On Over- and Under- Reaction in Liquid Markets

2-3 February, 2010The Interface of Behavioural Finance and Quantitative Finance1

On Over- and Under- On Over- and Under- Reaction in Liquid MarketsReaction in Liquid Markets

Alexei ChekhlovColumbia UniversitySystematic Alpha Management, LLC


MotivationMotivationBehavioral Finance (BF) vs. Statistical Physics (SP): BF has gained some popularity in illustrating irrational behavior of investors (including that of “professional investors”). BF however offers little help in analysis of actual financial historical data. After some significant progress in explaining many complex natural phenomena (such as: critical phenomena, turbulence, for example) SP has produced numerous rational means for such analyses. Phenomenological Approach. Hard science approach to finance (theoretical math, theoretical finance & economics) has been disproportionally over-focused on creation of theoretical models rather then (as SP approach would be) on verification of any model against the actual experiment, i.e. financial data. Our approach is not to impose our model on the financial reality, but rather to listen to what the data is “telling” us. Careful Use of Simple Statistical Measurements: We would like to focus on the question of robust existence of a certain price behaviour rather than on the existence (or non-existence) of a profitable trading strategy based on it under some transaction cost (and other) assumptions.


We would assume that “if the financial world consisted only of rational agents” – the financial price series of any “liquidly traded” financial asset were to follow a RW. The question of looking for price inefficiencies we replace with the question of studying the differences in statistics of price differences with that of RW. As our approach will be phenomenological and statistical – “the more data – the better”, with the necessary checks for stationarity. Illustrative examples in the high-frequency cases (1-minute resolution) are the most liquid futures such as: S&P 500 E-Mini, NASDAQ 100 E-Mini, Dow Jones mini, FTSE-100, CAC 40, DAX, D.J. Euro Stoxx 50, Gold, Crude Oil, Euro, British Pound, Swiss Franc, Japanese Yen, Canadian Dollar, and Australian Dollar. Unless otherwise mentioned, the sample is “all”, that is, since inception until present. Characteristic number of records in such time series is 1 million (for example: 1.2 million for S&P 500 E-mini, 2.1 million for British Pound). Illustrative example in the daily resolution case is: the survivorship bias-free universe of all U.S. traded equities. Here, the sample of around 19,000 of tickers/QUSIPs was taken from 1992 until present.

Comparisons with Random Walk (RW)Comparisons with Random Walk (RW)


Over-Reaction. Mean-reversion, when agents over-react to new information by overselling on new bad information with later correction and/or over-buying on good new information with later opposite correction. Under-Reaction. Trend-following, when agents under-react to new information, by establishing a partial position, waiting for confirmations to their actions from other agents. Once received, they continue to increase their position in the same direction – self-reinforcement. Thus, through delayed chain reactions, the new information is gradually priced into the market.

Two Simple Biases or Two Simple Biases or PredictabilitiesPredictabilities


Data type used: 1 minute frequency, back-adjusted futures since inception (different for each market) until present. Markets studied: S&P 500 E-mini (ES); D.J. Euro STOXX 50 (VG), Euro (EC); British Pound (BP); Gold (GC); Crude Oil (CL). In both of these experiments the frequency (1-minute) is chosen to: be small enough in order to reveal the self-similar statistical properties within the continuous price assumption p=p(t), and be large enough as compared to the so-called “bid-ask bounce” (“fake” mean-reversion). This can be easily verified by comparing the standard deviation of 1-minute price changes with the average ask-bid spread, the standard deviation has to be several times (5-10) larger. Both experiments are inspired by early experiments of Andrew W. Lo (summarized in Campbell, Lo, MacKinlay, “The Econometrics of Financial Markets”).

Experiments 1 & 2Experiments 1 & 2


Experiment 1: Counting Experiment 1: Counting Continuations and ReversalsContinuations and Reversals

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Evidence of short-term (up to a couple of hours) over-reaction or mean-reversion and longer-term (beyond a day) under-reaction or trend-following; Short-term over-reaction or mean-reversion is quite strong and robust statistically, is present in all markets studied. Longer-term under-reaction or trend-following is weaker and less robust statistically, is observed in all markets in the set but the D.J. Euro STOXX 50. The agreement with the RW model gets better as time-separation gets larger.


Experiment 2: Counting Up- and Experiment 2: Counting Up- and Down- TrendsDown- Trends

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Not only the numbers of trends above theoretical values indicate under-reaction or trend-following behaviour, but conversely, the numbers of trends below theoretical values indicate possible over-reaction or mean-reversion; There is a reasonable agreement between the two experiments, although this experiment provides further evidence on how weak the under-reaction or trend-following regime is;Short length trends counts have better agreement with the RW formulas.


Experiment 3: Variance Ratio Experiment 3: Variance Ratio TestTest

We will now transition from the signs under- and over-reaction to the price change under- and over-reaction studies; We will estimate the Variance Ratio for a set of two very liquid futures markets: equity indices and currencies;Time series will be taken since inception to present at 1-min resolution with time-separation from 1 min to 90 trading hours, during most liquid session (pit session);Equity index futures: S&P 500 E-Mini, NASDAQ 100 E-Mini, Dow Jones mini, FTSE-100, CAC 40, DAX, D.J. Euro STOXX; Currency futures: Euro, British Pound, Swiss Franc, Japanese Yen, Canadian Dollar, Australian Dollar.



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General inspection of the test results confirms the previous sign-tests results: a general pattern is statistically strong short-term over-reaction or mean-reversion, beyond which either inconclusive results or statistically weaker, selective longer-term under-reaction or trend-following properties; Beyond a couple of trading days time-separation shows virtually no predictabilities (flat VR);This test is more general than the previous two price signs tests because it considers both the price change sign and magnitude - positive; This test could be somewhat biased if the price-difference distributions function is “fat tailed” – negative.


Experiment 4: Price Response in Experiment 4: Price Response in Stocks Conditional on Earnings Stocks Conditional on Earnings

“Surprise”“Surprise”Price data frequency is daily, accounting variables frequency is quarterly, however recorded at a certain precise announcement date; The database is a full merger of two sources: survivorship-bias-free CRSP database and proprietary Bloomberg Back Office product for the accounting variables;Surprise is not based on analysts (IBES), but technically determined by me; The database consists of over 19,000 tickers/CUSIPS from 1992 until present.



“Surprise”“Surprise”

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“Surprise”“Surprise”

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“Surprise”“Surprise”On the Open of the day subsequent to the announcement date the stock will be bought if it has a Positive Surprise and sold if it has a Negative Surprise, minus the transaction cost; Once in a position, the total return will be calculated at the end of each subsequent day from 1 up to 50 days in a position;Both total cumulative and daily return in such position average over all such events and all times conditional on separately Positive and Negative Surprises will be measured (Conditional Response).

measured. be willSurprise Negative

and ,Surprise Positive

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“Surprise”“Surprise”In the case of “Positive Surprise” filter we observe a strong long-term (up to 20 days) under-reaction in both absolute compounded and market-neutral (with S&P 500 return subtracted out) forms; In the case of “Negative Surprise” filter we observe a strong short-term (up to 5 days) over-reaction in both absolute compounded and market-neutral (with S&P 500 return subtracted out) forms;Although the sample size however large is still smaller than in the previous high-frequency cases, we did not find any statistical biases in these results, we did not find a dependency on market cap, growth-value factor or bull or bear market; There is a small evidence to the so-called “dead cat bounce” effect in the negative surprise filter.


SummarySummary

Properly constructed statistical tests of the financial data for most liquid financial instruments can reveal sufficient evidence for both over- and under-reaction.

In contrast with classical finance, more liquidity does not necessarily mean more efficiency.

Shorter time scales (minutes-to-hours) over-reaction and longer time scales (over a couple of days) under-reaction seem to be a reasonably general pattern.

Such and similar tests bridge the gap between BF and SP.

If the source of over- and under-reaction is hidden in human-like properties of the trading agents, then there is a possibility of reduction/elimination of such inefficiencies with the replacement of human trading agents with the non-human ones.

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On Over- and Under- Reaction in Liquid Markets

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