The Efficient Market, Debugged

What is the link between the price discovery process and fixing software bugs? In a debugging process, one can never eliminate all the bugs. This is because fixing a known bug can potentially create more unknown bugs, implying that there exists a point of diminishing returns where fixing more bugs will not yield any more benefits.

The stock market shares the same essential characteristics as open source software: anyone can participate. In the stock market, anyone can buy and sell securities. Likewise, any programmer can participate in an open source project. When a stock market participant discovers the “solution” to a price (i.e. fixes a bug) based on certain information that he’d gathered, he will simultaneously affect the price (i.e. creates a bug). This newly arrived at price becomes a new piece of information that acts as a signal to other traders who cause the price to change again (i.e. creates more bugs). And because not all bugs can be fixed, prices at any time cannot be correct and never will be.

How much money should one devote to “fixing bugs” in the stock market at most? The answer is: spend money up to the point of diminishing returns! This point is defined simply by the Kelly Criterion.

Where E[r] is the expected return, r_f is the risk-free rate of borrowing and lending, and s² is the variance of the expected return.

Wealth is destroyed when more resources are allocated than necessary (Kelly Criterion’s f). This is exactly what caused the current boom / bust cycle of the finance industry – there was simply too much finance. The society had overspent its resources (beyond the point of diminishing returns) to making the markets more efficient. Isn’t it ironic that in the pursuit of more efficiency, we have made it more inefficient, and destroyed our own wealth?

Comments

[morph366:]

Always refreshing to be presented with a new model for thinking about markets - and the equation is quite elegant.
I'm unclear as to whether you take the EMH (Efficient Market Hypothesis) as a given. There's a lot of evidence - noisy markets, abnormally successful long term investors etc. - which suggests that EMH is a fallacy.
Also I don't quite follow your reasoning about too much finance- are you equating that somehow with overspending resources? What would add a whole new level of complexity to your simple model is the role of credit and leverage in the financial economy and that alas is also something that the EMH fails to address.

Feb 08 05:14 AM

[Ferdinand E...:]

Funny, isn't it. I taught international finance for about 15 years, and I never ran into this so-called Kelly criterion. Of course, if I had run into it I would have informed anyone who wanted to discuss it that it was probably a crock.

Incidentally Morph366, Eurgene Fama should win a nobel in economics any year now. If you really and truly believe that the EMH is a fallacy, attend one of his lectures and inform him of your belief. I don't think that he will praise your insight.

Feb 08 09:13 AM

[J. Stevens:]

I find the opening to your piece somewhat fanciful, however what really popped out at me is your description of the Kelly Criterion (i.e., Optimal-f). This is incorrect.

The Kelly formula is often expressed as: ((g+1)*p-1)/g

Where, g = the ratio of the amount gained when there is a gain, over the amount lost when there is a loss; and p = probability of a gain.

While I’ve never seen anyone else break this down before, this is simply the mathematical equivalent of: M/ag

Where M = the mean return; and ag = the average gain when there is a gain.

Your description on the other hand, (expected return - risk-free rate) / variance, sounds more like a description of the Sharpe Ratio, where variance would be the standard deviation of returns (not SD squared, which is how you have it illustrated in your formula (“s2”).

Feb 08 12:41 PM

[auto44:]

I don't think Warren Buffet uses all these fancy formulas and he seems perfectly capable of exploiting market inefficiency. I am sure he is a very smart man and has no trouble understanding them but he states the highest math he ever employs is simple algebra and dosen't use that very often.

Feb 08 01:39 PM

[Sigmund:]

The 'Efficient Market Hypothesis' is bunkum!! There is ample evidence that markets march thru equilibrium points with great regularity. An important cause of this phenomena is that supply tends to be specific in the short run while demand is subjective. Similarly; why do so many price time series demonstrate such high propensity for mean reversion? The sigma for mean reverrting price series is a clear and definitive rejection of the Efficient Market Hypothesis! Interestingly, it does not matter whether one is considering an absolutely free market or a managed one, markets do fail.

Feb 08 02:38 PM