Standard economic theory
Standard economic theory would predict that markets are efficient. This means that stock prices reflect all available information such that there is no way for any given investor to, on average, make money off the markes. This also means that when we buy a stock we are paying the fair price.
Empirical evidence
Empirical observations such as excess volatility suggest that markets are not efficient. Excess volatility refers to the stylized fact that actual stock prices move much more than their fundamental value does. This is a mathematical contradiction because the prices, when efficient, are an unbiased estimate of the fundamental value given all available information (including the price itself). Yet it would seem that, on average, high prices imply overpriced stocks and low prices undervalued.
Behavioural theories
Some researchers (e.g. Lo, 2004) have posited the idea that heuristics in human behaviour could create a market whereby markets are, at times, inefficient. Human heuristics are necessary to approximate optimal behaviour without having to use extremely complicated mathematical formulas which only even work under simplifying assumptions which may not hold in the real world.
Overview
Our model explores one of these behavioural theories. Namely, what if agents base their strategizing strategies off of what their most successful friends do? Then, one can imagine waves of speculation as everyone rushes to buy into stocks as quick as possible since the first one there makes the most money — as a real life example, take the 2000 dot com bubble.
Trading strategies
We include 3 investing strategies for the agents in our model:
The network
Agents are initialised on a Watts–Strogatz small-world network. Each period they submit their trades based on their strategy and at the end of the round a new price is calculated. Each agent’s utility is then computed based on capital gains (or losses) and dividends (these are negative for overvalued stocks). With some probability, agents in each period chose the most profitable strategy of the agents they are connected to. The fundamental value is updated stochastically in each period. We run each simulation over 100 timesteps.
Learning and network topology
Our main experiment was iterating over two variables: (1) the probability that an agent chooses another more profitable strategy, and (2) how many other nodes each node is connected to. The first one is the primary mechanism that we theorised to cause excess market volatility. Namely, we predict when agents are quick to copy their neighbour’s markets can become unstable. The network topology is an interesting study because the world is and has become ever more connected through the internet and social media. Platforms such as WallStreetBets on Reddit have arisen, which allow traders to quickly communicate their strategies with a vast audience. The dependent variable we study is the average squared deviation of price from fundamental value — a very intuitive measure of market inefficiency. The results of a parameter sweep with 100 iterations of the model over 100 timesteps is seen in the figure below.
A Theory of Learning Behaviour and Asset Prices
Cyrus Redjaee, Andrew Kaplan
University of Michigan
Market efficiency
The model
Results