converge on a new price for the company... which is a case that, oddly enough, those who tout the Free Market Fairy as the solution for all problems never seem to consider. Yet I might argue that it might well be the *typical* case, because there are so many things that are constantly affecting a company's fundamentals (the state of the economy, the unexpected bankruptcy of a major customer, etc.) that convergence may never actually occur, every time prices start converging upon true value, something happens to *change* that true value and the wild wobble above and below true value starts again.

In short, your short term graph doesn't say much about the efficient markets theory because the efficient markets theory predicts short-term fluctuations in price above and below the fundamentals, it simply predicts that over time they'll converge towards the true price. On the other hand, that in essence is an admission by the efficient markets advocates that their theory is, in fact, useless in the real world... though they'll stammer "that's not so!" if you try to pin'em down on that.

-- Badtux the Economics Penguin

Jazzbumpa said...

but one thing you're missing is that they predict that prices will trend towards the true value of the company over time.

I didn't miss that. I willfully ignored it.

You're talking about a long time frame, but "efficient market" implies near instantaneous reaction - hours or days, not weeks, months or years. I know about the random walk idea, but I think it's free-market-fairy BS.

Bottom line: people don't make important decisions based on rational though processes. We humans are ruled by fear, greed, and ego -- and those things drive our decisions.

This includes marriage, divorce, investment, speculation, and M&A activity - where overpayment is typical, and the success rate is dismal.

My basic point is that if the market price, absent a take over option, is right, then the higher take-over price can't be. And paying a premium isn't rational, because the presumed efficiencies are almost never realized.

Something is not efficient; something is not rational.

JzB the occasionally rational real-world trombonist

BadTux said...

But rational thought processes actually aren't necessary in order for the price to converge. One thing we've found out in the AI business is that training a neural network to, say, detect a bomb in someone's luggage, doesn't require anything that approaches reason or rationality. It simply requires a supply of tokens, and a reasonable definition of "success" or "failure". The tokens eventually train the neural network to detect bombs despite the fact that the neural network has not an iota of rationality.

In the context of a market, the supply of tokens is called "money", and the supply of neural network neurons are called "customers" and "businesses", and the reasonable definition of "success" or "failure" are called "profitable business" and "bankruptcy". The problem is that the process of training these irrational neurons towards the rational price of some item on the market takes so long -- years, at the very least -- that by the time the market has been "trained" to produce optimal prices, market conditions have changed such that the original optimal price is now something else entirely.

In other words, there's nothing wrong with the fundamental theory. We've validated that the fundamental theory actually works, despite the fact that not a single player in a market can be judged 'rational'. The problem is that the time frame over what it works is so long that the theory is useless, no matter how true it is -- by the time the market converges on a rational price for a commodity, market conditions have changed so much that said rational price is no longer rational.

Consider an integration using Newton's Method of a function where the function itself changes over time. If you converge the series to an acceptable number of decimal places you find an answer, but it is no longer the correct answer because the base function has now changed! That is the situation that the rational markets people find themselves in -- and refuse to admit, because admitting that the convergence takes so long that the fundamentals have changed and thus the market's original "ideal price" is no longer applicable is admitting that their theory is useless in real life.

- Badtux the Mathematical Penguin

Jazzbumpa said...

You're throwing a lot of unfamiliar stuff at me (I'm a materials guy: glass, rubber, lubricants - in varying degrees) so I want to make sure I'm getting this right.

But first, there are a number of ways of rationally estimating theoretical value for a company - Net present value of future dividend cash flow, for example. Of course they all involve a number of assumptions, and therefore have a level of uncertainly that is probably close to indeterminate.

So the FMF gets to define the right number of tokens for a neuron to expend or a given investment. And the neurons use trial and error (hence the random walk) to determine success vs failure, and via some feedback mechanism there is a learning process that informs future decisions. But success and failure is not as simple as profit vs bankruptcy, since fund Mgr A has to outperform fund Mgr B, and the aggregate Mkt. Many profitable situations are not considered successes. I don't how this effects the neural network analogy.

Anyway, the neurons don't have to be rational, but isn't important that they not be irrational - as in exuberance, frex?

And, in a market where there are many millions of transactions per day, with billions of tokens changing hands, why would it take years to understand what market value at time X ought to be?

And if it does, isn't it irrational to play the game?

JzB the don't know nuthin' bout no neural networks trombonist.

BadTux said...

Well, the deal is that we're getting the reinforcement on a quarterly basis, when the quarterly results are released. Meanwhile the suitcase x-ray machine's neural network widget is getting confronted with thousands upon thousands of "bomb... not bomb..." images per second (in random order), and being given immediate feedback as to whether it was correct or not. BTW, this Bayesian process is also the fundamental process underlying spam filtering, which is why email providers like Gmail and Hotmail that have hundreds of thousands of customers individually training their spam filters with "spam" / "not spam" indications tend to have less spam getting into their inboxes than smaller email providers.

Bayesian filters converge in roughly ten thousand sample messages before they start getting reasonably reliable in their "spam"/"not spam" decisions. This would indicate that for any particular market that has, say, a dozen real competitors, we would need approximately 208 years for the series to converge... errrmmm....

"And if it does [take years to converge], isn't it irrational to play the game?"

Uhm, erm... yeah :). It just goes to show that the rational expectations folks aren't exactly rational, heh!

- Badtux the Mathematics Penguin