Dr Andrew Urquhart
Dr Andrew Urquhart
- Associate Professor of Finance
Profile & Expertise
Dr Andrew Urquhart is Associate Professor of Finance at the ICMA Centre, Henley Business School. Dr Andrew joined the ICMA Centre in September 2018 and holds a PhD from Newcastle University where his thesis examined the Adaptive Market Hypothesis and investor sentiment in extreme circumstance. He also holds a MSc Finance (distinction) and BA (Hons) in Economics and Politics, also from Newcastle University.
Andrew’s main research interests are financial markets, investor behaviour, high-frequency trading, cryptocurrencies and investor sentiment. He has published over 20 papers in a range of leading international journals such as the Journal of Financial Markets, Institutions and Money, Quantitative Finance, the European Journal of Finance, Economics Letters, International Review of Financial Analysis and many others.
His research has received considerable attention, with well over 250 citations. He regularly presents his work at leading international conferences such as the Financial Management Association, INFINITI, Paris Financial Management, British Accounting and Finance Association, European Financial Management Association, Economic History Society and Forecasting Financial Markets conferences. He has also received over £500,000 in research income and acted as a reviewer for leading journals such as the Journal of Money, Credit and Banking, the International Journal of Forecasting, the European Journal of Finance, Economics Letters and many others. Andrew is also an associate editor at the European Journal of Finance (3*), International Review of Financial Analysis (3*) and Research in International Business and Finance (2*).
He is also an external examiner for Imperial College London for their summer school programme. Recently, Andrew received the best paper award at the 2018 Cryptocurrency Research Conference, Cambridge, UK. In 2017, Andrew was awarded the Deans award for leadership in research and he was also awarded the Tom Fetherston award for the best paper in International Review of Financial Analysis in 2013. He is currently working on projects involving high-frequency trading, CEO education and the effect on firm performance, as well as numerous projects related to cryptocurrencies and their impact on financial markets and society.
Key publications, books, research & papers
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The intraday dynamics of bitcoin
Eross, A., MCGroarty, F., Urquhart, A.
Bitcoin has received much investor attention in recent years and following this, there has been an explosion of academic studies examining this new financial asset. We contribute to the growing literature of Bitcoin by examining the intraday variables of the leading Bitcoin exchange with the highest information share over 4 years’ worth of data to reveal the intraday stylized facts of Bitcoin and how they have developed over time. Employing GMT-timestamped tick data aggregated to the 5-mintuely frequency, we find that Bitcoin returns have increased over time, while trading volume, volatility and liquidity varied substantially over time. We also find that volume increases throughout the day and falls from around 4pm until midnight, which is consistent with the intraday patterns found in currency markets. Realised volatility is fairly consistent throughout the day although it is highest during the opening times of the three major global stock markets. Also liquidity is highest during the opening times of the major global exchanges and the markets tend to be illiquid during the early morning. Finally, we show evidence of the mixture of distribution hypothesis of Clark (1973).
The Brexit vote and currency markets
Dao, T. M., McGroarty, F. and Urquhart, A.
This paper studies the effect of the Brexit vote on the intraday correlation and volatility transmission among major currencies. We find that the vote causes an increase in the correlation among the safe-haven currencies of the Swiss franc and Japanese yen as well as gold, and also find a decrease in their correlation with the directly involved currencies of British sterling and the Euro. These changes are due to the appreciation of the former group and the depreciation of the latter group which represents a flight to quality of investors. We also observe a substantial decrease in volatility transmission between British sterling and the Euro following the Brexit vote due to lower levels of market integration. However the volatility transmission among the currencies has increased in general and their net spillover is positively correlated with their level of volatility and trading activities. Therefore we document the significant impact of the politically important Brexit vote on the high frequency correlation and volatility spillover in the foreign exchange market.
Portfolio management with cryptocurrencies: the role of estimation risk
Platanakis, E. and Urquhart, A.
This paper contributes to the literature on cryptocurrencies, portfolio management and estimation risk by comparing the performance of naïve diversification, Markowitz diversification and the advanced Black–Litterman model with VBCs that controls for estimation errors in a portfolio of cryptocurrencies. We show that the advanced Black–Litterman model with VBCs yields superior out-of-sample risk-adjusted returns as well as lower risks. Our results are robust to the inclusion of transaction costs and short-selling, indicating that sophisticated portfolio techniques that control for estimation errors are preferred when managing cryptocurrency portfolios.
Is Bitcoin a hedge or safe haven for currencies? An intraday analysis
Bitcoin has attracted a wealth of attention in the media and by investors alike and this paper investigates whether Bitcoin can act as a hedge or safe haven against world currencies. Contrary to previous studies, we assess the relationship between Bitcoin and currencies at the hourly frequency since Bitcoin experiences quite large volatility throughout the day. We employ an ADCC model and find that Bitcoin can be an intraday hedge for the CHF, EUR and GBP, but acts as a diversifier for the AUD, CAD and JPY. We also implement the non-temporal Hansen (2000) test to examine the safe haven properties of Bitcoin and find that Bitcoin is a safe haven during periods of extreme market turmoil for the CAD, CHF and GBP. Therefore our results indicate that Bitcoin does act as an intraday hedge, diversifier and safe haven for certain currencies, which will be of great interest to currency, cryptocurrency and high-frequency investors alike.
Investigating risk contagion initiated by endogenous liquidity shocks: evidence from the US and eurozone interbank markets
Eross, A., Urquhart, A.
This paper investigates liquidity spillovers between the US and European interbank markets during turbulent and tranquil periods. We show that an endogenous model with time-varying transition probabilities is effective in describing the propagation of liquidity shocks within the interbank market, while predicting liquidity crashes characterised by changed dynamics. We show that liquidity shocks, originating from movements of the spread between the Asset Backed Commercial Paper and T-bill, drive regime changes in the euro fixed-float OIS swap rate. Our results support the idea of endogenous contagion from the US money market to the eurozone money market during the global financial crisis.
Does Twitter predict Bitcoin?
Shen, D., Urquhart, A.
This paper adds to the growing literature of Bitcoin by examining the link between investor attention and Bitcoin returns, trading volume and realized volatility. Unlike previous studies, we employ the number of tweets from Twitter as a measure of attention rather than Google trends as we argue this is a better measure of attention from more informed investors. We find that the number of tweets is a significant driver of next day trading volume and realized volatility which is supported by linear and nonlinear Granger causality tests.
Cryptocurrencies as a financial asset: a systematic analysis
Corbet, S., Lucey, B., Urquhart, A.
This paper provides a systematic review of the empirical literature based on the major topics that have been associated with the market for cryptocurrencies since their development as a financial asset in 2009. Despite astonishing price appreciation in recent years, cryptocurrencies have been subjected to accusations of pricing bubbles central to the trilemma that exists between regulatory oversight, the potential for illicit use through its anonymity within a young under-developed exchange system, and infrastructural breaches influenced by the growth of cybercriminality. Each influences the perception of the role of cryptocurrencies as a credible investment asset class and legitimate of value.
An early warning indicator for liquidity shortages in the interbank market
Eross, A., Urquhart, A.
This study investigates an early warning indicator for liquidity shortages in the short‐term interbank market. To identify structural breaks and their persistence, an autoregressive two‐state regime switching model is presented. The variability in the LIBOR–OIS spread along with thresholds, which delimit four intensities, reveals regime changes consistent with liquidity crashes. The transition between the states is state dependent, and the posterior estimates for the crisis and noncrisis states are estimated using the Gibbs sampler. We forecast our early warning indicator up to December 2011 and show that the estimates are superior to a random walk with drift. Therefore, the model is an effective early warning indicator of an imminent liquidity shortage impacting the interbank market.
What causes the attention of Bitcoin?
Bitcoin has received enormous attention both by the media and investors alike. But why has Bitcoin received such attention? This paper answers this question by examining the relationship between investor attention and Bitcoin fundamentals and finds that realized volatility and volume are both significant drivers of next day attention of Bitcoin.
Ultra-high-frequency lead–lag relationship and information arrival
Dao, T. M., McGroarty, F. and Urquhart, A.
To our knowledge, this paper is the first study on the effect of information arrival on the lead–lag relationship amongst related spot instruments. Based on a large data-set of ultra-high-frequency transaction prices time-stamped to the millisecond of the S&P500 index and its two most liquid tracking ETFs, we find that their lead–lag relationship is affected by the rate of information arrival whose proxy is the unexpected trading volume of these instruments. Specifically, when information arrives, the leadership of the leading instrument may strengthen or weaken depending on whether the leading or lagging instrument responds to that information. An increase in the unexpected volume of the leader strengthens its leadership whereas an increase in the unexpected volume of the lagger weakens this leadership. In addition to the strength of leadership, an increase in the unexpected volume in response to information arrival may also have opposite effects on the lead–lag correlation coefficient depending on whether that volume increase belongs to the leader or the lagger. Finally, we find that sophisticated investors have a more significant effect on the lead–lag relationship than non-sophisticated ones.
Pairs trading across mainland China and Hong Kong stock markets
Zhang, H. and Urquhart, A.
Motivated by the rationale that market inefficiency arises from a combination of less than fully rational demand and limits to arbitrage, this paper investigates the profitability of pairs trading across Mainland China and Hong Kong on highly liquid large‐cap and midcap stocks from January 1996 to July 2017. We have three main findings. First, we find that pairs trading constrained within each market generates no significant abnormal returns. However, if investors can trade across Mainland China and Hong Kong, pairs trading is profitable after adjusting for risk and transaction costs, where the annualized abnormal return is 9% over the full sample. Second, by using a rolling‐window regression, we find that the profitability of the strategy is time‐varying. The bootstrap simulations suggest that the decline in profitability of the strategy since 2012 is due to random chance rather than poor ability of identifying mispriced stocks. However, the vast majority of profitable periods reflect the strategy’s ability to choose profitable stocks rather than random chance. Third, the profitability of the strategy is somewhat sensitive to market conditions, most notably, the strategy is more profitable during longer term market turbulence. Overall, our empirical findings are consistent with the Adaptive Market Hypothesis in that the integration of financial markets and market conditions determine the level of market efficiency.
Optimal vs naïve diversification in cryptocurrencies
Platanakis, E., Sutcliffe, C.
This paper contributes to the literature on cryptocurrencies by examining the performance of naïve (1/N) and optimal (Markowitz) diversification in a portfolio of four popular cryptocurrencies. We employ weekly data with weekly rebalancing and show there is very little to select between naïve diversification and optimal diversification. Our results hold for different levels of risk-aversion and an alternative estimation window.
High frequency trading from an evolutionary perspective: financial markets as adaptive systems
Manahov, V., Hudson, R. and Urquhart, A.
The recent rapid growth of algorithmic high‐frequency trading strategies makes it a very interesting time to revisit the long‐standing debates about the efficiency of stock prices and the best way to model the actions of market participants. To evaluate the evolution of stock price predictability at the millisecond timeframe and to examine whether it is consistent with the newly formed adaptive market hypothesis, we develop three artificial stock markets using a strongly typed genetic programming (STGP) trading algorithm. We simulate real‐life trading by applying STGP to millisecond data of the three highest capitalized stocks: Apple, Exxon Mobil, and Google and observe that profit opportunities at the millisecond time frame are better modelled through an evolutionary process involving natural selection, adaptation, learning, and dynamic evolution than by using conventional analytical techniques. We use combinations of forecasting techniques as benchmarks to demonstrate that different heuristics enable artificial traders to be ecologically rational, making adaptive decisions that combine forecasting accuracy with speed.
Future directions in international financial integration research - a crowdsourced perspective
Lucey, B. M., Vigne, S. A., Ballester, L., Barbopoulos, L., Brzeszczynski, J., Carchano, O., Dimic, N., Fernandex, V., Gogolin, F., González-Urteaga, A., Goodell, J. W., Helbing, P., Ichev, R., Kearney, F., Laing, E., Larkin, C. J., Lindblad, A., Lončarski, I., Ly, K. C., Marinč, M., McGee, R. J., McGroarty, F., Neville, C., O'Hagan-Luff, M., Piljak, V., Sevic, A., Sheng, X., Stafylas, D., Urquhart, A.
This paper is the result of a crowdsourced effort to surface perspectives on the present and future direction of international finance. The authors are researchers in financial economics who attended the INFINITI 2017 conference in the University of Valencia in June 2017 and who participated in the crowdsourcing via the Overleaf platform. This paper highlights the actual state of scientific knowledge in a multitude of fields in finance and proposes different directions for future research.
Does intraday technical trading have predictive power in precious metal markets?
Batten, J. A., Lucey, B. M., McGroarty, F., Peat, M. and Urquhart, A.
Previous research has identified that investors place more emphasis on technical analysis than fundamental analysis, however the research has largely been confined to daily data and stock market indices. This paper studies whether intraday technical trading rules have any significant predictive power in the precious metals market through three popular mov- ing average rules. We find that using the standard parameters previously used in the liter- ature, technical trading rules offer no predictive power whatsoever. However after utilising a universe of parameters, we find a number of parameter combinations offer significant predictability in the gold market, but there remains no significant predictability in the sil- ver market. Our results show that the longer parameters of the technical trading rules are more successful than the traditional parameters chosen in the literature. Therefore intra- day technical trading rules have some predictive power in the gold market but offer no sig- nificant predictability in the silver market.
Stylized facts of intraday precious metals
Batten, J., Lucey, B., McGroarty, F., Peat, M. and Urquhart, A.
This paper examines the stylized facts, correlation and interaction between volatility and returns at the 5-minute frequency for gold, silver, platinum and palladium from May 2000 to April 2015. We study the full sample period, as well as three subsamples to determine how high-frequency data of precious metals have developed over time. We find that over the full sample, the number of trades has increased substantially over time for each precious metal, while the bid-ask spread has narrowed over time, indicating an increase in liquidity and price efficiency. We also find strong evidence of periodicity in returns, volatility, volume and bid- ask spread. Returns and volume both experience strong intraday periodicity linked to the opening and closing of major markets around the world while the bid-ask spread is at its low- est when European markets are open. We also show a bilateral Granger causality between returns and volatility of each precious metal, which holds for the vast majority subsamples.
Sampling frequency and the performance of different types of technical trading rules
Hudson, R., McGroarty, F. and Urquhart, A.
The predictive ability of technical trading rules has been studied in great detail however many papers group all technical trading rules together into one basket. We argue that there are two main types of technical trading rules, namely rules based on trend-following and mean reversion. Utilising high-frequency commodity ETF data, we show that mean-reversion based rules perform increasingly better as sampling frequencies increase and that conversely the performance of trend-following rules deteriorate at higher-frequencies. These findings are possibly related to noise created by high-frequency traders.
Price clustering in Bitcoin
Investor and media attention in Bitcoin has increased substantially in recently years, reflected by the incredible surge in news articles and considerable rise in the price of Bitcoin. Given the increased attention, there little is known about the behaviour of Bitcoin prices and therefore we add to the literature by studying price clustering. We find significant evidence of clustering at round numbers, with over 10% of prices ending with 00 decimals compared to other variations but there is no significant pattern of returns after the round number. We also support the negotiation hypothesis of Harris (1991) by showing that price and volume have a significant positive relationship with price clustering at whole numbers.
How predictable are precious metal returns?
This paper provides strong evidence of time-varying return predictability of three precious metals from January 1987 to September 2014. We use three variations of the variance ratio test, the nonlinear Brock, Dechert and Schieinkman test as well as the Hurst exponent to evaluate the time-varying return predictability of precious metals to reduce the risk of spurious results. Our full sample results report mixed findings where some tests indicate significant predictability while some suggest no predictability. However through a time-varying procedure, we show that each precious metal market goes through periods of significant predictability as well as periods of unpredictability. Therefore this finding suggests that return predictability does vary over time and is not a static, all-or-nothing condition and therefore is consistent with the adaptive market hypothesis. We also show that platinum is the most predictable of the three precious metals and silver the least predictable, which may be of great to investors who include precious metals in their investment portfolios.
The inefficiency of Bitcoin
Bitcoin has received much attention in the media and by investors in recent years, although there remains scepticism and a lack of understanding of this cryptocurrency. We add to the literature on Bitcoin by studying the market efficiency of Bitcoin. Through a battery of robust tests, evidence reveals that returns are significantly inefficient over our full sample, but when we split our sample into two subsample periods, we find that some tests indicate that Bitcoin is efficient in the latter period. Therefore we conclude that Bitcoin in an inefficient market but may be in the process of moving towards an efficient market.
Liquidity risk contagion in the interbank market
Eross, A., Urquhart, A.
This paper studies liquidity risk contagion within the interbank market by assessing the long-run relationship of short-term interest rate spreads from January 2002 to December 2015. In particular, we model the interaction between the LIBOR–OIS spread, euro fixed- float OIS swap rate and the three-month US-German bond spread and discover strong evidence of structural innovations affecting the interbank market. We find that when the short-term interbank market is affected by a liquidity shock, the LIBOR–OIS spread is a leader in moving back to equilibrium, while the euro-dollar currency swap rate and the US-German bond spreads are followers. Moreover, we find long-run cointegrating relation- ships and bi-directional causality between the spreads. However, structural breaks identified as prospective financial crises affect the long-run relationships and liquidity shocks drive interbank rates and spread fluctuations. Therefore, liquidity shocks propagating within the interbank market can forecast benchmark interest movements, and ultimately this has significant implications for policy-makers and market players alike.
Investor sentiment and local bias in extreme circumstances: the case of the Blitz
This paper treats the Blitz, the bombing of Britain during World War Two, as a natural experiment which can provide insights into the effects of investor sentiment on stock returns. The period of the Blitz is very interesting in that one of the world’s major financial centres was under regular and severe air attack, as were many other industrial and commercial centres. These conditions provide a unique opportunity to study both investor sentiment and local bias effects in extreme circumstances. We show that negative investor sentiment during the Blitz as a whole was not evident. However major bombings in London gener- ate negative investor sentiment on stock returns while major bombings outside of London generate no negative investor sentiment on stock returns, which is consistent with local bias effects.
Are stock markets really efficient? Evidence of the adaptive market hypothesis
This study examines the adaptive market hypothesis in the S&P500, FTSE100, NIKKEI225 and EURO STOXX 50 by testing for stock return predictability using daily data from January 1990 to May 2014. We apply three bootstrapped versions of the variance ratio test to the raw stock returns and also whiten the returns through an AR-GARCH process to study the nonlinear predictability after accounting for conditional heteroscedasticity through the BDS test. We evaluate the time-varying return predictability by applying these tests to fixed- length moving subsample windows and also examine whether there is a relationship between the level of pre- dictability in stock returns and market conditions. The results show that there are periods of statistically signifi- cant return predictability, but also episodes of no statistically significant predictability in stock returns. We also find that certain market conditions are statistically significantly related to predictability in certain markets but each market interacts differently with the different market conditions. Therefore our findings suggest that return predictability in stock markets does vary over time in a manner consistent with the adaptive market hypothesis and that each market adapts differently to certain market conditions. Consequently our findings suggest that in- vestors should view each market independently since different markets experience contrasting levels of predict- ability, which are related to market conditions.
A calendar effect: weekend overreaction (and subsequent reversal) in spot FX rates
Dao, T. M., McGroarty, F. and Urquhart, A.
This paper investigates a calendar effect, namely the weekend overreaction, in spot foreign exchange markets of 8 major and 9 emerging currencies. We find that after a large price difference between Friday close and subsequent Monday open, most markets are likely to reverse in multiple horizons during the following week, which is consistent with the over- reaction hypothesis. We develop a reversal trading strategy to exploit this effect which we show are robust to transaction costs and interest rates. In the out-of-sample test, the strat- egy is able to generate abnormal risk-adjusted returns, which suggests that these currency markets might be weak-form inefficient.
War and stock markets: the effect of World War Two on the British stock market
Hudson, R. and Urquhart, A.
This paper studies the effect of World War Two (WWII) on the British stock market. It contributes to the literature in several ways. First, this paper thoroughly investigates the impact of historically major events on the British stock market using a variety of empirical approaches in order to ensure a comprehensive examination of the im- pact of WWII on British stock returns. We utilise an event study of pre-selected historically major events, an in- vestigation of the possible causes of the largest price movements as well as utilising an endogenous procedure testing for structural breaks. Secondly we extend the literature on behavioural finance and investor sentiment in extreme circumstances. In particular we examine the ‘negativity effect’, documented by Akhtar et al. (2011) and determine whether stock returns reacted more strongly to negative events or positive events. Overall we find limited evidence of strong links between war events and market returns although there is support for the ‘negativity effect’.
Political uncertainty and the 2012 US presidential election: a cointegration study of prediction markets, polls and a stand-out expert
Goodell, J. W., McGroarty, F. and Urquhart, A.
Political uncertainty is increasingly seen as important to financial markets. Particularly US presidential election uncertainty is linked to uncertainty regarding future US macroeconomic policy. But what is the best vehicle to measure political uncertainty? We examine both the cointegration and causal relationships between the Iowa and Intrade presidential futures markets (IOWA, INTRADE), along with the results of election polls (POLLS); as well as published election predictions of Nate Silver (SILVER), who was arguably the most followed political forecaster during the 2012 presidential election season. We document strong evidence that SILVER and the two prediction markets were all highly cointegrated; while POLLS was not. Consistent with the assertion made by others that INTRADE prices were manipulated in 2012 for non-pecuniary reasons, we also evidence that IOWA and SILVER both Granger-caused INTRADE. Our findings are also consistent with previous findings that election markets outperform polls as prediction vehicles. Overall, while confirming that INTRADE, IOWA and SILVER are cointegrated, we note that the three series consistently differed in the degree of optimism in an Obama victor. These results pose important questions for researchers interested in estimating political uncertain- ty, and assessing the efficacy of prediction markets and their international integration.
How exactly do markets adapt? Evidence from the moving average rule in three developed markets
The seminal study by Brock, Lakonishok and LeBaron (1992) (BLL hereafter) found that the moving average rule had strong predictive power over 90 years in the DJIA, and this result was confirmed by Hudson et al. (1996) for the FT30 in the UK and Chen et al. (2009) for the TOPIX in Japan. However, according to the Adaptive Market Hypothesis, trading rules are only likely to be successful for a limited period of time and, as investors and markets adapt, their predictive power will diminish. We examine the moving average (MA) rule using post-BLL (1987–2013) data and find that after 1986 the rule’s predictive power has diminished in all three markets. We investigate the exact process behind the weakening of the predictive power of moving average rules and find that post-1987 markets react to new buy/sell signals not on the days those signals are generated, but the day before. In support of this finding, we show that trading strategies based on anticipation of signals would have yielded superior profits to investors. Hence, trading on anticipated signals constitutes a feasible explanation of price reactions to future, one-day-ahead new signals, and thus in line with the Adaptive Market Hypothesis.
The Euro and European stock market efficiency
This article examines the impact of the introduction of the Euro currency on the market efficiency of 10 of the most developed European stock markets during the period 1988 to 2012. We use an autocorrelation test, a runs test, various formulations of the variance ratio test and the nonlinear BDS test, which are performed on daily data for the full sample period, as well as two subsets dictated by the introduction of the Euro currency. The full sample results are mixed, with the Netherlands accepting market efficiency and Ireland completely rejecting it, with the other markets providing mixed evidence for market efficiency. The subsample period results show that while some markets became more efficient after the introduction of the Euro currency (Spain and Finland) and some markets became more inefficient (France), some were unaffected by the introduction of the Euro (the Netherlands and Italy). Overall our results show that the impact of the Euro currency is mixed, indicating that its introduction was not a decisive factor in the behaviour of stock returns in European markets.
Calendar effects, market conditions and the Adaptive Market Hypothesis: evidence from long-run U.S. data
In this paper, we examine the Adaptive Market Hypothesis (AMH) through four well-known calendar anomalies in the Dow Jones Industrial Average from 1900 to 2013. We use subsample analysis as well as rolling window analysis to overcome difficulties with each method type of analysis. We also create implied investment strategies based on each calendar anomaly as well as determining which market conditions are more favourable to the calendar anomaly performance. The results show that all four calendar anomalies support the AMH, with each calendar anomaly’s performance varying over time. We also find that some of the calendar anomalies are only present during certain market conditions. Overall, our results suggest that the AMH offers a better explanation of the behaviour of calendar anomalies than the Efficient Market Hypothesis.
Efficient or adaptive markets? Evidence from major stock markets using very long run historic data
This paper empirically investigates the Adaptive Market Hypothesis (AMH) in three of the most established stock markets in the world; the US, UK and Japanese markets using very long run data. Daily data is divided into five-yearly subsamples and subjected to linear and nonlinear tests to determine how the independence of stock returns has behaved over time. Further, a five-type classification is proposed to distinguish the differing be haviour of stock returns. The results from the linear autocorrelation, runs and variance ratio tests reveal that each market shows evidence of being an adaptive market, with returns going through periods of independence and dependence. However, the results from the nonlinear tests show strong dependence for every subsample in each market, although the magnitude of dependence varies quite considerably. Thus the linear dependence of stock returns varies over time but nonlinear dependence is strong throughout. Our overall results suggest that the AMH provides a better description of the behaviour of stock returns than the Efficient Market Hypothesis.