Investing during a Fintech Revolution: Ambiguity and return risk in cryptocurrencies

https://doi.org/10.1016/j.intfin.2021.101362Get rights and content

Highlights

  • The degree of ambiguity aversion is a prominent source of abnormal returns from investment in Bitcoin markets.

  • Bitcoin investors exhibit, on average, an increasing aversion to ambiguity.

  • Investors are found to earn abnormal returns only when ambiguity is low.

Abstract

Rationally justifying Bitcoin’s immense price fluctuations has remained a persistent challenge for both investors and researchers in this field. A primary reason is our potential weakness toward robustly quantifying unquantifiable risks or ambiguity in Bitcoin returns. This paper introduces a behavioral channel to argue that the degree of ambiguity aversion is a prominent source of abnormal returns from investment in Bitcoin markets. Using data over a ten-year period, we show that Bitcoin investors exhibit, on average, an increasing aversion to ambiguity. Furthermore, investors are found to earn abnormal returns only when ambiguity is low. Robustness exercises reassure on the validity of our results.

Introduction

“But Bitcoin is an example of ambiguity, and the efficient market theory does not capture what is going on in the market for this cryptocurrency.”.

—— Robert Shiller1

“Bitcoin valuation is ‘exceptionally ambiguous’.”.

—— Robert Shiller2

These quotes from Robert Shiller could hardly be more accurate in pinpointing the aim of the present study, in which we attempt to answer the broad question of how ambiguity determines abnormal returns in virtual currencies, such as Bitcoin. Virtual currencies represent both the emergence of a new trend in the form currency can take and a new payment technology in purchasing goods and services. Bitcoin has undoubtedly proven to be the most prominent in each case (Dwyer, 2015, Gillaizeau et al., 2019, White et al., 2020), with its growing centrality among financial institutions and increasing tendency to be the first choice over other established theory-backed assets (Trimborn and Härdle, 2018). Ambiguity plays a major role in quantifying the magnitude of abnormal returns. This paper fills a gap in the literature by rigorously studying the impact of ambiguity on Bitcoin returns in the spirit of Brenner and Izhakian (2018).3

As the leading cryptocurrency, Bitcoin continues to draw wide attention from practitioners, regulators, and scholars. Many of the recent academic discussions on Bitcoin have been motivated by the substantial fluctuations in Bitcoin prices (García-Monleón et al., 2021), speculative bubbles and zero fundamental value (Cheah and Fry, 2016), and concerns about unstructured regulatory policy (Akyildirim et al., 2020, Alexander and Heck, 2020). A large strand of literature attempts to understand cryptocurrency market phenomena through the lens of the traditional neoclassical finance theories (Borri, 2019, Corbet et al., 2020). Specifically, Urquhart (2016) documents evidence of market inefficiency in the early years and improving market efficiency through time. Corbet et al. (2018b) investigate the relationship between cryptocurrencies and a variety of traditional financial assets and show that cryptocurrencies may offer diversification benefits for investors. Liu and Tsyvinski (2020) show that cryptocurrency returns have no exposure to commonly used stock market, macro-economic, foreign exchange, and commodity market factors.4 Lucey et al. (2021) introduce a new Cryptocurrency Uncertainty Index (UCRY) that captures policy and price uncertainty in cryptocurrency markets, showing the index to increase following major events such as cryptocurrency exchange hacks.

All that aside, Bitcoin usefully exemplifies uncertainty and ambiguity, and neoclassical theory fails to explain the market behavior for this cryptocurrency.5 There has been inadequate empirical daily information to rationally explain Bitcoin’s high volatility. As indicated by Giudici et al. (2020), the general uncertainty may arise both from unsophisticated investors finding blockchain technology opaque and complicated, and more importantly, from the fundamental value of cryptocurrencies remaining unclear.6 It is difficult for investors to manage their cryptocurrency portfolios. Therefore, we attempt to extend our understanding of this market using a behavioral finance perspective. This paper examines the role of unquantifiable risk, or ambiguity, in Bitcoin returns.

Since the seminal studies of Keynes (1921) and Knight (1921), the concept of uncertainty has been analyzed from two distinct perspectives: risk and ambiguity. In the condition of risk, the beliefs of a decision-maker are captured by a well-defined probability distribution of possible outcomes. However, under the ambiguous condition, decision-makers beliefs on the probabilities of the outcome are unknown due to a lack of information (Snow, 2010; Cavatorta and Schröder, 2019). Epstein and Schneider (2008) investigate the impact of information quality on investor behaviors and show that ambiguity-averse investors tend to react more to negative than positive information. Kelsey et al. (2011) document that when momentum trading investors face ambiguity, they react differently to past winners and losers which creates an asymmetric momentum effect. Driouchi et al. (2018) investigate the lead-lag relationship between option and stock markets during the 2006–2008 subprime crisis. Their results suggest that ambiguity played an important role in the increased volatility of stock markets during the crisis. Bianchi and Tallon (2019) show that ambiguity averse investors exhibit a form of home bias, which leads to higher exposure to the domestic stock market and higher risk due to a lack of diversification.

Most research on ambiguity focuses on traditional financial assets while a few studies explore the role of ambiguity in emerging digital currencies such as Bitcoin.7 Using an incentivized survey, Anantanasuwong et al. (2019) investigate ambiguity held toward traditional financial assets and cryptocurrency. Their findings suggest that individuals’ perceptions of ambiguity levels differ according to asset type. Asano and Osaki (2020) explore the role of ambiguity aversion in portfolio allocation to show that as it rises it decreases the optimal proportion invested in ambiguous assets such as cryptocurrency.

In this paper, we refer to ambiguity as uncertainty over the probability of potential future outcomes, while risk refers to uncertainty over those outcomes, following Knight (1921). Specifically, we estimate ambiguity using five-minute Bitcoin returns based on the model of Brenner and Izhakian (2018). Our findings show that ambiguity plays an important role in Bitcoin returns and that investors have an increasing aversion to ambiguity.

We conduct a battery of robustness tests to verify our findings. For example, we use the forward-looking implied volatility index from the S&P 500 (VIX) in our regression model as it is used as a proxy for ambiguity in prior studies (e.g., Williams, 2015). We control for higher moments, including skewness and kurtosis. We also test for unstructured attitude toward risk that does not impose a specific functional form (e.g., constant relative risk aversion or constant absolute risk) over attitude toward risk. Further, we conduct sub-sample analysis, control for information flow, and use an alternative sampling interval of the return series.

In the spirit of Baker and Wurgler (2006), we further examine the performance of Bitcoin returns conditional on ambiguity. Liu and Tsyvinski (2020) show that cryptocurrency returns cannot be explained by the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), the Fama and French (1993) three-factor model (FF3FM), the Carhart (1997) momentum-extended FF3FM, or the Fama and French (2015) five-factor model (FF5FM). We initially confirm their findings and proceed to demonstrate that investors earn abnormal returns of Bitcoin only when ambiguity is low, but not when ambiguity is high.

We contribute to the literature in several ways. First, we make a behavioral attempt at identifying the potential impact of ambiguity on asset pricing and the risk-return relationship. This is useful, because the use of Bitcoin, in a wider portfolio management strategy, has been shown to provide hedging benefits (Kajtazi and Moro, 2019, Atsalakis et al., 2019, Ma et al., 2020, Thampanya et al., 2020); yet Bitcoin markets are typically characterized by crashes (Fry and Cheah, 2016), excessive volatility (Katsiampa, 2017), and positive returns when the fundamental value is shown to be zero (Cheah and Fry, 2015, Corbet et al., 2018a). It is widely accepted that traditional asset pricing models have difficulties in explaining Bitcoin returns. Our study extends our understanding of the cryptocurrency market using a behavioral finance perspective, and we find that ambiguity plays an important role in explaining the abnormal returns of Bitcoin. Second, our study is related to general research, primarily into attitudinal theory, such as aversion toward ambiguity, rather than the actual measurement of it. Indeed, only a few studies use market data to measure ambiguity; for example, Ulrich (2013) uses the entropy of inflation and Williams (2015) uses the volatility index (VIX). Following Brenner and Izhakian (2018), we explore the importance of ambiguity in the cryptocurrency markets using Bitcoin data.

Our study has important implications for sustainability. By studying the uniquely ambiguous characteristic of Bitcoin, we aim to take into account, at least partially, “the dynamics” of this highly volatile currency to empower investors regardless of size with the required information to make optimal decisions regarding their choices. Our work has practical importance too. Not only individual investors but various funds have an increasing proclivity toward risk exposure with Bitcoin. This paper helps shed light on their investment decisions with Bitcoin: if investors can earn a risk premium after adjusting for systematic risk, then it is helpful to allocate their wealth to Bitcoin.8 However, if the risk premium is conditional on ambiguity as shown in our results, caution should be exercised by investors in “real-time” trading because the risk premium becomes insignificant during periods of high ambiguity.

Our work also has important implications for policymakers. While Bitcoin markets are largely unregulated under current market conditions, policymakers can use our study to guide regulatory development. For example, they could use our method to estimate the ambiguity of Bitcoin, in helping to identify potential market bubbles. They could also harness the ambiguity of Bitcoin to cool off trading in Bitcoin markets.

The remainder of the paper proceeds as follows. Section 2 discusses the construction of the ambiguity measure. Section 3 describes the data, while Section 4 reports the main empirical results and performs various robustness tests. Section 5 concludes the paper.

Section snippets

The ambiguity measure

As we have noted, ambiguity refers to situations where an agent’s subjective knowledge about the likelihoods of contingent events is consistent with multiple probability distributions. We follow Izhakian (2020) and define ambiguity as2[r]=E[φ(r)]Var[φ(r)]dr,where r is the Bitcoin return, φ(r) is the marginal probability, E[] is the expectation of probability, and Var[] is the variance of probability. While risk can be measured by the volatility of returns, ambiguity can be measured by the

Data

We obtain data from multiple databases to construct our variables. Specifically, we collect Bitcoin price (in dollars) and volume between 2012 and 2019 from bitcoincharts.com. We obtain the number of trades from data.bitcoinity.org. We download the daily excess market returns (MKTRF), size factor (SMB), book-to-market factor (HML), profitability factor (RMW), investment factor (CMA), momentum factor (UMD), and treasury bill rate (RF) from Kenneth French’s website.9

Estimating expected values

In our empirical exercise, we use the estimated expectations of the following four variables, namely the volatility of Bitcoin (σ), the average absolute deviation of Bitcoin returns from the mean (ϑ), the probability of favorable Bitcoin returns (P), and the degree of Bitcoin ambiguity (). Following Andersen et al. (2003) and Brenner and Izhakian (2018), we estimate the expected volatility based on realized volatility using the coefficients obtained from the time-series autoregressive moving

Conclusion

Investors invariably face a choice between known and unknown risks. Therefore, an ambiguity-averse investor would rather choose an alternative where the probability distribution of an investment outcome is known over, one where it is unknown. This paper studies the important role of ambiguity in Bitcoin returns, an asset that has captured investor attention like no other in recent times. Because virtual currencies like Bitcoin tend not to conform to conventional asset pricing theoretical

References (71)

  • N. Borri

    Conditional tail-risk in cryptocurrency markets

    Journal of Empirical Finance

    (2019)
  • M.W. Brandt et al.

    On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach

    J. Financ. Econ.

    (2004)
  • M. Brenner et al.

    Asset pricing and ambiguity: Empirical evidence

    J. Financ. Econ.

    (2018)
  • C.C. Chan et al.

    Realized volatility and transactions

    Journal of Banking & Finance

    (2006)
  • E.-T. Cheah et al.

    Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin

    Economics Letters

    (2015)
  • S. Corbet et al.

    Cryptocurrency reaction to fomc announcements: Evidence of heterogeneity based on blockchain stack position

    Journal of Financial Stability

    (2020)
  • S. Corbet et al.

    Datestamping the Bitcoin and Ethereum bubbles

    Finance Research Letters

    (2018)
  • S. Corbet et al.

    Exploring the dynamic relationships between cryptocurrencies and other financial assets

    Economics Letters

    (2018)
  • G.P. Dwyer

    The economics of Bitcoin and similar private digital currencies

    Journal of Financial Stability

    (2015)
  • E.F. Fama et al.

    Common risk factors in the returns on stocks and bonds

    J. Financ. Econ.

    (1993)
  • E.F. Fama et al.

    A five-factor asset pricing model

    J. Financ. Econ.

    (2015)
  • K.R. French et al.

    Expected stock returns and volatility

    J. Financ. Econ.

    (1987)
  • J. Fry et al.

    Negative bubbles and shocks in cryptocurrency markets

    International Review of Financial Analysis

    (2016)
  • M. Gillaizeau et al.

    Giver and the receiver: Understanding spillover effects and predictive power in cross-market Bitcoin prices

    International Review of Financial Analysis

    (2019)
  • Y. Izhakian

    A theoretical foundation of ambiguity measurement

    Journal of Economic Theory

    (2020)
  • E. Jondeau et al.

    Average skewness matters

    J. Financ. Econ.

    (2019)
  • A. Kajtazi et al.

    The role of bitcoin in well diversified portfolios: A comparative global study

    International Review of Financial Analysis

    (2019)
  • P. Katsiampa

    Volatility estimation for Bitcoin: A comparison of GARCH models

    Economics Letters

    (2017)
  • A.D. Lee et al.

    Bitcoin: Speculative asset or innovative technology? Journal of International Financial Markets

    Institutions and Money

    (2020)
  • Y. Ma et al.

    Portfolio optimization in the era of digital financialization using cryptocurrencies

    Technol. Forecast. Soc. Chang.

    (2020)
  • M. Rothschild et al.

    Increasing risk: I. a definition

    Journal of Economic Theory

    (1970)
  • M. Scholes et al.

    Estimating betas from nonsynchronous data

    J. Financ. Econ.

    (1977)
  • N. Thampanya et al.

    Asymmetric correlation and hedging effectiveness of gold &s066amp; cryptocurrencies: From pre-industrial to the 4th industrial revolution

    Technol. Forecast. Soc. Chang.

    (2020)
  • S. Trimborn et al.

    CRIX an index for cryptocurrencies

    Journal of Empirical Finance

    (2018)
  • M. Ulrich

    Inflation ambiguity and the term structure of US government bonds

    Journal of Monetary Economics

    (2013)
  • Cited by (0)

    We thank Jonathan Batten (the Editor), an anonymous referee, Hisham Farag, Armin Schwienbacher, and Ganesh Viswanath-Natraj for their insightful comments and suggestions. We are grateful to conference participants at the Cryptocurrency Research Conference, UK, 2020, the SFiC conference, University of Birmingham, UK, 2021, and the 37th International Conference of the French Finance Association (AFFI), France, 2021 for their helpful comments and suggestions. Di Luo is grateful for financial support from the National Natural Science Foundation of China (Grant No.71991473 and No.71671076). All remaining errors are our own.

    View full text