# On the nature and financial performance of bitcoin

Elise Alfieri (CERAG, Universite Grenoble Alpes, Grenoble, France)
Radu Burlacu (CERAG, Universite Grenoble Alpes, Grenoble, France)
Geoffroy Enjolras (CERAG, Universite Grenoble Alpes, Grenoble, France)

ISSN: 1526-5943

Publication date: 18 March 2019

## Abstract

### Purpose

The purpose of this article is to provide some insights on the true nature of bitcoin and to study empirically its performance by using robust models, widely used in the academic literature. Previous studies assess performance with simple measures such as the Sharpe ratio. Such measures are insufficient because they do not take into account the bitcoin’s specificities, such as the possibilities to diversify risk.

### Design/methodology/approach

The authors use quantitative methodologies to assess the performance of financial assets. Performance is defined as a risk-adjusted return. The authors use regression analysis and measure bitcoin’s performance as the constant term (α) of the projection of its returns on the returns of relevant factors of risk.

### Findings

Bitcoin has low correlation with the market index and with factor-mimicking portfolios, which indicates opportunities to diversify risk. The performance of bitcoin (α) is positive and significant; this result is robust across period and world region specifications.

### Research limitations/implications

The true nature of bitcoin is subject of debate and needs further research. Furthermore, other factors should be considered in analysing the bitcoin’s performance, such as those related to investors’ behaviour or political risk.

### Practical implications

The empirical results obtained in this paper may be used by professional portfolio managers to diversify risk and to enhance their portfolio’s performance.

### Originality/value

This paper adds to the literature by arguing that bitcoin has the nature of common stock, and therefore, its performance has to be assessed with models that are relevant for this type of securities. This paper is the first using performance models that adjust returns for relevant sources of risk.

## Keywords

#### Citation

Alfieri, E., Burlacu, R. and Enjolras, G. (2019), "On the nature and financial performance of bitcoin", Journal of Risk Finance, Vol. 20 No. 2, pp. 114-137. https://doi.org/10.1108/JRF-03-2018-0035

### Publisher

:

Emerald Publishing Limited

## 1. Introduction

Bitcoin is a cryptocurrency, and therefore a part of the so-called “electronic currency” family (Nakamoto, 2008). On 04 January 2017, the bitcoin price was equal to US$1,126, thus reaching the threshold of US$1,000 for the second time in its history. Incredibly unexpected, and even more so, the price raised to more than US$10,000 one year after reaching US$16,808 on 13 December 2017.

Electronic currencies, which are recorded on a computer or other electronic devices, may take two forms: digital cash and cryptographic currency. The former is a simple digital version of physical money. The latter, which is studied in this article, uses cryptographic principles to ensure security. This type of currency is developed in a decentralised system that uses the blockchain technology.

Whilst bitcoin has common characteristics with currencies (bitcoin is indeed an exchange medium), and with gold (the monetary creation of bitcoin looks like that concerning gold), we hereafter consider bitcoin as a financial contract, and more specifically common stock. Bitcoin indeed has specific economic and legal profiles, risk-return characteristics and its liquidity bring it close to the common stock family (Glaser et al., 2014; Baur et al., 2018).

The objective of this article is to study empirically the bitcoins’ performance. The justification of studying the performance of bitcoin relies on the fact that it is a relatively young, risky financial innovation, not yet well assimilated by the market. Bitcoin is affected by informational asymmetries between investors, mainly because many of them do not understand the technology behind it. Consequently, the market value of this financial contract may differ from its true value, that is, the value on a market without informational asymmetries, thus providing opportunities to earn positive risk-adjusted returns. In line with this view, the objective of some mutual funds is to track bitcoins. This suggests the possibility of earning superior risk-adjusted returns by trading this financial contract.

In most existing articles, the performance of bitcoin is assessed by using simple measures, such as the Sharpe ratio (Brière et al., 2015; Burniske and White, 2017). The problem with this measure is that it does not take into account the huge potential for portfolio diversification with bitcoins. Being highly uncorrelated with most existing assets, most of the bitcoin variability can be diversified away, which strengthens its performance. Based on this important aspect, and on the premise that bitcoin has the nature of a financial contract, our paper is the first, to our knowledge, that attempts to measure its performance by using models such as the capital asset pricing model (CAPM), which uses the market portfolio as a benchmark, and also the three-factor Fama and French (1992) model, hereafter FF, and also other extensions of these models by considering other factors related to bitcoin.

To take into account the international dimension of bitcoin, we use the global market portfolio as a benchmark and the global versions of the FF factors (Fama and French, 2012). To test bitcoin performance, we compute the α estimated with these models for the period between 22 September 2010 and 30 December 2016 for different regions: World, Europe, Asia-Pacific and China. In addition, we take into consideration the market sentiment variable in our models to check the robustness of our results and to take into account behavioural aspects that are plausibly related to bitcoin.

The rest of the paper is organised as follow. Section 2 presents bitcoin characteristics. Section 3 describes the models used to assess bitcoin performance and the data sets used in our study. Section 4 discusses the results. Section 5 proposes some robustness tests related to the violations of the regression model assumptions, mainly the normality of errors, and also to some behavioural aspects. Section 6 presents the conclusion.

## 2. About the nature of bitcoin

The nature of bitcoin is subject of debate. Academics and professionals suggest various definitions and do not always agree on whether bitcoin is a currency, a commodity, a “safe” investment such as gold, a debt contract or common stock. In this section, we present bitcoin characteristics, and we attempt to show that bitcoin has also the characteristics of an asset, more precisely common stock (Glaser et al., 2014; Baur et al., 2018).

### 2.1 What is bitcoin?

Bitcoin is basically a payment system that is independent from any government and operates without a third party (such as a Central Bank). Any participant in this system may check the behaviour of other participants to ensure the reliability of transactions and system stability. In other words, the well-functioning responsibility is not assumed by a third party. Moreover, all participants have the possibility to know the transactions made by everyone. However, the identity of participants remains pseudo-anonymous, in the sense that the identity is hidden by a pseudonym, the bitcoin “address”, which is a number sequence.

There are three ways to obtain bitcoins: exchanging money, selling goods and services or mining. The first two ways, which are exchanging money and selling goods or services through e-businesses that accept bitcoin units, make bitcoin behave like a fiat currency. However, a fundamental aspect that makes bitcoin behave like a financial asset is that one may create bitcoins through the mining process, whose underlying technology is named “Blockchain”. This is a secured and distributed database that contains the history of transactions. The technology may be considered as a ledger that stores all exchanges realised on the network (Nakamoto, 2008; Tschorsch and Scheuermann, 2016). This ledger is composed of blocks linked to each other. Each block contains a transaction list of some exchanges. Special users, named miners, create a block locally by choosing different pending transactions. Then, each new block is drawn by a mathematical process, comparable to Sudoku. When a miner finds the grid solution, he/she wins a predetermined number of bitcoins, and other participants must start again the competition with another grid. Grid difficulty is adjusted so that miners may find the grid solution with an interval of 10 min on average between each discovery (Antonopoulos, 2015).

Miners are compensated for their work of integrating transactions to the blockchain and making the system reliable. They obtain a number of bitcoins when they succeed to add a block to the blockchain. This compensation is predefined in advance and the number of released bitcoins decreases with time because the maximum number of bitcoins is capped at 21 million.

### 2.2 Is bitcoin a currency?

From an economic perspective, the question whether bitcoin has common characteristics with currency is subject to debate. According to its basic properties, a currency should be a convenient medium of exchange, a stable unit of account and a durable store of value (Grant, 2014). Bitcoin is a medium of exchange, in the sense that a high number of businesses, such as Dell, Microsoft or PayPal, are willing to accept bitcoins (Figuet, 2016).

The popularity of using bitcoins is based on the user’s anonymity and the system transparency (because it uses the blockchain technology). However, participants could be reluctant to participate in this new system because bitcoin has no legal basis; companies make the choice to use bitcoin or not; the fixed costs of adopting this technology are high (sophisticated technical knowledge is needed); and there are network externalities effects (if few businesses accept bitcoin, few consumers may accept them, which in turn implies that few companies decide to accept them). Resolving this “vicious circle” is difficult because bitcoin is not regulated by an institution, and there is no possibility to make loans on the market (Kancs et al., 2015). Empirical studies confirm the controversial property of “medium of exchange” based on the fact that users do not entirely turn to bitcoin for this property (Baur et al., 2018).

Bitcoin may be considered to some extent as a “unit of account”. However, merchants do not display prices in bitcoin for two reasons. First, its supply is inelastic (a bitcoin price of a given product needs many digits after the comma). Second, volatility does not ensure price stability. Because of high volatility, merchants are forced to change frequently the price of their products. So, prices are usually displayed in US dollars and are then converted in bitcoins at the time when the transaction takes place (Figuet, 2016).

Finally, whilst bitcoin has features that make it behave like a “store of value”, the possible cybersecurity risks reduce trust in this currency. The trade-off between inflation and deflationary pressure, as well as the unstable purchasing power make it difficult to consider bitcoin as a store of value.

To conclude, bitcoin is different from traditional money because it does not fully respect the fiat currency properties, and in particular, there is no issuer responsible for it. In fact, bitcoin is governed by a protocol run by a network of computers that are distributed around the world; government monetary policies have no direct impact on it.

In economics, there are different perspectives related to a currency. Another point of view is to see currency through institutionalist economics as a “unit of account”. Based on this, bitcoin could be considered as a “currency” in the sense of money being a “social institution” (Lakosmki-Laguerre and Desmedt, 2015).

### 4.2 Multivariate results

This section estimates the performance of bitcoin by the alpha (risk-adjusted return) of the regression models in equations (1), (2) and (3). Table IV shows the descriptive statistics for the dependent and independent variables. Bitcoin has higher return and higher risk than the global market portfolio and the Fama–French factor-mimicking portfolios. Table V presents the Person correlation coefficients and shows that bitcoin is lowly correlated with these portfolios.

Table VI presents the results of the regression analyses. The bitcoin’s factor loadings are low and insignificant for all the factors considered, and this is true for all regression specifications. The regressions’ intercept, α, is positive and highly significant, with daily values between 0.52 per cent and 0.53 per cent across models and regions (which represents between around 540 per cent and 580 per cent per annum). The Asia-Pacific region provides a slightly higher α than Europe, regardless the model. It can, therefore, be affirmed that investing in bitcoin gives the possibility to earn, both from an economic and statistical perspective, highly significant positive risk-adjusted returns, regardless the region.

Table VII presents the bitcoin’s α by year and by region. α is measured by running the above-specified regressions for each year. Overall, α is relatively higher between 2010 and 2014, and mostly during 2013, with a value of 1.5 per cent per day and exhibits lower values during more recent periods. Over time, the market becoming more efficient and more mature relative to this financial innovation, bitcoin performance has decreased. In particular, informational asymmetries between investors, notably linked to technology understanding, decrease, which may explain this pattern. According to the literature, bitcoin is inefficient on the sub-period 2010-2013 and moves towards efficiency afterwards (Urquhart, 2016; Bartos, 2015). The trend is consistent with the Sharpe ratio trend presented in the previous subsection.

As most bitcoin transactions take place in the Chinese market, we replicate our analyses and estimate α with the three models in which the market, size and B/M factor-mimicking portfolios are composed exclusively of common stocks traded in the Chinese market. These factors are built according to the procedure used by Fama and French used for forming size and B/M portfolios; this procedure is explained in detail on the Kenneth French’s website.

Table VIII presents the correlation coefficients between bitcoin and the explanatory variables used in our regressions in the Chinese market. As for the other regions, bitcoin has a low correlation with the size and B/M factor-mimicking portfolios in China. This result suggests diversification benefits by including bitcoin in a portfolio composed of common stocks in the Chinese market.

The α values estimated with the three performance models on the Chinese market are presented in Table IX. As for the other regions, the α values are economically and statistically highly significant. Despite that the Chinese market is known to be more mature with respect to the bitcoin than other markets (Kajtazi and Moro, 2017), our results show, as for the other regions, strong possibilities to earn positive performance.

## 5. Robustness checks

### 5.1 Regression specification

The bitcoin risk-return profile being atypical, it is important to check for problems that may appear with our regressions. Tables XI and XII show that our regressions do not seem to suffer from problems related to multicollinearity (the VIF is always lower than 4), time-series correlation between residuals (the Durbin–Watson statistic is close to the value of 2) and the White’s tests show that the homoscedasticity hypothesis cannot be rejected in most cases.

Another important problem resides in the normality of bitcoin returns. Non-normal returns imply, under the hypothesis that explanatory variables are not stochastic, non-normal errors, in which case the estimators of the regression coefficients are no more efficient. Figures 6 and 7 show that bitcoin returns are skewed to the right, with a skewness of 0.68, and exhibit a “heavy-tailed” distribution, with a kurtosis of 15.98 (see also Table X). Our results are similar to those obtained in previous empirical studies (Baur et al., 2018). Despite that returns look like being normally distributed, normality tests such as Shapiro–Wilk reject the null hypothesis of normality.

We use the residual augmented least squares (RALS) estimators to measure bitcoin performance in a more robust way. This estimation technique is known to provide a more efficient estimation of regression coefficients without imposing specific restriction on the returns’ distribution (Im and Schmidt, 2008; Gallagher and Taylor, 2000). This technique has proved to be useful in analysing, for example, the performance of hedge funds as measured by their α. Heuson and Hutchinson (2015) show that, for such funds, the error generated by regression models depends systematically on skewness. OLS assessment errors prove to be economically significant, and RALS estimation technique proves to be robust to this bias.

We have estimated the RALS α for each one of the three performance models used in our article and for each one of the four regions studied. For expositional convenience, we do not present the procedure in this paper (the reader can refer to Gallagher and Taylor, 2000, amongst others, for a detailed description of this procedure). The qualitative interpretations of our results do not change; they are even reinforced. The RALS α is highly significant both economically and statistically. In the world, Europe, Asia-Pacific and China regions, the RALS α is between 0.52 per cent and 0.59 per cent per day, which is similar to the OLS α . The RALS t-statistic is about 4.43, which is higher than the t-statistic with the OLS procedure (the latter is, on average, of about 3.6).

### 5.2 Behavioural aspects

Performance results can be controversial if, in reality, the economic value of bitcoin is close to zero. Cheah and Fry (2015) apply econometric modelling on bitcoin prices and find empirical evidence that bitcoin exhibits speculative bubbles and has a fundamental value of zero. However, other authors find that speculation does not explain the high volatility of bitcoin and find evidence that bitcoin has a significantly positive economic value (Blau, 2018; Dwyer, 2015).

The low correlation between bitcoin and asset classes together with the high α obtained in the world, Europe and Asia-Pacific regions may be indicative of a speculative bubble. In this section, we attempt to control for speculative behaviour on bitcoin by using market sentiment as a control variable. Including such control variables is also a way to test the robustness of our results regarding the bitcoin’s performance.

Market sentiment takes into consideration the fact that the efficient market hypothesis does not necessarily apply in the real market. The value of an asset may deviate from its fundamental value because of market’s imperfections, such as information asymmetry under noise, or investors’ behaviour. Market sentiment, or investor sentiment, measures the investors’ behaviour on the market based on their expectations. Prices reveal this expectation, and consequently are an indicator to appraise investor sentiment. If an investor expects that prices are going to increase, thus leading to returns higher than the average, then he/she is bullish and enters on the market with a buyer attitude. On the contrary, a bearish investor expects that prices are going to decrease, and therefore s/he enters the market with a seller attitude. Bullish investors expect positive and greater returns than the fundamental value, whilst bearish investors expect a smaller return on the market.

Based on the literature and especially on the article of Brown and Cliff (2004), we identify four proxies for the market sentiment variable, amongst which three are related to trading and one is related to derivatives, to capture the attitude of investors relative to bitcoin. The first one, named Trade1, is the ratio of advancing issues on declining issues:

where advancing (declining) issues are the number of stocks that increased (decreased) between two dates (in our daily case, between the day before and the day after). This variable captures the market movement on a long or short run. A positive (negative) and significant Trade1 variable reveals a bullish (bearish) market: the number of advancing issues exceeds (is lower than) the declining ones. When the market is neutral, the ratio equals 1.

The second proxy, Trade2, is based on advancing and declining issues but also on volume, as follows:

where advancing (declining) issues are the number of stocks that increased (decreased) between two dates (in our daily case, between the day before and the day after). Advancing (declining) volume represents the total volume for advancing (declining) stocks. A positive (negative) and significant Trade2 variable reveals a bullish (bearish) market: the number of advancing issues exceeds (is lower than) the declining ones. When the market is neutral, the ratio equals 1.

The third variable related to the trading group, Trade3, deals with new highs and new lows and captures the relative market strength.

This variable compares the number of stocks reaching new highs and the number of stocks reaching new lows. More precisely, it compares the number of stocks having reached a 52-week high and the number of securities which having hit a 52-week low. A bullish (bearish) sentiment is captured when there are more stocks trading at their highs (lows) than the period before.

Finally, the last variable considered in our analysis is “Put-to-Call” (hereafter PtC) based on the Chicago Board Options Exchange:

PtC=Puts/Calls

A put (call) is the right to sell (buy) an underlying asset at a given price in the future. Buying put (call) means a bearish (bullish) behaviour, whilst selling put (call) means a bullish (bearish) attitude). A bearish (bullish) sentiment is detected when the ratio put/call is high (low).

We add these four variables in the models estimated above and present our results in Tables XIII, XIV and XV. Two of the trade variables, Trade1 and Trade3, are not significant, whilst Trade2 is highly significant. We also note that α is significant in most of the model specifications, except when the derivatives variable (PtC) is considered, in which case α is no more significant in all model specifications. Moreover, Trade2 is negative, whereas we expected a positive sentiment market variable. These results suggest that investors’ behaviour does influence bitcoin’s performance, but overall the performance continues to be positive and significant after controlling for this effect.

## 6. Conclusion

Bitcoin is a cryptocurrency that appeared in 2008. The growth of its value exhibits a very volatile price and provides a very specific risk-return profile for investors. After briefly justifying the asset nature of bitcoin, most precisely its common-stock-like nature, our article focuses on its main objective, which is to empirically test its performance. Even if bitcoin belongs to cryptocurrencies, this asset does not seem to respect all properties of a fiat money (medium of exchange, unit of account and store of value). Indeed, its economic and legal characteristics, together with its risk-return profile, make it look mostly like a financial contract. Moreover, its specific risk-return profile leads us to consider that bitcoin may be assimilated to common stock.

Fundamentally, we find that bitcoin is lowly correlated to existing asset classes, which provides opportunities for portfolio diversification, and generates highly significant risk-adjusted returns, of similar magnitude for global, Europe and Asia-Pacific regions. The same result applies for the Chinese market. These results are stable to the specifications of our regression models, which reside in the CAPM, Fama–French three-factor models, and their extensions that includes other factors. Our results are robust to econometric methodologies that account for non-normality problems with the regressions’ errors and to market sentiment variables.

Research could be improved by performing a more robust analysis to test whether bitcoin is a speculative bubble. The high performance obtained by bitcoin in the regions analysed in this paper, and the low correlation with existing assets may be a consequence of this. Furthermore, after controlling for market sentiment with the PtC variable, the bitcoin’s α is no more significant in all model specifications and for all regions. It could be useful in further research to test the market sentiment associated to bitcoin performance by using additional proxies, such as the proxy of closed-end fund which we find in the international market sentiment literature (Lee et al., 1991). Another proxy is the fear and greed Index which takes in consideration different proxies of market sentiment (market momentum, put and call, safe haven demand, stock price breadth and stock price strength, market volatility and junk bond demand) in only one index.

## Figures

#### Figure 1.

Bitcoin market price

Sharpe ratio

#### Figure 3.

Annual Sharpe ratio for bitcoin

#### Figure 4.

Sharpe ratio: MSCI indexes, stocks indexes and bitcoin

#### Figure 5.

Sharpe ratio: bonds, commodities, currencies and bitcoin

#### Figure 6.

Bitcoin return analysis – histogram

#### Figure 7.

Bitcoin return analysis – QQplot

## Table I.

Descriptive statistics

Variable N Mean (%) SD (%) Skewness Kurtosis
Bitcoin 1,638 568.82 111.69 0.68 15.98
S&P 500 1,638 19.74 17.73 –0.48 5.02
FTSE 100 1,638 5.63 23.02 –0.74 7.29
DAX30 1,638 8.95 28.49 –0.32 3.42
NIKKEI225 1,638 11.71 24.65 –0.48 4.69
CAC40 1,638 5.94 28.94 –0.33 4.06
NASDAQ 1,638 22.31 20.02 –0.45 3.83
MSCI World 1,638 13.50 16.33 –0.57 4.55
MSCI Europe 1,638 6.54 23.75 –0.48 4.24
MSCI Asia-Pacific 1,638 7.40 19.79 –0.37 3.12
Oil 1,638 –7.25 29.02 0.37 4.59
Gold 1,638 –2.14 20.50 –0.82 7.57
Commodity index 1,638 –2.95 25.54 –0.11 13.03
Bonds 1,638 6.16 5.83 –0.32 1.55
Dollar index 1,638 25.15 30.43 –0.98 19.28
Yen 1,638 7.21 11.75 0.22 4.27
Euro 1,638 5.00 11.37 –0.03 1.48
Yuan 1,638 0.80 2.50 1.56 29.77
Note:

This table presents summary statistics (annualised mean, annualised volatility, skewness and kurtosis) based on daily returns for bitcoin, stock indices (represented by S&P 500 and nasdaq for the USA, FTSE 100 for the UK, DAX30 Germany, NIKKEI225 for Japan and CAC40 for France), MSCI indexes for the world, Europe and Asia-Pacific regions, commodity indexes (gold, oil and commodity), bond index (Pimco) and currencies (dollar, yen, euro and Yuan). The sample is drawn from the blockchain info website and the Datastream database over the period 22 September 2010 to 30 December 2016

## Table II.

Correlation coefficients between bitcoin and various asset classes

Stock index
Variable S&P 500 FTSE 100 DAX30 NIKKEI225 CAC40
Bitcoin 0.04* 0.03 0.04 0.00 0.04
p-value 0.09 0.24 0.15 0.91 0.08
MSCI index
MSCI World MSCI Europe MSCI Asia-Pacific
Bitcoin 0.04 0.04 0.00
p-value 0.11 0.13 0.89
Commodities
Oil Gold Commodity index
Bitcoin 0.04 0.04 0.00
p-value 0.15 0.13 0.97
Bonds
Bonds
Bitcoin 0.01
p-value 0.616
Currencies
Dollar index Euro Yuan Yen
Bitcoin –0.01 –0.03 0.00 –0.01
p-value 0.64 0.31 0.88 0.67
Notes:

This table presents Pearson correlation coefficients between bitcoin returns and asset classes such as stock indices (represented by S&P 500 and nasdaq for the USA, FTSE 100 for the UK, DAX30 for Germany, NIKKEI225 for Japan and CAC40 for France), MSCI indexes for the world, Europe and Asia-Pacific regions, commodity indexes (gold, oil and commodity), bond index (Pimco) and currencies (dollar, yen, euro and Yuan). The sample is drawn from the blockchain info website and the Datastream database over the period 22 September 2010 through 30 December 2016. If the p-value is higher than 5 per cent, then the null hypothesis of no-correlation (rho = 0) is accepted. ***, ** and * indicate that the coefficient is significant at 1%, 5% and 10% level, respectively

## Table III.

Sharpe ratios

Variable 2010 2011 2012 2013 2014 2015 2016 2010-2016
N 73 260 261 261 261 261 261 1,638
Bitcoin 8.87 9.53 14.46 112.37 –0.77 1.87 2.33 5.09
S&P 500 4.70 0.11 1.53 3.64 1.46 0.10 1.09 1.11
FTSE 100 1.95 –0.13 1.01 1.97 –0.49 –0.42 –0.02 0.24
DAX30 3.10 –0.54 1.56 2.22 –0.70 –0.09 0.19 0.31
NIKKEI225 4.36 –0.53 0.92 1.64 –0.28 0.67 0.28 0.48
CAC40 0.62 –0.50 1.02 1.82 –0.74 0.03 0.30 0.21
NASDAQ 5.46 –0.04 1.43 4.14 1.26 0.49 0.66 1.11
MSCI World 4.13 –0.27 1.58 3.40 0.72 –0.03 0.74 0.83
MSCI Europe 1.60 –0.41 1.18 2.20 –0.53 –0.16 0.00 0.28
MSCI Asia-Pacific 4.63 –0.73 1.32 1.41 –0.22 0.24 0.27 0.37
Oil 7.25 0.79 0.17 0.07 –3.18 –1.18 2.02 –0.25
Gold 3.39 0.63 0.43 –1.39 –0.16 –0.86 0.66 –0.10
Commodity index 4.96 –0.21 –0.04 –0.27 –0.63 –0.65 0.79 –0.12
Bond –0.28 1.09 3.31 –0.40 2.33 –0.20 1.66 1.06
Dollar Index 1.89 1.56 0.37 1.87 0.85 0.16 0.16 0.83
Yen –1.92 –0.63 1.97 2.16 2.23 0.05 –0.29 0.61
Euro –0.70 0.33 –0.21 –0.66 2.89 1.15 0.38 0.44
Yuan –2.88 –2.91 –0.83 –3.22 1.51 2.01 2.93 0.32
Notes:

This table presents Sharpe ratios per year for Bitcoin, Stock indexes (represented by S&P500 and Nasdaq for the US, FTSE100 for the UK, DAX30 Germany, NIKKEI225 for Japan and CAC40 for France), MSCI indexes for the World, Europe and Asia-Pacific regions, Commodity indexes (Gold, Oil and Commodity), the bond index (Pimco), and cur-rencies (dollar, yen, euro and yuan). The data come from the Datastream database, the Blockchain Info and Fama French websites over the period 22 September 2010 to 30 December 2016 in the World, Europe and Asia-Pacific regions

## Table IV.

Descriptive statistics of explanatory variables used in regressions

Region N Mean (/day) SD Sum Min Max Mean (/year) SD (/year)
World
Rbitcoin-Rf 1,638 0.52 5.85 855.15 –47.83 51.53 568.99 111.70
RMkt-Rf 1,638 0.04 0.84 60.21 –5.12 4.16 14.36 16.14
SMB 1,638 0.00 0.33 –2.11 –1.86 1.92 –0.47 6.35
HML 1,638 0.00 0.29 2.69 –1.20 1.58 0.60 5.62
Gold 1,638 –0.01 1.07 –9.72 –10.16 5.43 –2.14 20.50
Bonds 1,638 0.02 0.30 26.81 –1.58 1.12 6.16 5.82
Europe
Rbitcoin-Rf 1,638 0.52 5.85 855.15 –47.83 51.53 568.99 111.70
RMkt-Rf 1,638 0.02 1.16 40.16 –8.80 5.60 9.36 22.12
SMB 1,638 0.01 0.48 11.62 –2.13 3.28 2.62 9.22
HML 1,638 –0.01 0.45 –14.26 –2.17 1.84 –3.13 8.57
Gold 1,638 –0.01 1.07 –9.72 –10.16 5.43 –2.14 20.50
Bonds 1,638 0.02 0.30 26.81 –1.58 1.12 6.16 5.82
Asia-Pacific
Rbitcoin-Rf 1,638 0.52 5.85 855.15 –47.83 51.53 568.99 111.70
RMkt-Rf 1,638 0.02 0.91 25.11 –5.70 4.67 5.75 17.42
SMB 1,638 –0.01 0.47 –10.48 –3.41 4.79 –2.31 9.07
HML 1,638 0.02 0.45 27.84 –1.82 1.95 6.40 8.60
Gold 1,638 –0.01 1.07 –9.72 –10.16 5.43 –2.14 20.50
Bonds 1,638 0.02 0.30 26.81 –1.58 1.12 6.16 5.82
Note:

This table presents summary statistics (mean, standard deviation (StD), sum, minimum, maximum, annualized mean and annualized volatility) of daily returns expressed in US $for the dependent variable (RBitcoin-Rf) representing Bitcoin return minus the risk-free rate (proxied by the one-month US Treasury Bill) and for independent variables (RMkt-Rf, which represents the excess return of the market portfolio, SMB, which is the size premium, HML, which is the value premium, bond and gold). The data come from the Datastream database, the Blockchain Info and Fama French websites over the period 22 September 2010 to 30 December 2016 in the World, Europe and Asia-Pacific re-gions. All results are in percentages (%) ## Table V. Correlation matrix Region RMkt-Rf SMB HML Gold Bonds World Rbitcoin-Rf 0.04 –0.03 0.02 0.04 0.01 RMkt-Rf –0.39*** 0.16*** 0.07*** –0.11*** SMB –0.15*** 0.14*** 0.14*** HML –0.04* –0.09*** Gold 0.18*** Europe Rbitcoin-Rf 0.03 –0.04* 0.03 0.04 0.01 RMkt-Rf –0.69*** 0.46*** 0.09*** –0.07*** SMB –0.37*** 0.01 0.13*** HML 0.00 –0.14*** Gold 0.18*** Asia-Pacific Rbitcoin-Rf 0.03 –0.01 –0.04* 0.04 0.01 RMkt-Rf –0.35*** –0.36*** 0.16*** 0.02 SMB –0.13*** 0.02 –0.01 HML –0.12*** –0.01 Gold 0.18*** Notes: This table presents the correlation matrix between the excess return of the Bitcoin (RBitcoin-Rf) and independent variables (RMkt-Rf, SMB, HML, Gold, Bond). The sample is drawn from the Datastream database, the Blockchain Info and Fama-French websites over the period from September 22, 2010, to December 30, 2016, in the World, Europe and Asian-Pacific regions. ***, ** and * indicate that the coeffi-cient is significant at 1%, 5% and 10% level respectively ## Table VI. Performance using the CAPM (Model 1), FF (Model 2) and extensions (Model 3) Region α (%) RMkt-Rf SMB HML Bonds Gold R2 (%) Annual α (%) World Model 1 0.51*** 0.27 0.15 545.53 p-value < 0.01 0.11 Model 2 0.51*** 0.21 –0.29 0.25 0.19 548.75 p-value < 0.01 0.26 0.53 0.62 Model 3 0.51*** 0.17 –0.45 0.29 0.20 0.26 0.35 544.03 p-value < 0.01 0.35 0.35 0.55 0.15 0.59 Europe Model 1 0.52*** 0.17 0.11 558.91 p-value < 0.01 0.17 Model 2 0.53*** 0.03 –0.38 0.17 0.18 577.23 p-value < 0.01 0.86 0.36 0.64 Model 3 0.52*** –0.01 –0.46 0.21 0.19 0.25 0.33 574.75 p-value < 0.01 0.95 0.27 0.56 0.16 0.60 Asia-Pacific Model 1 0.52*** 0.22 0.11 560.97 p-value < 0.01 0.17 Model 2 0.53*** 0.10 –0.14 –0.49 0.23 583.18 p-value < 0.01 0.57 0.68 0.17 Model 3 0.53*** 0.07 –0.17 –0.47 0.16 0.12 0.32 580.55 p-value < 0.01 0.70 0.62 0.19 0.24 0.79 Notes: This table presents regression estimates for the 3 models in equations 1,2,3. The sample is drawn from the Datastream database, the Blockchain Info and Fama-French websites over the period 22 September 2010 to 30 December 2016 in the World, European, and Asia-Pacific regions. ***, ** and * indicate that the coefficient is sig-nificant at 1%, 5% and 10% level respectively and ## Table VII. Bitcoin’s α based on Model 2 (Fama and French three-factor model) Region 2010-2016 2010 2011 2012 2013 2014 2015 2016 World α (%) 0.51*** 0.47 0.73 0.61*** 1.42*** –0.24 0.29 0.20 p-value < 0.01 0.71 0.18 <0.01 <0.01 0.31 0.23 0.20 Annualised α (%) 548.75 452.47 1,300.36 810.92 17,076.26 –57.98 189.34 106.43 Europe α (%) 0.53*** 0.4383 0.83 0.64*** 1.55*** –0.25 0.30 0.19 p-value < 0.01 0.73 0.13 <0.01 <0.01 0.28 0.23 0.22 Annualised α (%) 577.23 393.47 1,940.03 914.80 27,716.86 –59.84 193.25 99.73 Asia-Pacific α (%) 0.53*** 0.38 0.81 0.68*** 1.47*** –0.27 0.24 0.23 p-value < 0.01 0.764 0.14 < 0.01 < 0.01 0.25 0.32 0.15 Annualised α (%) 583.18 297.41 1,799.39 1,089.78 20,653.39 –62.49 140.02 129.16 Notes: This Table presents the regression results for model 2, year by year, in equation 2. The sample is drawn from the Datastream database, the Blockchain Info and Fama-French websites over the period 2010 2016 in the World, Eu-rope and Asian-Pacific regions. We run year by year model 2 to estimate alpha evolution in the World, European and Asia-Pacific regions. ***, ** and * show that the coefficient is significant at 1%, 5% and 10% level respective-ly ## Table VIII. Correlation matrix on the Chinese market Explanatory variable RMkt-Rf SMB HML Gold Bonds Rbitcoin-Rf 0.08*** 0.01 0.03 0.01 0.02 RMkt-Rf 0.04* 0.13*** 0.05** –0.06** SMB 0.14*** 0.02 –0.02 HML 0.04* –0.05** Gold 0.18*** Notes: This table presents the correlation matrix between the dependent variable (RBitcoin-Rf) and independent variables (Mkt-Rf, SMB, HML, Gold, Bonds). The sample concerns the period between September 23, 2010, and December 30th, 2016. ***, ** and * show that the coefficient is significant at 1%, 5% and 10% level respectively ## Table IX. Bitcoin’s α on the Chinese market Model α (%/day) α (%/year) RMkt-Rf SMB HML Gold Bonds R2 (%) Model 1 0.59*** 763.61 0.35*** 0.65 p-value < 0.01 < 0.01 Model 2 0.58*** 737.77 0.33*** 0.09 0.08 0.66 p-value < 0.01 < 0.01 0.78 0.72 Model 3 0.57*** 704.46 0.34*** 0.10 0.09 0.91 58.02 0.75 p-value < 0.01 < 0.01 0.76 0.70 0.95 0.25 Notes: This table presents the regression results for the 3 models in equations 1,2 and 3 for the Chinese Market. The data needed to construct the proxies for the Chinese market, the size and the B/M indices are extracted from the Datasteam database, while the data needed for computing the Bitcoin’s returns are extracted from Blockchain Info. The period of analysis is from September 23, 2010, and December 30th, 2016. ***, ** and * show that the coefficient is significant at 1%, 5% and 10% level re-spectively ## Table X Bitcoin return normality test Variable Shapiro–Wilk Kolmogorov–Smirnov Cramer–Von Mises Anderson–Darling Statistics 0.79*** 0.16*** 18.44*** 94.04*** p-value < 0.01 < 0.01 < 0.01 < 0.01 Notes: This table presents the normality test for Bitcoin returns. The sample is drawn from the Blockchain Info website over the period 2010-2016. The normality hypoth-esis is based on Shapiro-Wilk test: if the p-value is lower than alpha, the null-hypothesis of normality is rejected ## Table XI. Collinearity: test of independent variables World Europe Asia-Pacific Model VIF TOL VIF TOL VIF TOL Model 1 α 0 0 0 Mkt-Rf 1 1 1 1 1 1 Model 2 α 0 0 0 Mkt-Rf 1.2 0.8 2.13 0.47 1.4 0.71 SMB 1.2 0.8 1.9 0.5 1.2 0.81 HML 1 1 1.3 0.8 1.3 0.8 Model 3 α 0 0 0 Mkt-Rf 1.2 0.8 2.17 0.46 1.43 0.7 SMB 1.2 0.8 2 0.5 1.2 0.8 HML 1 1 1.3 0.8 1.3 0.8 Bonds 1.1 0.9 1.1 1 1.1 0.94 Gold 1.1 0.9 1.1 0.9 1 0.97 Notes: This table shows collinearity test of independent variables. The sample is drawn from the Blockchain Info and Fama-French websites over the period 2010 to 2016 for the World. Europe and Asia-Pacific regions and for the 3 models in equations 1, 2 and 3. VIF is the variance inflation factor: if VIF is higher than 4 and TOL is lower than 0.25, then the variable is considered collinear with the dependent variable ## Table XII. Residual analysis Region Autocorrelation Durbin–Watson Homoscedasticity Normality Shapiro–Wilk World Model 1 1.72 3.54 0.79*** p-value 0.17 < 0.01 Model 2 1.71 10.10 0.79*** p-value 0.34 < 0.01 Model 3 1.72 27.51 0.79*** p-value 0.12 < 0.01 Europe Model 1 1.72 1.14 0.79*** p-value 0.56 < 0.01 Model 2 1.71 3.61 0.79*** p-value 0.93 < 0.01 Model 3 1.72 22.74 0.79*** p-value 0.30 < 0.01 Asia-Pacific Model 1 1.71 0.01 0.79*** p-value 0.99 < 0.01 Model 2 1.71 6.36 0.79*** p-value 0.70 < 0.01 Model 3 1.72 23.52 0.79*** p-value 0.26 < 0.01 Notes: This table presents the residuals analysis from the long-run regressions in the world, Europe and Asia-Pacific regions. The sample is drawn from the blockchain info and Fama-French websites over the period 2010 to 2016 in the world, Europe and Asia-Pacific regions for the three models in equations (1), (2) and (3). The residuals autocorrelation hypothesis is tested using the Durbin-Watson statistic: if the Durbin-Watson statistic is around 2, then the residuals are considered uncorrelated. The homoscedasticity hypothesis is tested based on the White test: if the p-value is lower than 5 per cent, the null hypothesis of homoscedasticity is rejected. The normality hypothesis is based on the Shapiro-Wilk test: if the p-value is lower than 5 per cent, the null hypothesis of normality is rejected ## Table XIII. Controlling for market sentiment in the CAPM (Model 1) Model α (%/day) α (%/year) RMkt-Rf Trade1 Trade2 Trade3 Ptc R2 (%) Model 1 0.51*** 545.53 0.27 0.15 p-value < 0.01 0.11 Model 1a 0.68** 1095.19 0.42 –0.13 0.18 p-value 0.02 0.12 0.45 Model 1b 0.89*** 2473.01 0.20 –0.34*** 0.6 p-value < 0.01 0.24 <0.01 Model 1c 0.50*** 514.60 0.26 –0.001 0.14 p-value < 0.01 0.14 0.95 Model 1d 0.33 1428.02 0.27 0.26 0.14 p-value 0.74 0.16 0.86 Notes: This table controls bitcoin performance by including proxies for market sentiment in the CAPM model (Model 1). We use four proxies of market sentiment: Trade1 is the ratio of advancing issues on declining issues; Trade2 is the ratio of advancing issues on declining issues including volume; Trade3 is the ratio of new highs on news lows; PtC is the ratio of puts to calls. The sample is drawn from the blockchain info website, Datastream, and the NYSE and CBOE website and covers the period between 22 September 2010 and 30 December 2016 ## Table XIV Controlling for market sentiment in the FF model (Model 2) Model α (%/day) α (%/year) RMkt-Rf SMB HML Trade1 Trade2 Trade3 PtC R2 (%) Model 2 0.51*** 548.75 0.21 –0.29 0.25 0.19 p-value < 0.01 0.26 0.53 0.62 Model 2a 0.69** 1125.55 0.36 –0.34 0.21 –0.13 0.22 p-value 0.02 0.20 0.47 0.69 0.43 Model 2b 0.89*** 2422.31 0.16 –0.28 0.09 –0.34*** 0.62 p-value < 0.01 0.41 0.55 0.86 < 0.01 Model 2c 0.50*** 514.07 0.20 –0.33 0.21 –0.0004 0.18 p-value < 0.01 0.31 0.50 0.68 0.96 Model 2d 0.38 292.68 0.21 –0.32 0.22 0.20 0.18 p-value 0.71 0.33 0.51 0.67 0.91 Note: This table controls bitcoin performance by including proxies for market sentiment in the FF model (Model 2). We use four proxies of market sentiment: Trade1 is the ratio of advancing issues on declining issues; Trade2 is the ratio of advancing issues on declining issues including volume; Trade3 is the ratio of new highs on news lows; PtC is the ratio of puts to calls. The sample is drawn from the blockchain info website, Datastream, and the NYSE and CBOE website and covers the period between 22 September 2010 and 30 December 2016 ## Table XV. Controlling for market sentiment in the FF extended model (Model 3). Model α (%/day) α (%/year) RMkt-Rf SMB HML Bonds Gold Trade1 Trade2 Trade3 PtC R2 (%) Model 3 0.51*** 544.03 0.17 –0.45 0.29 0.20 0.26 0.35 p-value < 0.01 0.36 0.35 0.55 0.15 0.59 Model 3a 0.72** 1257.34 0.34 –0.51 0.25 0.21 0.26 –0.15 0.4 p-value 0.02 0.22 0.31 0.62 0.14 0.60 0.36 Model 3b 0.88*** 2366.90 0.13 –0.44 0.14 0.17 0.37 –0.33*** 0.77 p-value < 0.01 0.51 0.37 0.78 0.22 0.46 < 0.01 Model 3c 0.50*** 526.39 0.16 –0.48 0.26 0.20 0.25 0.01 0.35 p-value < 0.01 0.41 0.33 0.61 0.15 0.62 0.91 Model 3 0.55 638.77 0.15 –0.48 0.26 0.20 0.26 –0.07 0.35 p-value 0.60 0.47 0.33 0.60 0.15 0.60 0.96 Notes: This table controls bitcoin performance by including proxies for market sentiment in the extended FF model (Model m 3). We use four proxies of market sentiment: Trade1 is the ratio of advancing issues on declining issues; Trade2 is the ratio of advancing issues on declining issues including volume; Trade3 is the ratio of new highs on news lows; PtC is the ratio of puts to calls. The sample is drawn from the blockchain info website, Datastream, and the NYSE and CBOE website and covers the period between 22 September 2010 and 30 December 2016 ## Notes 4. DAO is the first “Decentralized Autonomous Organization” which is “an organization operating through a computer program that provides rules of governance to a community. These rules are transparent and immutable because they are written in the blockchain” according to BlockchainInfo. DAO was created in 2016 with the objectives of crowdfunding using the Ethereum platform (the second payment platform which provides both a cryptocurrency, named Ether, and a blockchain platform). In a short period (four weeks), the project involved 20,000 participants and reached US$160m. A failure in the code provoked a huge attack by hackers, which implied the closure of the structure.

6.

Mt. Gox was a bitcoin exchange platform based in Tokyo and created in 2010. It was a very popular platform until the closure of its activities notably linked to bitcoins embezzlement.

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