Adaptive Markets

(Image: Zen Buddha Silence by Marilyn Barbone.)

May 28, 2017

Adaptive Markets (Princeton University Press, 2017) is an interesting book by Andrew W. Lo. Lo considers whether an Adaptive Markets Hypothesis can potentially supplantthe Efficient Markets Hypothesis (EMH).

The EMH states that an asset price fully reflects all available information. Most people agree that the U.S. stock market, for example, is highly efficient most of the time. And it's clear that the best long-term investment for most investors is a low-cost, broad market index fund.

THE BIRTH OF EFFICIENT MARKETS

The famous economist, Paul Samuelson, thought that markets are efficient:

Samuelson reasoned as follows. If investors were able to incorporate all the potential impact of future events on an asset's price today, then future price changes could not be predicted based on any of today's information. If they could, investors would have used that information in the first place. As a result, prices must move unpredictably. If a market is informationally efficient - that is, if prices fully incorporate the expectations of all the players in the market - then the following price changes will necessarily be impossible to forecast. (page 21)

Finance professor Eugene F. Fama put it as follows:

An "efficient" market is defined as a market where there are large numbers of rational profit-maximizers actively competing, with each trying to predict future market values of individual securities, and where important current information is almost freely available to all participants... In an efficient market, on the average, competition will cause the full effects of new information on intrinsic values to be reflected "instantaneously" in actual prices.

As a side note, while Samuelson believed in the EMH, he also recognized that at least a few investors were clearly capable of beating the market over time. Samuelson purchased stock in Berkshire Hathaway because he knew that Warren Buffett and Charlie Munger had an outstanding long-term record of outperformance that was likely to continue.

But Buffett has repeatedly - and correctly - argued that most investors would be best off buying and holding index funds. Buffett has given the same advice to his friends of modest means. See: https://boolefund.com/warren-buffett-jack-bogle/

BOUNDED RATIONALITY

The Efficient Markets Hypothesis has often been interpreted as implying that human beings, at least in their market behavior, can be modeled as rational agents. Herbert Simon, a polymath who was the first psychologist to receive the Nobel Prize for Economics, disagreed with the notion that human beings are rational.

According to Simon, when people make economic forecasts, they use only part of the available information and they do not process this information with perfect rationality. Simon called thisbounded rationality. Lo writes that other economists, including Milton Friedman, believed in the theory ofadaptive expectations, according to which people use earlier circumstances to shape their future expectations. In a world ofbounded rationality, markets are often not perfectly efficient. Supply and demand will often notreach a rational equilibrium.

John Muth argued, however, in favor of a theory ofrational expectations. In this view, even if individual agents are not perfectly rational, markets themselves reach a rational equilibrium. Muth was not saying that every agent is rational, only that markets behave as ifagents were rational.

Simon supported Muth's theory. Lo quotes Simon:

Jack clearly deserves the Nobel for it, even though I do not think it describes the real world correctly. Sometimes an idea that is not literally correct can have great scientific importance.

PREDICTION MARKETS

Lo writes that we can use the power of efficient markets in order to determine the probability of various events such as elections.

In fact, such markets already exist. They're called prediction markets because that's exactly what they do - make predictions. Their structure is fiendishly simple: create a financial security that pays $1 dollar if a particular future event takes place, and pays nothing if it doesn't. Through the wisdom of crowds and the power of efficient markets, the current price of this security will reflect the market's assessment of the likelihood of this future event. (page 38)

Lo writes that even in the nineteenth and early twentieth century, prediction markets were used in the United States to forecast elections. Even then, prediction markets were viewed as producing the most accurate information about elections.

PROBABILITY MATCHING

An experiment psychologists have done many times is as follows. Every sixty seconds, "A" or "B" appears on the computer screen. Each time before that happens, the subject must guess whether it will be "A" or "B". If they're right they get $1. If they're wrong they lose $1.

What is the optimal strategy? If there's a fifty-fifty chance of "A" or "B", then there is no optimal strategy. But if "A" appears 75% of the time, then the optimal strategy is to choose "A" every time. By picking "A" 100% of the time, the subject will be right 75% of the time. Picking "A" less than 100% of the time will lead to a lower total payoff over time.

But in that scenario where "A" appears 75% of the time, people don't pick "A" 100% of the time. Instead, people pick "A" 75% of the time. This is called probability matching. It's not the optimal strategy for this scenario, although it's better than random guessing. Why do people do probability matching?

Andrew Lo and his collaborator Tom Brennan have come up with possible theory to explain probability matching. They call it thebinary choice model.

Lo says to consider a creature called a tribble. This creature either lives on a plateau or in a valley during its life. It also reproduces once, creating three offspring if it can, and then dies. The tribble has to make one important decision during its life: whether to live on the plateau or in the valley.

The weather is also simple. Either it's sunny or rainy. If it turns out to be sunny, then living in the valley allows the tribble and any offspring to survive, while living on the plateau means they all perish. But if it rains, then living on the plateau means life while living in the valley means death.

Lo then asks us to consider the following scenario: the probability of sunshine is 75%, while the probability of rain is 25%. If that's the case, then what is the optimal strategy for the tribble? Lo next asks us to imagine the different tribbles have different heuristics. Some tribbles have a deterministic strategy of always picking the valley. This means that if it's sunny 75% of the time, this particular group will reproduce the fastest. So these tribbles appear to be rational optimizers according the economic theory.

The only problem for these optimizers is that when it rains, they are completely wiped out. Lo explains:

In the same way, the tribbles who always choose to nest on the plateau will become extinct the first time the sun shines. It turns out that the only heuristics that can persist over time are those involving some form of randomizing behavior. For tribbles with those heuristics, some portion of them in each generation will choose to nest in the valley, and the remainder will nest on the plateau. No matter whether it rains or shines, a fraction of these types of tribbles will survive and be able to reproduce, passing on their heuristic to the next generation. (page 192)

Lo asks: Which group of tribbles grows the fastest over time? In other words, which group is making the optimizing decision for long-term survival? The group that uses probability matching achieves the highest long-term growth rate. If it is sunny 75% of the time, the group that chooses the valley 75% of the time will grow faster than any other group over time. Based on thisbinary choice model, probability matching is the best long-term biologicalstrategy for survival - not for each individual tribble, but for the entire group.

BOOLE MICROCAP FUND

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There are 15-25 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 10-15% (at cost), while the average position is 5-7% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The goal of the Boole Microcap Fund is to outperform the Russell Microcap Index over time, net of fees. The Boole Fund has low fees.

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: jb@boolefund.com

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