Over- and Under-Reaction in Liquid Markets

High liquidity may not mean high market efficiency


Behavioural Finance teaches us that human beings have biases. Among them is under-reaction, which might best be described as trend- or crowd-following – in violation of the commandment to not covet your neighbour’s goods. The other principal bias is over-reaction, the tendency to become hysterical at reverses, then noticeably overdo your response before somewhat correcting your own actions.

Behavioural Finance plays a significant role in explaining the irrational behavior of investors, including that of professional investors. Though some good examples that illustrate this do exist – notably the recent book by Dan Ariely, “Predictably Irrational”, as well as a more classical collection by Richard H. Thaler, “The Winner’s Curse” – they provide few, if any, practical examples of irrational behavior in actual financial price series.

In the examples alongside (see Fig.1 & Fig.2) we present some direct quantitative statistical testing of raw financial data which gives Behavioural Finance some practical justification. These examples are based on the assumption that if the financial world consisted of only rational agents, then the series of price changes of financial assets would follow a Random Walk. Given this assumption, we can pinpoint inefficiencies by comparing the statistics for price differences (or returns) of a given financial asset to that of a Random Walk.



Various statistical measurement techniques allow us to register and quantify such deviations from Random Walk as existence of serial autocorrelation in price changes (negative or positive); long memory effects; “fat” tails of probability density functions, and multi-scaling or intermittency effects. In this we are more concerned with the purely phenomenological question of the existence of inefficiency, rather than the more complex question of whether it “survives” some transaction costs for a particular trading strategy.

First we will need to look at the price changes of the best known and most liquid index in the world, the S&P 500, traded through E-Mini futures. Due to its ample liquidity, this instrument is widely perceived as very efficient. To analyze the agreement with the Random Walk model, we have considered two simple experiments for which we have used 1-minute back-adjusted futures data since 9/10/1997 (inception) until 8/31/09. The first experiment shows that the S&P 500 index futures market at high-frequencies has a significant excess of simple reversals over sequence or continuation patterns, which is a signature of short-term over-reaction or mean-reversion. The second experiment illustrates such properties as long-term under-reaction and long memory for the same market.

The third experiment confirms the finding of the first experiment: that over-reaction or mean-reversion is concentrated at high-frequencies, although the confirmation was arrived at by different means and addresses a much wider groups of markets, such as global equity index futures and currency futures (see Fig.3 & Fig.4). As the examples alongside involve some of the most liquid futures instruments in the world, this illustrates that high instrument liquidity is not necessarily synonymous with high market efficiency.



To summarize, properly constructed statistical tests of the financial data even for the most liquid financial instruments reveal evidence for both over- and under-reaction, with over-reaction concentrated in shorter time scales. Such and similar tests bridge the gap between the rational scientific view and Behavioural Finance view on quantitative finance. If, according to Behavioural Finance, the source of over- and under-reaction is hidden in human-like properties of the trading agents, then the best way to exploit these inefficiencies is to trade via automated “robots” or algorithms specifically designed to trade against such human-inflicted market inefficiencies.

“Robots” do not need sleep, they are emotionally agnostic, they are free from “anchoring”, and they will relentlessly pursue the objectives built into them. Ironically, their Achilles’ heel is that as these rational “robots” out-perform human traders, the efficiencies described in this article will cease to exist.

Alexei Chekhlov is a Partner and the Portfolio Manager of New York-based Systematic Alpha Management, LLC and a Visiting Assistant Professor at Columbia University