Longterm price overreactions: are markets inefficient?
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Abstract
This paper examines longterm price overreactions in various financial markets (commodities, US stock market and FOREX). First, a number of statistical tests are carried out for overreactions as a statistical phenomenon. Second, a trading robot approach is applied to test the profitability of two alternative strategies, one based on the classical overreaction anomaly, the other on a socalled “inertia anomaly”. Both weekly and monthly data are used. Evidence of anomalies is found predominantly in the case of weekly data. In the majority of cases strategies based on overreaction anomalies are not profitable, and therefore the latter cannot be seen as inconsistent with the EMH.
Keywords
Efficient market hypothesis Anomaly Overreaction hypothesis Abnormal returns Contrarian strategy Trading strategy Trading robot Inertia anomalyJEL Classification
G12 G17 C631 Introduction
The Efficient Market Hypothesis (EMH) is one of the central tenets of financial economics (Fama 1965). However, the empirical literature has provided extensive evidence of various “anomalies”, such as fat tails, volatility clustering, long memory etc. that are inconsistent with the EMH paradigm and suggests that it is possible to make abnormal profits using appropriate trading strategies (Plastun 2017). A wellknown anomaly is the socalled overreaction hypothesis, namely the idea that agents make investment decisions giving disproportionate weight to more recent information (see De Bondt and Thaler 1985). Clements et al. (2009) report that the overreaction anomaly has not only persisted but in fact increased over the last twenty years. Its existence has been documented in several studies for different markets and frequencies such as monthly, weekly or daily data (see, e.g., Bremer and Sweeney 1991; Clare and Thomas 1995; Larson and Madura 2003; Mynhardt and Plastun 2013; Caporale et al. 2018).
There exist a significant number of studies on market overreactions but most of them analyse shortterm price overreactions based on daily data (Atkins and Dyl 1990; Bremer and Sweeney 1991; Cox and Peterson 1994; Choi and Jayaraman 2009) and focus only on a single market/asset. By contrast, this paper analyses longterm overreactions and a variety of markets and frequencies by (i) carrying out various statistical tests to establish whether overreaction anomalies exist using both weekly and monthly data, and (ii) using a trading robot method to examine whether they give rise to exploitable profit opportunities, i.e. whether price overreactions are simply a statistical phenomena or can also be seen as evidence against the EMH. The analysis is carried out for various financial markets: the US stock market (the Dow Jones Index and 10 companies included in this index), FOREX (10 currency pairs) and commodity markets (gold and oil). A similar investigation was carried out by Caporale et al. (2018); however, their analysis focused on shortterm (i.e., daily) overreactions, whilst the present study considers a longer horizon, namely a week or a month.
The remainder of the paper is organised as follows. Section 2 reviews the existing literature on the overreaction hypothesis. Section 3 describes the methodology used in this study. Section 4 discusses the empirical results. Section 5 provides some concluding remarks.
2 Literature review
The seminal paper on the overreaction hypothesis is due to De Bondt and Thaler (DT, De Bondt and Thaler 1985), who followed the work of Kahneman and Tversky (1982), and showed that the best (worst) performing portfolios in the NYSE over a threeyear period tended to under (over)perform over the following threeyear period. Their explanation was that significant deviations of asset prices from their fundamental value occur because of agents’ irrational behaviour, with recent news being given an excessive weight. DT also reported an asymmetry in the overreaction (it is bigger for undervalued than for overvalued stocks), and a “January effect”, with a clustering of overreactions in that particular month.
Other studies include Brown et al. (1988), who analysed NYSE data for the period 1946–1983 and reached similar conclusions to DT; Ferri and Min (1996), who confirmed the presence of overreactions using S&P 500 data for the period 1962–1991; Larson and Madura (2003), who used NYSE data for the period 1988–1998 and also showed the presence of overreactions. Clements et al. (2009) confirmed the original findings of DT using CRSP data for the period 1926–1982, and also showed that the overreaction anomaly had increased during the following twenty years.
In addition to papers analysing stock markets (Alonso and Rubio 1990; Brailsford 1992; Bowman and Iverson 1998; Antoniou et al. 2005; Mynhardt and Plastun 2013 among others), some consider other markets such as the gold (Cutler et al. (1991)), or the options market (Poteshman 2001). Finally, Conrad and Kaul (1993) showed that the returns used in many studies (supporting the overreaction hypothesis) are upwardly biased, and “true” returns have no relation to overreaction; therefore this issue is still unresolved.
The other aspect of the overreaction hypothesis is its practical implementation, i.e. the possibility of obtaining extra profits by exploiting this anomaly. Jegadeesh and Titman (1993) and Lehmann (1990) found that a strategy based on overreactions can indeed generate abnormal profits. Baytas and Cakici (1999) also tested a trading strategy based on the overreaction hypothesis, and showed that contrarian portfolios on the longterm horizons can generate significant profits.
The most recent and thorough investigation is due to Caporale et al. (2018), who analyse different financial markets (FOREX, stock and commodity) using the same approach as in the present study. That study shows that a strategy based on countermovements after overreactions does not generate profits in the FOREX and the commodity markets, but it is profitable in the case of the US stock market. Also, it detects a brand new anomaly based on the overreaction hypothesis, i.e. an “inertia” anomaly (after an overreaction day prices tend to move in the same direction for some time). Here we extend the analysis by considering longterm overreactions and the possibility of making extra profits over weekly and monthly intervals. The variety of assets and markets (FOREX, stock market, commodities) as well as of time frequencies (weekly, monthly) considered in this study can help to address issues such as robustness, data snooping, data mining etc. Moreover, since according to the Adaptive Markets Hypothesis (Lo 2004) financial markets evolve and anomalies may disappear during this process, it is important to include the most recent data as we do.
3 Data and methodology
We analyse the following weekly and monthly series: for the US stock market, the Dow Jones index and stocks of two companies included in this index (Microsoft and Boeing  for the trading robot analysis we also add Alcoa, AIG, Walt Disney, General Electric, Home Depot, IBM, Intel, Exxon Mobil); for the FOREX, EURUSD, USDCHF and AUDUSD (for the trading robot analysis also USDJPY, USDCAD, GBPJPY, GBPUSD, EURJPY, GBPCHF, EURGBP); for commodities, gold and oil (only gold for the trading robot analysis owing to data unavailability). The choice of assets is based on their liquidity, trading volume, data availability, and extent of use. The sample covers the period from January 2002 till the end of December 2016, and for the trading robot analysis the period is 2002–2014 for the FOREX and 2006–2014 for the US stock market and commodity market. These dates are selected on the basis of data availability (especially for the purpose of trading robot analysis) and to include the most recent data since markets can evolve as stressed by the Adaptive Market Hypothesis.
3.1 Student’s ttests
First we carry out Student’s ttests to confirm (reject) the presence of anomalies after overreactions. Our dataset is quite large, and therefore on the basis of the Central Limit Theorem (see Mendenhall et al. 2003) it can be argued that normality holds as required for carrying out ttests. To provide additional evidence we also conduct ANOVA analysis, and carry out Mann–Whitney U tests not relying on the normality assumption.
 Y_{t}

volatility on the period t;
 a_{0}

mean volatility for a normal day (the day when there was no volatility explosion);
 a_{1}

dummy coefficient;
 D_{1t}

a dummy variable for a specific data group, equal to 1 when the data belong to a day of volatility explosion, and equal to 0 when they do not;
 ε_{t}

Random error term for period t.
The size, sign and statistical significance of the dummy coefficient provide information about possible anomalies.
Then we apply the trading robot approach to establish whether the detected anomalies create exploitable profit opportunities. According to the classical overreaction hypothesis, an overreaction should be followed by a correction, i.e. price countermovements, and this should be bigger than after normal days. If one day is not enough for the market to incorporate new information, i.e. to overreact, then after oneday abnormal price changes one can expect movements in the direction of the overreaction bigger than after normal days.

H1: Counterreactions after overreactions differ from those after normal periods.

H2: Price movements after overreactions in the direction of the overreaction differ from such movements after normal periods.
The null hypothesis is in both cases that the data after normal and overreaction periods belong to the same population.
 1)
when the current weekly (monthly) return exceeds the average plus one standard deviation
 2)
when the current weekly (monthly) return exceeds the average plus two standard deviations, i.e.,
 3)
when the current weekly (monthly) return exceeds the average plus three standard deviations, i.e.,
The next step is to determine the size of the price movement during the following week (month). For Hypothesis 1 (the counterreaction or countermovement assumption), we measure it as the difference between the next period’s open price and the maximum deviation from it in the opposite direction to the price movement in the overreaction period.
In the case of Hypothesis 2 (movement in the direction of the overreaction), either eq. (9) or (8) is used depending on whether the price has increased or decreased.
Two data sets (with cR_{i + 1} values) are then constructed, including the size of price movements after normal and abnormal price changes respectively. The first data set consists of cR_{i + 1} values after period with abnormal price changes. The second contains cR_{i + 1} values after a period with normal price changes. The null hypothesis to be tested is that they are both drawn from the same population.
3.2 Trading robot analysis
The trading robot approach considers the longterm overreactions from a trader’s viewpoint, i.e. whether it is possible to make abnormal profits by exploiting the overreaction anomaly, and simulates the actions of a trader using an algorithm representing a trading strategy. This is a programme in the MetaTrader terminal that has been developed in MetaQuotes Language 4 (MQL4) and used for the automation of analytical and trading processes. Trading robots (called experts in MetaTrader) allow to analyse price data and manage trading activities on the basis of the signals received.
MetaQuotes Language 4 is the language for programming trade strategies built in the client terminal. The syntax of MQL4 is quite similar to that of the C language. It allows to programme trading robots that automate trade processes and is ideally suited to the implementation of trading strategies. The terminal also allows to check the efficiency of trading robots using historical data. These are saved in the MetaTrader terminal as bars and represent records appearing as TOHLCV (HST format). The trading terminal allows to test experts by various methods. By selecting smaller periods it is possible to see price fluctuations within bars, i.e., price changes will be reproduced more precisely. For example, when an expert is tested on onehour data, price changes for a bar can be modelled using oneminute data. The price history stored in the client terminal includes only Bid prices. In order to model Ask prices, the strategy tester uses the current spread at the beginning of testing. However, a user can set a custom spread for testing in the “Spread”, thereby approximating better actual price movements.

Strategy 1 (based on H1): This is based on the classical overreaction anomaly, i.e. the presence of abnormal counterreactions after the overreaction period. The algorithm is constructed as follows: at the end of the overreaction period financial assets are sold or bought depending on whether abnormal price increases or decreased respectively have occurred. An open position is closed if a target profit value is reached or at the end of the following period (for details of how the target profit value is defined see below).

Strategy 2 (based on H2): This is based on the nonclassical overreaction anomaly, i.e. the presence the abnormal price movements in the direction of the overreaction in the following period. The algorithm is built as follows: at the end of the overreaction period financial assets are bought or sold depending on whether abnormal price increases or decreases respectively have occurred. Again, an open position is closed if a target profit value is reached or at the end of the following period.

Total net profit: this is the difference between “Gross profit” and “Gross loss” measured in US dollars. We used marginal trading with the leverage 1:100, therefore it is necessary to invest $1000 to make the profit mentioned in the Trading Report. The annual return is defined as Total net profit/100, so, for instance, an annual total net profit of $100 represents a 10% annual return on the investment;

Profit trades: % of successful trades in total trades;

Expected payoff: the mathematical expectation of a win. This parameter represents the average profit/loss per trade. It is also the expected profitability/unprofitability of the next trade;

Total trades: total amount of trade positions;

Bars in test: the number of past observations modelled in bars during testing.

Criterion for overreaction (symbol: sigma_dz): the number of standard deviations added to the mean to form the standard period interval;

Period of averaging (period_dz): the size of the data set used to calculate base mean and standard deviation;

Time in position (time_val): how long the opened position has to be held.
We carry out ttests to examine whether the results we obtain are statistically different from the random ones. We chose this approach because the sample size is usually less than 100. A ttest compares the means from two samples to see whether they come from the same population. In our case the first is the average profit/loss factor of one trade applying the trading strategy, and the second is equal to zero because random trading (without transaction costs) should generate zero profit.
The null hypothesis (H0) is that the mean is the same in both samples, and the alternative (H1) that it is not. The computed values of the ttest are compared with the critical one at the 5% significance level. Failure to reject H0 implies that there are no advantages from exploiting the trading strategy being considered, whilst a rejection suggests that the adopted strategy can generate abnormal profits.
ttest for the trading simulation results for Strategy 1 (case of EURUSD, testing period 2001–2014)
Parameter  Value 

Number of the trades  96 
Total profit  −1331.03 
Average profit per trade  −13.86 
Standard deviation  192,27 
ttest  −0.70 
z critical (0,95)  1.78 
Null hypothesis  Accepted 
As can be seen, H0 cannot be rejected, which implies that the trading simulation results are not statistically different from the random ones and therefore this trading strategy is not effective and there is no exploitable profit opportunity.
4 Empirical results
The first step is to set the basic overreaction parameters/criterions by choosing the number of standard deviations (sigma_dz) to be added to the average to form the “standard” period interval for price fluctuations and the averaging period to calculate the mean and the standard deviation (symbol: period_dz).
Number of abnormal returns detections in DowJones index during 1991–2014 (weekly data)
Period_dz  3  5  10  20  30  

Indicator  Number  %  Number  %  Number  %  Number  %  Number  % 
Overall  1241  100  1239  100  1233  100  1223  100  1213  100 
Number of abnormal returns (criterion = mean + sigma_dz)  251  20  239  19  206  17  198  16  198  16 
Number of abnormal returns (criterion = mean + 2*sigma_dz)  0  0  0  0  56  5  65  5  69  6 
Number of abnormal returns (criterion = mean + 3*sigma_dz)  0  0  0  0  0  0  13  1  19  2 
Number of abnormal returns detections in DowJones index during 1991–2014 (monthly data)
Period_dz  3  5  10  20  30  

Indicator  Number  %  Number  %  Number  %  Number  %  Number  % 
Overall  285  100  283  100  278  100  268  100  258  100 
Number of abnormal returns (criterion = mean + sigma_dz)  56  20  52  18  45  16  42  15  44  15 
Number of abnormal returns (criterion = mean + 2*sigma_dz)  0  0  0  0  16  6  20  7  22  8 
Number of abnormal returns (criterion = mean + 3*sigma_dz)  0  0  0  0  0  0  4  1  6  2 
Ttest of the counterreactions after the overreaction for the DowJones index during 1991–2014 (weekly data) for the different values of sigma_dz parameter case of period_dz = 30
Number of standard deviations  1  2  3  

abnormal  normal  abnormal  normal  abnormal  normal  
Number of matches  198  1015  69  1144  19  1194 
Mean  2,36%  1,74%  2,77%  1,78%  3,57%  1,81% 
Standard deviation  2,22%  1,52%  2,43%  1,59%  3,15%  1,62% 
tcriterion  3,91  3,38  2,44  
tcritical (р = 0.95)  1,96  1,96  1,96  
Null hypothesis  rejected  rejected  rejected 
Ttest of the counterreactions after the overreaction for the DowJones index during 1991–2014 (monthly data) for the different values of sigma_dz parameter case of period_dz = 30
Number of standard deviations  1  2  3  

abnormal  normal  abnormal  normal  abnormal  normal  
Number of matches  44  214  22  236  6  252 
Mean  4,39%  3,22%  4,25%  3,34%  7,97%  3,31% 
Standard deviation  4,09%  2,83%  4,37%  2,96%  6,78%  2,90% 
tcriterion  1,90  0,98  1,68  
tcritical (р = 0.95)  1,96  1,96  1,96  
Null hypothesis  accepted  accepted  accepted 
Ttest of the counterreactions after the overreaction for the DowJones index during 1991–2014 (weekly data) for the different averaging periods case of sigma_dz = 1
Period_dz  3  5  10  20  30  

abnormal  normal  abnormal  normal  abnormal  normal  abnormal  normal  abnormal  normal  
Number of matches  251  990  239  1000  206  1027  198  1025  198  1015 
Mean  2,05%  1,78%  2,05%  1,78%  2,11%  1,78%  2,24%  1,76%  2,36%  1,74% 
Standard deviation  1,78%  1,62%  1,82%  1,61%  1,89%  1,60%  1,94%  1,59%  2,22%  1,52% 
tcriterion  2,45  2,26  2,50  3,51  3,91  
tcritical (р = 0.95)  1,96  1,96  1,96  1,96  1,96  
Null hypothesis  rejected  rejected  rejected  rejected  rejected 
Ttest of the counterreactions after the overreaction for the DowJones index during 1991–2014 (monthly data) for the different averaging periods case of sigma_dz = 1
Period_dz  3  5  10  20  30  

abnormal  normal  abnormal  normal  abnormal  normal  abnormal  normal  abnormal  normal  
Number of matches  56  229  52  230  45  233  42  226  44  214 
Mean  3,59%  3,40%  3,51%  3,42%  3,73%  3,37%  3,80%  3,32%  4,39%  3,22% 
Standard deviation  3,37%  2,94%  3,41%  2,95%  3,66%  2,93%  3,80%  2,90%  4,09%  2,83% 
tcriterion  0,40  0,20  0,66  0,82  1,90  
tcritical (р = 0.95)  1,96  1,96  1,96  1,96  1,96  
Null hypothesis  accepted  accepted  accepted  accepted  accepted 
Therefore the key parameters for the tests of longterm overreaction in different financial markets analysis are set as follows: the period_dz (averaging period) is set equal to 30 and sigma_dz (the number of standard deviations added to mean used as a criterion of overreaction) equal to 1.
Statistical tests results: case of Hypothesis 1 (weekly data)
Financial market  FOREX  Commodities  US stock market  

Financial asset  EURUSD  USDCHF  AUDUSD  Gold  Oil  Boeing  Microsoft 
Ttest  –  –  –  +  +  –  – 
ANOVA  –  +  +  +  +  +  – 
Mann–Whitney U test  –  –  –  +  +  +  – 
Regression analysis with dummy variables  –  +  +  +  +  +  – 
Statistical tests results: case of Hypothesis 1 (monthly data)
Financial market  FOREX  Commodities  US stock market  

Financial asset  EURUSD  USDCHF  AUDUSD  Gold  Oil  Boeing  Microsoft 
Ttest  –  –  –  –  –  –  – 
ANOVA  –  +  –  +  –  –  – 
Mann–Whitney U test  +  –  –  –  –  –  – 
Regression analysis with dummy variables  –  +  –  +  –  –  – 
As can be seen in the case of weekly data strong statistical evidence in favour of the overreaction anomaly can be found for both Gold and Oil prices, and to some extent for the US stock market (in the case of Boeing) and the FOREX (in the case of USDCHF and AUDUSD).
The results for the monthly data are significantly different from those for the weekly ones. The evidence of anomalies almost completely disappears, except for EURUSD and USDCHF (in the case of the FOREX) and Gold (in the case of commodities).
Overall, it appears that in the case of H1 weekly data provides the strongest evidence for the classical shortterm countermovement after an overreaction day, which is most noticeable in the case of commodities.
Statistical tests results: case of Hypothesis 2 (weekly data)
Financial market  FOREX  Commodities  US stock market  

Financial asset  EURUSD  USDCHF  AUDUSD  Gold  Oil  Boeing  Microsoft 
Ttest  +  –  +  –  +  –  + 
ANOVA  +  +  +  +  +  –  + 
Mann–Whitney U test  +  –  +  –  +  –  + 
Regression analysis with dummy variables  +  +  +  +  +  –  + 
Statistical tests results: case of Hypothesis 2 (monthly data)
Financial market  FOREX  Commodities  US stock market  

Financial asset  EURUSD  USDCHF  AUDUSD  Gold  Oil  Boeing  Microsoft 
Ttest  –  –  –  +  +  –  – 
ANOVA  –  +  +  +  +  –  + 
Mann–Whitney U test  –  –  +  +  +  –  – 
Regression analysis with dummy variables  –  +  +  +  +  –  + 
Hypothesis 2 is not rejected in many cases with weekly data. We find very strong evidence in favour of an “inertia anomaly” (prices tend to move in the direction of the overreaction in the following period). This applies to EURUSD and AUDUSD, Oil and Microsoft data, and represents evidence of market inefficiency caused by overreactions.
The results for the monthly data again are significantly differing from those for the weekly ones. Evidence in favour of the inertia anomaly is present for commodities and only for AUSUSD in the FOREX.
Overall the results from testing Hypothesis 2 suggest that the weekly frequency is the most appropriate to detect the inertia anomaly. The commodity market again look like the most inefficient among those analysed.
The general conclusion from the statistical tests are as follows: anomalies are generally detected using weekly but not monthly data; the commodity markets are the most affected by the overreaction anomalies; the results for the FOREX and US stock markets are mixed.
Next, we analyse whether these anomalies give rise to exploitable profit opportunities. If they do not, we conclude that they do not represent evidence inconsistent with the EMH. We expand the list of assets in order to provide more extensive results. The complete list of assets includes: FOREX (EURUSD, USDCHF, AUDUSD, USDJPY, USDCAD, GBPJPY, GBPUSD, EURJPY, GBPCHF, EURGBP), US stock market (Alcoa, AIG, Boeing Company, Walt Disney, General Electric, Home Depot, IBM, Intel, Microsoft, Exxon Mobil), commodity (Gold).

Period_dz = 30 (see above for an explanation);

Time_val = week (see above);

Sigma_dz = 1 (see above).
Trading results for Strategy 1
Asset  Total trades  Succesfull trades, %  Profit, USD  Return  Annual return  ttest 

FOREX  
EURUSD  108  63%  −1584  −158,4%  −11,3%  Accepted 
USDCHF  112  63%  −1815  −181,5%  −13,0%  Accepted 
AUDUSD  114  66%  −1690  −169,0%  −12,1%  Accepted 
USDJPY  116  69%  1662  166,2%  11,9%  Rejected 
USDCAD  118  66%  −2121  −212,1%  −15,2%  Accepted 
GBPJPY  111  71%  3541  354,1%  25,3%  Rejected 
GBPUSD  116  68%  −135  −13,5%  −1,0%  Accepted 
EURJPY  107  64%  −1829  −182,9%  −13,1%  Accepted 
GBPCHF  106  74%  3721  372,1%  26,6%  Rejected 
EURGBP  118  71%  169  16,9%  1,2%  Accepted 
US stock market  
Alcoa  64  63%  −2280  −228,0%  −25,3%  Accepted 
AIG  64  67%  480  48,0%  5,3%  Accepted 
Boeing Company  87  71%  3290  329,0%  36,6%  Rejected 
Walt Disney  63  70%  −289  −28,9%  −3,2%  Accepted 
General electric  67  64%  −39  −3,9%  −0,4%  Accepted 
Home Depot  79  64%  290  29,0%  3,2%  Accepted 
IBM  65  63%  −3090  −309,0%  −34,3%  Accepted 
Intel  70  54%  −1055  −105,5%  −11,7%  Accepted 
Microsoft  74  66%  430  43,0%  4,8%  Accepted 
Exxon Mobil  72  67%  773  77,3%  8,6%  Accepted 
Commodities  
Gold  78  64,0%  −2091  −209,1%  −23,2%  Accepted 
Trading results for strategy 2
Asset  Total trades  Succesfull trades, %  Profit, USD  Return  Annual return  ttest 

FOREX  
EURUSD  112  58%  848  84,8%  6,1%  Rejected 
USDCHF  119  57%  690  69,0%  4,9%  Rejected 
AUDUSD  117  56%  416  41,6%  3,0%  Accepted 
USDJPY  116  50%  −479  −47,9%  −3,4%  Accepted 
USDCAD  117  58%  1829  182,9%  13,1%  Rejected 
GBPJPY  114  47%  −6766  −676,6%  −48,3%  Accepted 
GBPUSD  116  53%  −566  −56,6%  −4,0%  Accepted 
EURJPY  107  58%  476  47,6%  3,4%  Accepted 
GBPCHF  106  48%  −2991  −299,1%  −21,4%  Accepted 
EURGBP  118  49%  −2609  −260,9%  −18,6%  Accepted 
US stock market  
Alcoa  68  51%  877  87,7%  9,7%  Rejected 
AIG  65  60%  2390  239,0%  26,6%  Rejected 
Boeing Company  87  44%  −2470  −247,0%  −27,4%  Accepted 
Walt Disney  62  47%  −1475  −147,5%  −16,4%  Accepted 
General electric  69  51%  410  41,0%  4,6%  Accepted 
Home Depot  79  47%  −1557  −155,7%  −17,3%  Accepted 
IBM  65  38%  −9236  −923,6%  −102,6%  Accepted 
Intel  70  50%  −36,4  −3,6%  −0,4%  Accepted 
Microsoft  74  40%  −1814  −181,4%  −20,2%  Accepted 
Exxon Mobil  71  50%  −1711  −171,1%  −19,0%  Accepted 
Commodities  
Gold  78  58,0%  1011  101,1%  11,2%  Rejected 
Strategy 1, based on the classical overreaction hypothesis, trades on counterreactions after periods of abnormal price dynamics. In general, it is unprofitable in the case of the FOREX (7 pairs out of 10 produce negative or statistically insignificant results) and commodity markets (in the case of Gold). For the US stock market the results are mixed (50% of profitable assets), but in general this anomaly does not seem to be exploitable. The assets to be traded on the basis of the classical overreaction hypothesis with weekly data are therefore: GBPCHF (ROI = 27% per year), GBPJPY (25%), USDJPY (12%) and Boeing (36.6%). Although as previously shown a nonrejection of the null does not necessarily mean that there exist profit opportunities, it appears that it does mean a higher chance of profitable trading.
Strategy 2, based on the socalled “inertia anomaly”, trades on price movements in the direction of the overreaction in the following period. In general it is unprofitable for the US stock market (7 assets out of the 10 analysed produce negative results), whilst the results are mixed for the FOREX (there are 50% of profitable assets, but only 3 of the 5 profitable assets pass the ttest on randomness). There is evidence of profit opportunities in the commodity markets. The assets to be traded on the basis of the inertia anomaly with weekly data are therefore: USDCAD (ROI = 13% per year), USDCHF (5%), EURUSD (6%), AIG (27%), Alcoa (10%) and Gold (11%).
5 Conclusions
This paper examines longterm price overreactions in various financial markets (commodities, US stock market and FOREX). It addresses the issue of whether they should be seen simply as a statistical phenomenon or instead as anomalies giving rise to exploitable profit opportunities, only the latter being inconsistent with the EMH paradigm. The analysis is conducted in two steps. First, a number of statistical tests are carried out for overreactions as a statistical phenomenon. Second, a trading robot approach is applied to test the profitability of two alternative strategies, one based on the classical overreaction anomaly (H1: counterreactions after overreactions differ from those after normal periods), the other on an “inertia” anomaly (H2: price movements after overreactions in the same direction of the overreaction differ from those after normal periods). Both weekly and monthly data are used. Evidence of anomalies is found predominantly in the case of weekly data. More specifically, H1 cannot be rejected for the US stock market and commodity markets when the averaging period is 30, whilst it is rejected for the FOREX. The results for H2 are more mixed and provide evidence of an “inertia” anomaly in the commodity market and for some assets in the US stock market and FOREX. The trading robot analysis shows that in general strategies based on the overreaction anomalies are not profitable, and therefore the latter cannot be seen as inconsistent with the EMH. However, in some cases abnormal profits can be made; in particular this is true of (i) GBPCHF (ROI = 27% per year), GBPJPY (25%), Boeing (36%), ExxonMobil (8.6%) in the case of the classical overreaction hypothesis and weekly data, and (ii) USDCAD (13%), USDCHF (5%), EURUSD (6%), AIG (27%), Alcoa (10%) and Gold (11%) in the case of the inertia anomaly and also with weekly data.
A comparison between these results and the daily ones reported in Caporale et al. (2018) suggests that the classic overreaction anomaly (H1) occurs at both short and longterm intervals in the case of the US stock market and commodity markets. The results for the FOREX are mixed at both intervals, but mostly suggest no contrarian movements after overreactions. The findings concerning the “inertia” anomaly (H2) are more stable and consistent: it is detected for the commodity markets and US stock market at both short and longterm horizons. As for the FOREX, there is a short but not a longterm anomaly in most cases. The trading results imply that there is no single profitable strategy: the findings are quite sensitive to the specific asset being considered, and therefore it is necessary to investigate case by case whether it is possible to earn abnormal profits by exploiting the classical overreaction and/or inertia anomaly. Future research will extend the analysis focusing in particular on unusually low returns.
Notes
Acknowledgements
Comments from the Editor and an anonymous reviewer are gratefully acknowledged.
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