Saturday, April 14, 2012

The "Efficient-as-you-get" Market Hypothesis - Limits to Knowledge

Quantum Entanglement in markets: A new look at the EMH

The concept of tail risk in Chinese housing markets made me think more about the efficient market hypothesis.  If there truly are events that lie beyond the public's ability to predict, how can markets be truly efficient?

No doubt, the strong form of the EMH, which states that anything that is possibly known about an asset is incorporated into its price, seems unreasonable.  Given cognitive limits, it's doubtful that market participants could fully incorporate every shred of information into complex models that, in many instances, are necessarily non-linear and unpredictable.  Even the Weak and Semi-Strong versions have been called into question in light of persistent instances of momentum.  Market bubbles have also sometimes been used as reason to reject the EMH, saying that the fundamental decoupling of prices and fundamental value showing how markets can never be truly efficient.  And then there are the legions of behavioral economists argue that biases such as overconfidence and hyperbolic discounting prove that there are gaps in individual decision making.

These inefficiencies have been thoroughly discussed, but I think they miss another dimension: the fundamental unknowability of future events.  Prediction markets, in theory, incorporate all possible information into their judgments, but they are still contingent on what public information is available.  Also, just because prediction markets are more accurate than other forecasts, it doesn't mean they're sufficiently accurate to support highly leveraged and fragile investments.  The Black Swan events that shake the foundations of markets are, by definition, unknown unknowns.  These Black Swans can be even more pernicious because the information that could predict them may be out there.  However, the market may not be able to piece the information together, whether due to bounded rationality or the fact that certain information is not always public.  In the end, it may be these rogue investments that weren't obvious that makes much of the other information observed irrelevant.  Thus, this new formulation of the EMH differs from the other formulations by rejecting the idea that all information is incorporated.  Not all of it is, and if it is it might not be truly understood.

But what impact does this have on the practical application of the EMH?  Are there any meaningful practical implications that can be drawn from the fallibility of information inefficient markets?  On this issue, I like to view it like attempts to use quantum entanglement to transfer messages over long distances.  The theory of quantum entanglement offers a way to transfer a signal faster than the speed of light, but the information transferred is random.  As a result, no net, low entropy information can be communicated at faster than the speed of light .  As applied to markets, the EMH would say that even if prices deviate from their fundamental value, the deviation does not convey any information because there's no apriori way to know what the fundamental value is. Even if there's information that's not incorporated into the price, there's no way for you to know what the new information is, or how that new information should interact with the accumulated knowledge of all the other investors.  You don't know what the price is telling you.  The errors are unknowable ex-ante, and only obvious ex-post.

This model incorporates several aspects of the EMH and criticisms thereof very nicely.  First, it still maintains that there's no point in playing the market.  Even if prices don't reflect all information, it's impossible for you to consistently pluck reality out, save with enough time and invisible hands.  It's pointless to get good at trading, because the excess returns will always be gobbled up by firms who are smarter and computers that are faster.  When companies trade on the basis of milliseconds, do you really think your human thinking will get you anywhere?  This makes advertisements for the Online Trading Academy particularly laughable.  Pity in all those finance mini-lessons they don't teach the foundation of financial theory.

Second, crises don't disprove this formulation of the EMH.  "Seismic" price adjustments don't occur in any predictable manner, which means mispricings are random.  The price adjustment may not have even been the result of a new discovery of information, it could have just arisen from a new conceptualization of the already available information.  Again, there's no way to predict from the past.  This would then lead to Scott Sumner's disdain for tighter subprime regulation as a possible solution to 2006 housing bubble (my emphasis):
One can look at the sub-prime fiasco from a theoretical perspective, or a empirical perspective, but what one cannot do is compare an ideal regulatory scheme to actual banking practices.  No one doubts that we would be better off if we could go back in time and install a regulation banning sub-prime mortgages in 2004.  But if we had that ability, the bankers would have also known what was coming, and would never had made the loans in the first place.
Hindsight is 20/20; the efficiency of markets is a ex-ante postulate, not an ex-post proof.

Third, informational criticisms based on computer science seem to be particularly non-sensical.  This random information argument is not "perfect markets everywhere", but rather "ok markets everywhere".  Additionally, this new interpretation of the EMH actually focuses on limited rationality that is the result of algorithms that can only run in polynomial time.  But even if markets aren't efficient, there's no way for you to exploit it.  If there are more efficient allocations, your central planning algorithms can't target them on a case-by-case basis.

Fourth, while we can't prepare for any individual crisis, we can still take stock of certain warning signs.  With regard to these warning signs, I'm talking about payoffs, and not probabilities.  There are certain limits to our conception of small probabilities, but it's not infeasible to consider the issue of impact.  On this issue, I think specifically about the impact of debt.  Debt financed cycles seem to be particularly problematic, as they magnify the impact of the crisis.  I have no idea what's the fundamental stable value for debt, but I can definitely be scared of the deleveraging effects of debt.  The fragility of the financial system becomes really apparent when small shocks can propagate themselves through chains of defaults.

As a result, policy should be geared towards moderating these aggregates, such as debt, that give rise to fragility.  These may not allow policy makers to avoid crises, but the reduction in fragility should have substantial benefit in reducing the severity of crises.  NGDP targeting can even have a powerful role in this regard, as given enough crises, the high leverage strategy would become dominated by the more conservative strategy as the government could allow the fragile banks to fall apart.

This policy recommendation might seem a bit peculiar; if markets are truly efficient, how can the government have any recommendations for it?  As the argument for market efficiency is fundamentally an informational one, it's possible that information about systemic issues may be substantially less obvious than the fundamentals underlying each asset price.  But more importantly, the concern about the market aggregates arises less from an understanding of whether the crisis will unfold, but rather if the crisis unfolds.  I don't really know what a safe level of debt is and my estimates may be randomly wrong, but I don't want to be caught on the wrong side of the skew left distribution.  Nobody knows, but the individual investor is at freedom to guess wrong; he or she can take the chance.  However, policy makers are tasked with averting these large scale systemic crises, and therefore have to be much more aware of the fragility inducing effects of debt.

So while markets may not incorporate all information into prices, it's a fool's errand to try to figure out what the excluded information is.  Yet while markets may be efficient for investors, regulators may want to be aware of factors that lead to large scale systemic crises outside the domain of traditional models.  It's this focus on payoff, and not probabilities, that forms the basis of activist policy in an "efficient" market.

Edit: More analysis on the issue of timing


  1. "Debt financed cycles seem to be particularly problematic, as they magnify the impact of the crisis. The fragility of the financial system becomes really apparent when small shocks can propagate themselves through chains of defaults."

    But part of the goal for debt financed cycles is to moderate fragility. Assuming at the time of the crisis, consumers and businesses are in debt, government policy is (in emotional terms) geared to moderate fear in decisions. I understand that chains of defaults in government spending will only disrupt financial markets more (obvious example is Europe), but debt-induced stimulus can also have a positive impact on fragile markets.

  2. Frank,

    I can't deny the first order effects of a bailout; TARP has seemed to be quite effective in saving the financial industry and getting it back on its feet. However, it seems like there's an issue with fragility here. Instead of making it more resilient to shocks, now all we have is a financial industry that's alive but still linked and built in the same fragile manner.

    The fundamental issue when having to think about tail risk is that it's fundamentally unpredictable. We can never know what is an "acceptable" amount, because there's no way to measure. Low probability events are, by definition, intractable.

    Another issue is how does the government know what level of debt is acceptable? I've read Koo; I find his theory of a balance sheet recession quite interesting. Yet, how do we control this growth of debt? On your page, I noticed that you seem to like considering the role of institutions. What do you think would be a productive institutional shift to help with the bias towards debt?

    Thanks for Reading,


  3. Very interesting question. On the top of my head, one thing comes to mind.

    When it comes to household debt, our current financial institutions are geared towards taking large amounts of risk, without really understanding the true volatility of the markets. With the democratization of trading/investing technology (think eTrade), more households are taking risks with their money when they don't quite understand the full risks associated with them. Indeed, I would argue this was the case for pre-recession households, when families were taking out loans that they just couldn't afford.

    I think this is one of the biggest dilemmas we have in today's financial markets. But I don't quite know how to address it from an institutional standpoint. It seems as if investment transaction costs have fallen so low, but information about risks remains widely imbalanced.