The Adaptive Market Hypothesis and its implementation in a Trading System

In finance, the adaptive market hypothesis (AMH) is the theory that financial markets evolve and adapt to changing conditions, which in turn affects market participants' behavior. The AMH has been used to explain everything from asset prices to trading volume.

In his book, "Adaptive Markets: Financial Evolution at the Speed of Thought," Dr. Andrew Lo proposes the Adaptive Market Hypothesis, a new way of thinking about financial markets. According to the hypothesis, financial markets are constantly evolving and adapting to changing conditions. This means that what works today may not work tomorrow, and vice versa. Lo's research suggested that market participants must adapt their behavior to survive. The hypothesis has since been used to explain a wide range of phenomena, from asset prices to trading volume.

One of the key predictions of the adaptive market hypothesis is that efficient markets do not exist. This goes against the traditional view of the Efficient Market Hypothesis (EMH) in the financial markets, which holds that prices always reflect all available information. Instead, the AMH states that prices are only ever a best guess and that they will always be subject to change as new information becomes available.

The Adaptive Market Hypothesis is based on the idea of natural selection. Just as Darwin's theory of evolution states that only the fittest survive, Lo's hypothesis states that only the most adaptable market participants will survive and prosper in the long run. The adaptive market hypothesis has also been used to explain why some traders are more successful than those who cling to outdated methods or refuse to change their approach. It suggests that it is not just luck or skill that determines success but also the ability to adapt to changing market conditions. Also, investors who can identify companies that are adaptable and have a history of success in changing environments are also more likely to achieve long-term success.

This view has been supported by several empirical studies, which have shown that even the most efficient markets are subject to sudden and large swings. For example, in October 1987, the US stock market crashed by over 20% in a single day, despite no obvious fundamental reason for the sell-off. Or the more recent pandemic market crash of 2020 which was unprecedented. All these require traders to react and adapt rapidly to leverage the market.


How AMH can be implemented in a trading system? 

One interesting idea from the world of statistics is that of conditional probability. This can help you understand how likely it is for something to happen given that something else has already happened. For example, if you know that a stock has gone up for the past five days, you can use conditional probability to estimate the likelihood that it will continue going up over the next five days. This provides an interesting mechanism to model AMH as the conditional probability model beliefs can be dynamically updated as new information comes in. If you use conditional probability in conjunction with the AMH, you can get a better sense of how likely it is for a particular stock to continue going up (or down) and make more informed investment decisions accordingly.

How machine learning can be used to leverage conditional probability and AMH is using something like a Bayesian Belief Network model (BBN). This is a graphical model that encodes probabilistic relationships between variables of interest. BBNs are commonly used in computational finance and other decision-making contexts in which uncertainty is present.


How BBNs Work?


BBNs are composed of two types of nodes: chance nodes and decision nodes. Chance nodes represent random variables, while decision nodes represent variables that are under the control of the Decision Maker (DM).

A BBN is fully specified once the set of nodes and their relationships have been determined. The strength of the relationships between variables is represented by conditional probabilities, which can be estimated from data or expert knowledge.

Once a BBN has been constructed, it can be used to answer queries about the state of the world. For example, if the DM wants to know the probability that the interest rate increase by a certain basis point by the Feds would cause the market to either rise or fall by a certain points, they would query the BBN at the node representing the "Feds rate hike" variable. The BBN would then propagate this query through the network using the conditional probabilities, and return an answer to the DM.

Why Use BBNs?

BBNs offer several advantages over other modeling approaches. First, because they are graphical models, they are easy to interpret and understand. This is important in domains like finance, where model transparency is crucial for gaining stakeholder buy-in.

Second, BBNs can easily incorporate evidence from multiple sources of information. This is important in financial modeling, where data may be scarce or unreliable. By combining data with expert knowledge, BBNs can produce more accurate predictions than either data or expert knowledge alone.

Finally, BBNs can be used to make decisions under uncertainty and incorporate knowledge of continuous flow of data. By propagating different scenarios through the network (e.g., different possible outcomes for tomorrow's weather), the DM can compare the expected utility of each scenario and choose the one that is most favorable.

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The best way to approach the market in an adaptive way is to create a set of uncorrelated trading systems that have been designed to work under different market expected and unexpected environments. And then backtest, forward test, and simulation test them.

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