Efficient Market Hypothesis and Asset Price Bubbles

According to the EMH, presented by the Nobel laureate economist ^{Eugene Fama (1970)}, a market is efficient when the prices of any given asset reflect all available information and new information is quickly incorporated into market prices by rational investors. Hence, no one can outperform the market prices relying on the same information; it can occur only by chance, or as Fama called it, by random walks (^{Fama, 1991}). As outlined in EMH, it is not possible for investors to systematically gain a higher return than the equilibrium market return using historical information (weak form efficiency), public information (semi-strong form efficiency) and insider information (strong form efficiency) (^{Fama, 1970}). This implies that the market is efficient and reacts rapidly to any change or news related to the asset and the price reflects its fundamental value². Based on this principle, no investor can outperform the others and cannot generate extraordinary profits for a prolonged time.

Essentially, according to the EMH financial markets follow a random walk as market prices only move because of new information which initially changes fundamental values and consequently also market prices. As the occurrence of new information is basically impossible to predict, market price changes should be randomly distributed, i.e. follow a random walk (^{Samuelson, 1965}; ^{Fama, 1965}). According to the orthodox form of the random walk hypothesis, the future (uncertain) market price of an asset is the sum of the present market price and a random variable (normally distributed, expected value of 0). Hence, the best estimate of the future market price of an asset is its current market price as expected returns are 0 (martingale model) and consecutive market price changes are independent from one another, i.e. have an autocorrelation of 0 (^{Samuelson, 1965}). Consequently, tests of the random walk hypothesis are essentially seen as tests of the EMH.

As one major consequence of the EMH, no asset bubble can form persistently as it would quickly be eliminated by rational market participants when asset price deviate from their fundamental values. This concept, one of the most influential theories in the financial literature, has been tested and heavily debated by several other scholars in the academic literature, such as other Nobel-prize awarded economist ^{Robert Shiller (2015)}, who argued that asset bubbles do exist. He pointed out that during the 1990s in the technology sector there was a significant departure in stock prices from their fundamental value and used the term “irrational exuberance”, coined by Alan Greenspan, to describe the investor spirit of this era (^{Shiller, 2015}). Further, bubbles not only may be a result of economic euphoria, but they may be contagious from one market to another, crossing borders effortlessly (^{Kindleberger and Aliber, 2015}).

The term asset bubble refers precisely to this phenomenon, when the price of any asset departs significantly from its fundamental value and the subsequent process is characterized by dramatic increase in market prices that is later followed by a collapse, as ^{Brunnenmeier (2008)} summarized it. The author groups the asset price bubbles into four categories, according to the explanations offered for their formations: 1) rational bubbles under symmetric information, the least likely and accepted explanation, as not all investors are rational, nor do they possess the same information simultaneously; 2) rational bubbles under asymmetric information in which rational investors do not have the same information regarding the asset therefore they price it differently; 3) bubbles due to limits to arbitrage that result from different risks such as the existence of irrational noise traders or the costs of arbitrage; 4) heterogeneous beliefs of investors about the existence of bubbles in which investors differ in their judgement of the asset price, therefore prices may vary.

Despite that many academic articles that empirically documented the existence of asset bubbles and the circumstances of when and how they form, economists still hold differing views on asset bubbles. Most importantly, investors often behave rationally but then other times irrationally when pricing, buying, and selling assets. Several studies documented the psychological factors of investment strategies and behavior, such as herd behavior, the “sell to the greater fool” behavior, the over-confidence of investors or the positive feedback loop that may exacerbate an initially moderate optimistic investor sentiment and lead to major price increases, among other factors (^{Shiller, 2015}; ^{Demmler, 2017}).

Consequently, financial markets cannot be expected to behave solely rationally, but rather, bubbles are bound to occur under certain conditions which create a fertile environment for over-enthusiastic investment. One of these conditions is often related to the spread of a new technology that creates an optimistic investor sentiment in the financial market. Such was the case in the 1960s, at the appearance of the new “tronics” firms, or in 1990s with the emergence of “tech-firms”, as ^{Baker & Wurgler (2006)} have documented it. Another factor can be the availability of cheap financing, when the interest rates are low for a prolonged time, such as in the early 2000s (^{Shiller, 2015}) at the emergence of the subprime bubble in the US housing market. In addition to these circumstances, the authors ^{Froot & Obstfeld (1991)} have provided empirical evidence for the existence of “intrinsic bubbles” which means that asset bubbles are frequent and inevitable elements of financial markets and they may grow exponentially before they burst. Even more troublesome is the finding that not only do bubbles occur, but they may persist for a prolonged period, as the scholars Dhar and Goetzmann have observed: "A bubble can be sustained some time by investment sentiment and feedback trading despite a widespread awareness that assets are mis-valued". (^{Dhar and Goetzmann, 2006, p. 4}). Based on these market characteristics, it is not surprising to see the stellar boom and bust events that have occurred in the cryptocurrency markets since 2017.

It is important to note that there are several other examples of market inefficiencies in addition to the appearance of speculative financial bubbles. Other factors may include the predictability of future asset prices, calendar anomalies (predictable price changes on certain days of the week), overreaction and underreaction to public announcements in connection with an asset or the issuing company, among others (^{Demmler, 2017}). Nonetheless, considering that the most common and frequently studied phenomenon in the Bitcoin market is the emergence of bubbles, this feature is considered for the analysis of market efficiency/inefficiency in the present study.

Bitcoin (BTC)

Among the existing cryptocurrencies, Bitcoin is the most popular by far. Its popularity stems from various factors, documented by various authors (^{Böhme et al., 2015}; ^{Frisby, 2014}; Metha et al., 2019). For one, it was the first virtual cryptocurrency on the market that appeared and therefore there is more trust and experience accumulated with its use than with its peers. Second, its total future quantity is capped at 21 million BTC; in other words, it is not prone to foment inflation due to its limited availability. Third, the technology behind it - decentralized digital blockchain - is considered revolutionary and it is expected to spread to other areas beyond finance for widespread use, for example, registering ownership titles, diplomas, including public and private blockchains; most recently, for tracking COVID-19 vaccines (^{Korin, 2020}). Another positive aspect of BTC lies in its democratizing nature, as it is easily accessible to everyone in the world with a smartphone and internet access, including millions of people who have no bank account - the “unbanked” - and have been left out and are unattended by the traditional financial sector. In fact, another key factor of the rise in BTC and the other alternative digital coins (altcoins) popularity can be attributed to the disenchantment with the financial sector´s monopolistic and reckless behavior that became all too evident during the 2007 and 2008 financial crisis. (^{Mehta et al., 2019}).

Despite its numerous virtues, Bitcoin faces several criticism and challenges. To name a few, it appears to be designed by engineers, sidelining the considerations of legal and regulatory experts (^{Böhme et al., 2015}). This means that due to its technical decentralized setup in which payments go from peer-to-peer without the passing an intermediary financial institution, no central bank or financial supervisory board can intervene in Bitcoin´s creation and trading. Consequently, commercial disputes cannot be remedied by the authorities (^{Mehta et al., 2019}). Further, as erroneous or unwanted transactions cannot be reversed, transactional mistakes can be costly. Next, security breaches on online platforms are not uncommon, for example the hacking incident of the online trading site Mt. Gox in 2014 that resulted in a loss of more than 800,000 BTC, approximately 460 million USD (^{McMillan, 2014}) with no bulletproof solution so far. Thus, even if the blockchain technology has not been breached until now, the supporting exchange platforms and gadgets (such as firmware) have been subject to cyberattacks. The authors ^{Böhme et al., (2015)} categorize these aforementioned risks the following way: “We review market risk, the shallow market problem, counterparty risk, transaction risk, operational risk, privacy-related risk, and legal and regulatory risks. In addition, any user holding bitcoins faces market risk via fluctuation in the exchange rate between bitcoin and other currencies” (^{Böhme et al., 2015, p.226}).

Another criticism of BTC is related to its fundamental value, which, according to some scholars is zero (e.g., ^{Cheah & Fry, 2015}); in other words, it has no intrinsic value, unlike gold, silver, or stocks, for example. As an observation, common FIAT money³, such as the US dollar or the Euro bills, also lack intrinsic value. In addition, as BTC must be “mined” on very powerful computers that require a lot of energy, the sustainability of its functioning has been seriously questioned as it is too energy intensive. Finally, the high volatility of Bitcoin prices makes it unpractical and useless for signaling prices, usually a basic money function, to be able to use it as a unit of account. Figure 1 shows the historic price changes of Bitcoin since January 2017. As it is observable from Figure 1, the price changes of Bitcoin indicate huge volatility, going from about 800 USD in early 2017 to above 19,000 USD by the end of the same year, and a drop to 6,300 USD by February 2018. The latest trend in the second half of 2020 shows another explosive price increase from about 5,000 USD in March to above 40,000 USD by February 6, 2021 followed by an all-time high of 49,375.94 USD on February 14, 2021 (^{Coindesk, 2021}).

Source: ^{Coindesk (2021)}.

Figure 1 Behavior of Bitcoin Market Price, 2017-2021 

As empirical studies of the price history of financial assets usually use returns instead of market prices, Figure 2 shows also, the behavior of Bitcoin daily simple returns from 2017 to 2021. Once again one can observe the high volatility features of the cryptocurrency. Seemingly periods of high volatility alternate with periods of lower volatility. It appears that Bitcoin currently (beginning of 2021) undergoes a phase of relatively high volatility. Historically speaking the maximum (minimum) daily return occurred on December 10, 2017 (March 12, 2020) with 23.9% (-27.1%) (^{Coindesk, 2021}).

Source: ^{Coindesk (2021)}.

Figure 2 Behavior of Bitcoin Daily Returns, 2017-2021 

As the authors ^{Böhme et al., (2015)} reviewed the use of Bitcoin since it became a viable electronic payment system, there have been a few major transformations. Early adopters used BTC to test it and as a means of payment for many illicit items trading on the Silk Road site (drugs, weapons, pills, etc.).

Later, users bought BTC for payments and increasingly as a buy-and-hold asset, diversifying their financial portfolios. The most recent demand of BTC and trading is due to two circumstances: 1) people use it as a mainstream store of value, similar to that of other hard currencies, including gold; 2) due to the near zero interest rates in developed countries when quantitative easing is taking place from the US, the European and Japanese markets, investors expect inflationary pressure and look for better investment opportunities, hence they turn to the cryptomarkets, in addition to the traditional stock and asset markets. All these markets have experienced an increase due to more available cash in the financial markets. Moreover, as the authors ^{Schilling & Uhlig (2019)} outline, Bitcoin is financed with a US dollar tax, as dollars are supplied by the U.S. central bank and they are used for buying Bitcoins. This partially explains the rising demand for Bitcoin in 2020.

Additional explanations include cash savings in some segments of the society as people are not spending on many consumer goods, travel or eating out during the COVID-19 pandemic (^{Fitzgerald, 2020}). New Bitcoin adopters, such as Paypal, Mastercard or investors including Elon Musk who embraced openly Bitcoin also contribute to its recent price rise (^{Bradshaw & Murphy, 2020}; ^{Szalay, 2021}). Jim Rieder, CIO of the US investment firm BlackRock, stated that Bitcoin may soon replace gold (^{Coindesk, 2020}). Highly respected financial publications, such as the Financial Times, also describe a bullish tendency on the cryptomarkets indicating high earnings amid very high volatility and a possible steep fall (^{Szalay, 2020}; ^{Samson, 2020}, ^{Smith, 2021}). Although the long-term trend probably holds for more price jumps and collapses, analysists expect an overall upward trend, due the scarcity of Bitcoin and the promise of the stock-to-flow model (^{PlanB, 2020}).

Presentation of Results

The results of the present study can be seen summarized in Appendix A which is organized in two sections: Section A includes the group of articles that do not reject and potentially accept the EMH, while Section B presents the group of articles that do reject the EMH. Within both sections, the articles are first organized in chronological order according by the year of publication and within each year, the articles are listed in alphabetical order by author. The organization we use helps to have a better overview of the evolution of the interpretation within the literature.

In addition to basic information of each article - such as the authors and the year of publication, the title of article, the journal where it was published - Appendix A presents two additional columns that provide qualitative summary analysis of every article. In the column called Key Focus, in addition to the most relevant objective of the article, the time period of the data analysis is indicated, along with the most important models used by the authors and the cryptocurrencies or other assets that were the subject of the analysis. It is important to note that where it was possible, we mentioned both the month and the year the data was collected, and if more than 3 models were used. Often more than 8 models or tests were applied, and more than 5 currencies studied, but not all are included in this table, due to space limitations. We indicated in the table those cases where we encountered an excess of models and currencies, such as one study that included more than 450 currencies (^{Wei, 2018}). The abbreviations of the listed cryptocurrencies can be found in Appendix B and the statistical models and tests in Appendix C.

The column Conclusion presents the most relevant conclusions which are critical for the evaluation of the EMH in each study, resuming whether the article accepts or rejects the EMH.

Discussion of Results

After reviewing the summary table in Appendix A, it is apparent that there are far more research articles that reject the EMH than the ones that accept it: 20 articles (80%) rejected the EMH, while 5 (20%) accepted it, with only document no. 2, potentially accepting the hypothesis, which indicates that most researchers consider the Bitcoin market as inefficient, and that it is prone to develop speculative bubbles from time to time. It is noteworthy that three articles that considered the Bitcoin market as efficient used data prior to the late 2017 price surge; in other words, their data did not include the multiple episodes of boom and bust that were not seen previously. Only two studies included data from the 2^nd half of 2017 (^{Caporale & Plastun, 2019}; ^{Vidal-Tomás & Ibañez, 2018}), which indicates that despite a dramatic increase in Bitcoin prices in 2017, these authors did not find evidence that the Bitcoin market would be inefficient. The scholars ^{Vidal-Tomás & Ibañez (2018)} found evidence for the semi-strong form of market efficiency, observing that investors overreact to events and public announcements related to the Bitcoin market, but not to other monetary policy announcements. Similarly, the authors ^{Caporale & Plastun (2019)}, considered the 2017 price spike as an overreaction from investors in the cryptocurrency markets, which may be exploited to generate profits with the right strategy. However, the scholars could not reject the EMH based on their empirical test results.

The other 20 studies that reject the EMH often used data ranging from 2010 until 2018, most commonly over 4-7 years. However, there are a few studies that used only one- or two-year data periods, for example ^{Fry & Cheah, 2016}), and yet, they found enough evidence to reject the EMH. The sources of the data seem to be very consistent among all 25 studies, as they tend to use the most common cryptocurrency information providers, such as Coindesk or Coinmarketcap.

Considering the multiple and diverse tests that these 25 studies applied, there are also several reoccurring models and tests, which help to compare the results among the diverse currencies and time periods selected. Among the most used methods are the Ljung-Box test for autocorrelation, Bartel´s test used for independence of returns, vector autoregression (VAR) tests and its variations such as FCVAR for random walk analysis, Brock, Dechert and Scheinkman (or BDS) test for independence test, detrended fluctuation analysis (DFA), Hurst exponent test, OLS model, Augmented Dickey-Fuller (ADF) test, GARCH-type models, the PWY model (^{Phillips, Wu and Yu, 2011a} and ^2011b), PSY model (^{Phillips, Shi and Yu, 2015}). These latter two models, especially the PSY (2015) model, are often applied by other authors (e.g. ^{Cheung et al., 2015}; ^{Geuder et al., 2019}), making it one of the most ubiquitous among these papers, as these authors note that it offers the best predictive capacity.

Several recent articles favor the log-periodic power law (LPPL) model. This is more common in studies that include data for the 2017 price increase which required the analysis of exponential growth, for example, the study of ^{Geuder, Kinateder & Wagner, 2019}; ^{Wheatley et al., 2018}; ^{Xiong et al., 2020}. Testing for and confirming the presence of martingale for highly explosive speculative bubble tendencies on the Bitcoin market is also present in the article of ^{Schilling & Uhlig (2019)}. As mentioned previously, most studies use multiple models, often up to 6-8 models and tests.

With respect to the cryptocurrencies included in the 25 articles, there is also great diversity although Bitcoin is the common denominator and often the only digital currency analyzed. Other major cryptocurrencies that were present include Ethereum, Ripple, Litecoin, and DASH. The authors ^{Hu, Valera, & Oxley (2019)} analyzed a significantly higher number of cryptocurrencies testing 31 digital currencies, while ^{Wei (2018)} analyzed 456 cryptocurrencies. In addition to cryptocurrencies, several studies compared and tested the Bitcoin market behavior to that of other currencies, such as USD, GBP, AUD, etc. (e.g., ^{Cheah et al., 2018}) or to other types of assets, such as gold or U.S. stocks (^{Bartos, 2015}; ^{da Fonseca & da Fonseca, 2019}). When comparing Bitcoin to currencies or other types of assets the authors found more extreme behavior in the cryptomarkets and conclude that cryptocurrencies are more likely to present extreme speculative bubble cycles than other asset classes.

Further, it is noticeable that some scholars, for example ^{Stosic et al., 2019}, examined Bitcoin and seven other cryptocurrencies’ behavior from the point of view of chaos theory, analyzing its complexity and entropy, along with the seemingly chaotic behavior observed by its trading patterns. As the Brazilian authors noted, “cryptocurrencies range from being partially deterministic (predictable from the past) to being completely unpredictable (high entropy and zero complexity); Bitcoin and other major cryptocurrencies fall somewhere in between” (^{Stosic et al., 2019, p.555}).

One curious prediction of the authors ^{Xiong et al., published in early 2020}, using the LPPL model is that the “next large bubble is expected by the second half of 2020” (p.10) and seems to be on point. By early 2021, one Bitcoin was selling at the most recent all-time high levels of above 40,000 USD. Given Xiong et al.’s remarkably successful prediction, their proposed testing and predictive models will probably be re-tested by other researchers.