- Email: [email protected]
Media attention and Bitcoin prices
Accepted Manuscript
Media Attention and Bitcoin Prices Dionisis Philippas , Hatem Rjiba , Khaled Guesmi , Stephane Goutte ´ PII: DOI: Reference:
S1544-6123(19)30055-8 https://doi.org/10.1016/j.frl.2019.03.031 FRL 1138
To appear in:
Finance Research Letters
Received date: Revised date: Accepted date:
16 January 2019 22 March 2019 24 March 2019
Please cite this article as: Dionisis Philippas , Hatem Rjiba , Khaled Guesmi , Stephane Goutte , Media Attention and Bitcoin Prices, Finance Research Letters (2019), doi: ´ https://doi.org/10.1016/j.frl.2019.03.031
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Highlights
We use dual process diffusion model to identify jumps attributed to informative signals derived from Twitter and Google Trends on Bitcoin prices. The signals justify a sentimental appetite for information demand.
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Media Attention and Bitcoin Prices
Dionisis Philippas ESSCA School of Management, France [email protected]
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Hatem Rjiba ESSCA School of Management, France [email protected]
Khaled Guesmi Ipag Business School, France & Telfer School of Management, University of Ottawa, Canada [email protected]
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Stéphane Goutte University Paris 8, LED, France & Paris School of Business, PSB, Paris, France [email protected]
Abstract
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We present a dual process diffusion model to examine whether Bitcoin prices behave with jumps attributed to informative signals derived from Twitter and Google Trends. The empirical results indicate that Bitcoin prices are partially driven by a momentum on media attention in social networks, justifying a sentimental appetite for information demand.
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Keywords: bitcoin, twitter, google trends, jump diffusion JEL classification: G11, G15, C15
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ACCEPTED MANUSCRIPT 1. Introduction Bitcoin is a widely accepted payment system, among the so-called cryptocurrencies, first introduced by Nakamoto (2008). This letter examines the jump intensity of Bitcoin prices, partially attributed to increasing media attention in social networks.
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Over the last decade that Bitcoin has been traded, many alterations have taken place from exchanges to the likelihood of closure. Nevertheless, the Bitcoin has unique default benefits and properties by its structure. It is fully decentralized and depends on a sophisticated cryptographic protocol that it is difficult to counterfeit (Ron and Shamir, 2013; Dwyer, 2015). It also has the benefits of security and anonymity for investors because banks, governments, or organizations do not issue it. Thus, there is no central authority guaranteeing it or having control over it, thereby shifting the market to become more monopolistically competitive (Bohme et al., 2015). Finally, Bitcoin exchanges have been closely linked with the performance of hedge funds (Lee, 2015); therefore, it can be assumed that along with the increasing daily transactions, the performance of the exchanges increases, which is measured by whether the exchange is still trading or not.
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Due to the extensive trading of Bitcoin from investors over the last years, there is a considerable amount of media attention along with a mounting interest in the literature on Bitcoin electronic transactions, costs and inefficiencies, (see Fry et al., 2016; Dyhrberg, 2016; Hendrickson et al., 2017; Kim, 2017; Dastgir et al., 2019). In this letter, we empirically examine to what extent the increasing media attention in social networks may have an effect on jumps of Bitcoin prices.
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We employ the jump diffusion model of Kou (2002) focused on jump's intensity of Bitcoin prices, which is conditional on the momentum of informative signals, as a dual compound exponential process in the time domain, derived from the volume of corresponding hashtags on Twitter and attention on Google Trends. We emphasize on the daily jumps' effects, mostly because Bitcoin is a short-term horizon trading asset from retailers, thus potentially been affected to a degree by the direction of social networks momentum. Our analysis reveals that media attention in social networks, i.e. Twitter and Google Trends, are partial drivers to sentimental on Bitcoin prices, despite some overlapping expected influence between them. This evidence is more extensive during periods of higher uncertainty, highlighting that underlying reflected media attention has greater spillover effect on Bitcoin prices due to uncertainty. Nevertheless, we argue that investors partially consider media attention in social networks as oriented information demand source concerning Bitcoin prices.
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We believe our insights might be useful to a larger body of research, when defining the relationship between media coverage and Bitcoin prices.
2. Data
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Our data come from Bloomberg and span the period from January 1st 2016 to May 28th 2018. The sample includes daily price levels of Bitcoin (hereafter BTC) and, alternatively for robustness, the daily levels of Bitcoin to USD rate (hereafter XBTUSD). We compute daily returns, using the 1st log differences. Our proxies for media attention flows in social networks are derived from the Google Trends and Twitter. Both are quantitative data that capture the queries of interest using search keywords or hashtags, whereas users are connected to the same network of public information with full access and no costs. We use in Google Trends and Twitter1 the terms "bitcoin" and "btc" as search keyword and hashtag, respectively, to avoid arbitrariness and assure the reliability of our analysis building a market portfolio of 1
Recent studies have pointed out the link between financial markets and sentimental analysis derived from Google Trends and Twitter (see among others, Da et al., 2014; Nisar and Yeung, 2018). Google Trends data can be derived from: https://trends.google.com/trends/?geo=US. Twitter data is derived from: https://bitinfocharts.com/comparison/tweets-btc.html.
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ACCEPTED MANUSCRIPT information source on Bitcoin. We label the media coverage indices derived for our analysis as “google” and “tweets”. Our time span covers some major economic and market stress events occurred where Bitcoin prices have experienced high variations (see Figure 1 with triggered events in note). Within a highly connected financial system, domestic determined stress events can have global consequences. Figure 1. Bitcoin prices versus Google Trend and Twitter 25000
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Google
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BTC Price
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Note: This figure presents the Bitcoin prices along with the media attention flows of “google” and “tweets”. Google Trends data represents the number of searches for the specific query "bitcoin", divided by the total number of queries at that time cell and scaled to the highest value for the requested period so that the highest value of the sample is 100. Twitter data represents the volume for hashtag "btc" (in thousands). The timespan is rich enough to include many of the most significant economic and financial stress events as long as social and political events that have affected the global financial industry, including events originating in the US, Europe, and elsewhere. We can recount: the Brexit referendum (June 2016), the US presidential election (November 2016), the terrorist attacks (e.g. in Paris, London, etc.), the North Korea’s missile tests (July 2017), Theresa May’s Snap General Election (June 2017), Catalonia General Election vote (December 2017), the Venezuela crisis, the ultra-low bond yields (2016-2017), the return of OPEC as deal boosts the oil price (November 2016), the China’s debt pile (2018), the U.S Tax Reform Bill (December 2017), and so on.
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We perform a preliminary analysis for the bitcoin prices and we calculate the descriptive statistics, the tabulations for the mean, the standard deviation, the skewness and kurtosis over the total sample period. Finally, we implement the Granger causality approach building on a bivariate VARX framework, as a comparative analysis. Table 1 presents the results. We observe that although the majority of the bitcoin prices are below the value of $5000, the range of bitcoin values is wide while the normality exhibits different from zero skewness and excess kurtosis, for all intervals (panel B of Table 1), indicating sensitivity and variations of the prices. The results of panel C in Table 1 indicate that google index appears as a major volatility source for both Bitcoin indices (price and currency rate), but only episodically for tweets index. Google search engine is a major influencer when searching information for much more users than Twitter and, therefore, media attention influence is stronger in the case of Google.
Table 1. Preliminary analysis Panel A. Descriptive statistics
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Mean
Maximum
Minimum
Std. dev.
Skewness
Kurtosis
Bitcoin 3518.578 19114.20 364.330 4204.971 1.4936 4.4313 prices Note: The table reports the mean, the standard deviation, the maximum and minimum values, the skewness and the kurtosis for the bitcoin prices over the sample period.
Panel B. Tabulations of descriptive statistics Interval
Tabulation of mean
Tabulation of
Tabulation of skewness
Tabulation of kurtosis
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Std. dev. [0, 5000) 1301.823 1174.297 1.566 4.297 465 [5000, 10000) 7879.727 1199.222 -0.330 2.177 103 [10000, 15000) 11826.76 1610.272 0.795 2.138 43 [15000, 20000) 16715.11 1071.503 0.424 2.608 17 All 3518.578 4204.971 1.493 4.432 628 Note: The table reports the tabulation of the means, the standard deviations, the skewness and the kurtosis for the bitcoin prices over the sample period. The first column shows the interval values while the next column show the tabulations of mean, standard deviation, skewness and kurtosis, along with the number of corresponding observation by interval.
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Panel C. Granger causality
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→ (causes) XBTUSD BTC Tweets Google XBTUSD → Yes No Yes BTC→ No No Yes Tweets → Yes No No Google → Yes Yes Yes Note: Label “Yes” (“No”) indicates whenever we cannot (can) reject the existence of Granger causality, using 5% as a threshold level.
3. Empirical design
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Consider an informative signal introduced into a market for all market investors. Each investor has an initial asset value 𝑉0 and she should incorporate the signal to her individual investment strategy, given her priority and urgent. This asset value would change over time as the result of the volume of information arrival (random or scheduled, public or private) and the value of the volume of information arrival (evaluation). This change should be illustrated in a time-varying continuous model conditional to the effect of the value of new information arrivals.
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The volume of information arrivals and the evaluation of aggregate information arrived in time 𝑡 for any investor are unknown. Therefore, we can’t really know what an investor actually observes and how this observation is evaluated (modeled). We can only assume that on aggregate level, the market value is perfectly observed for any time cell, representing the aggregate value of information arrival for all investors in the market. Let assume a Levy process to model the asset value, which is a stochastic process defined on the probability space (Ω, ℜ, 𝑃), allowing diffusion with jumps, when the asset value changes in every time cell, using the formulation (Kou, 2002): 𝑉𝑡 = 𝑉0 exp(𝑋𝑡 ) 𝑤𝑖𝑡ℎ 𝑉0 > 0
(1)
where, 𝑉0 is the initial value of the asset and 𝑋𝑡 = {𝑋𝑡 }𝑡≥0 is a jumping diffusion process, defined as: 𝑁𝑡
𝑋𝑡 = 𝛾𝑡 + 𝜎𝑊𝑡 + ∑ 𝑦𝑡
(2)
𝑡=1
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ACCEPTED MANUSCRIPT Where, 𝑊𝑡 is the Brown motion, 𝛾 is the term of the linear tendency at the process, 𝜎 is the 𝑁𝑡 standard error of the diffusion process and 𝑦 = ∑𝑡=1 𝑦𝑡 the sequence of jumps, which have a continuous and random behavior. The jumping diffusion process 𝑦 is a compound process and can take any form. Solving equation (2), we get: 𝑁𝑡
1 𝑉𝑡 = 𝑉0 𝑒𝑥𝑝 [(𝛾 − 𝜎 2 ) 𝑡 + 𝜎𝑊𝑡 ] ∏ 𝑒𝑥𝑝(𝑦𝑡 ) 2
(3)
𝑡=1
In this study, we assume that 𝑦 is a dual exponential jumping diffusion process: 𝑓(𝑦) = 𝑝𝜆+ exp(−𝜆+ 𝑦𝑖 ) 𝐼𝑋>0 + (1 − 𝑝)𝜆− exp(−𝜆− 𝑦𝑖 ) 𝐼𝑋<0
(4)
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where, 𝑝 is the probability of positive jump, 𝜆+ 𝑜𝑟 𝜆− is the size of the jump (positive or negative) and duality refers to the fact that information can be either adopted with a jump or not. In this setting, the mean and standard deviation of the dual diffusion process are: 𝑝 1−𝑝 𝐸(𝑋𝑡 ) = 𝑡 (𝛾 + ( + )) 𝜆+ 𝜆−
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(5)
𝑝 1−𝑝 𝑣𝑎𝑟(𝑋𝑡 ) = 𝑡 (𝜎 2 + ( + )) 𝜆+ 𝜆−
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There are two interesting properties using the dual exponential jumping diffusion process. First, it has the leptokurtic feature of the jump size distribution, which is inherited by the return distribution. The second unique feature is the less memory property, which explains why the closed-form solutions (or approximations) for various pricing problems, are feasible under the exponential jumps-diffusion model, while it seems difficult for many other models, including the normal jump-diffusion model (Kou, 2004). Finally, all sources of randomness, size of the jumps, 𝑊𝑡 and 𝑁𝑡 are mutual independent.
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The asset value depends exponentially on the linear trend, the variance of diffusion of informative signal, the probability of adoption and the size of the jumps. If the diffusion of informative signal is limited during time (𝑝 → 0) then the asset value is influenced by two parameters: the negative jump and its size. This means that media attention is causing bigger negative jumps to Bitcoin prices so informative signals may curtail Bitcoin prices. If the diffusion is spreading from the start time point (𝑝 → 1), the asset value is influenced by two parameters: the positive jump and its size. This means that the greater the positive momentum is the greater the positive jump is and thereby the asset value increases.
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Finally, we can write the effect of jump diffusion on an asset price whose price is normally dictated by Brownian drift as a simple form of equation (3) conditional to equation (4), as: 𝑟𝑡 = 𝜇 + 𝜀𝑡 + 𝐼𝑡,𝑋 𝑢𝑡
(6)
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where 𝑟𝑡 is the log return, 𝜇 is the mean drift, 𝜀𝑡 is the diffusion, 𝐼𝑡,𝑋 is the dual exponential function, and 𝑢𝑡 is the value of the jump. 4. Empirical results Table 2 summarizes the main results of our analysis and reveals the casual relationship between Bitcoin prices and media attention in social networks that might provide a narrative consistent with the stress events observed during the time spanning. First, the results show that the number of jumps for both social networks are almost half of the days across the time spanning in our sample. This can be consider as robust volatile sources for Bitcoin prices (also Bitcoin to USD rate). Moreover, we observe that the percentage of positive jump values is less than the negative one, thereby indicating that higher uncertainty reflected in social
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ACCEPTED MANUSCRIPT networks can curtail Bitcoin prices. This can also be shown from the results in the following rows of Table 2, where diffusion rate and prices' variation take negative values. Table 2. Empirical results BTC and Tweets
BTC and Google
XTBUSD and Tweets
XTBUSD and Google
325
297
307
332
Positive jumps (average)
0.52%
0.50%
0.47%
0.57%
Negative jumps (average)
-0.81%
-0.74%
Diffusion (average)
-0.35%
-0.55%
Jump value (average)
-0.29%
-0.24%
Prices’ variation conditional to jump (average)
-63.034
-38.469
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Jumps
-0.78%
-0.35%
-0.55%
-0.16%
-0.21%
-28.623
-35.165
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-0.63%
Note: This table presents a summary of the average values of our empirical results for Bitcoin prices and Bitcoin to USD rate. The first row shows the number of jumps out of 627 observations in total, for each informative social network, i.e. Twitter and Google Trends. The second and the third rows show the values (percentages) of positive and negative values of jumps, respectively. The next row shows the average rate of diffusion and the fifth row shows the average rate of jump value. Finally, the last row shows the price values’ variation (in absolute values) on average.
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In this setting, the results converge to the first main conclusion that media attention in social networks is volatile source for Bitcoin prices during the time spanning; however, this can be only episodically, which is visually illustrated in comparing bar charts in Figure 2 as our second main result. We observe that during high variations of Bitcoin prices (i.e. starting 2017 onwards as noted in Figure 1), the unidirectional influences from media attention in social networks are greater, where negative jumps have a clearly more significant influences being exposed within the jump approach. In particular, we see several significant spillover effects identified for Twitter mainly after July 2017 and Google Trends across all the period, on Bitcoin prices. This indicates that Twitter is mostly an instantly related momentum factor, which are captured by the model, bringing influences based on debates when commenting current situation but not entirely working as a source of information demand.
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Figure 2. Bitcoin prices and Google Trend and Twitter jumps
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Note: This figure presents the Bitcoin prices’ variations along with the “google” and “tweets” jumps, distinguished of positive and negative jumps. The red bars correspond to negative jumps, the blue bars correspond to positive jumps of media attention flow, and the grey bars correspond to Bitcoin prices’ variations. Google Trends and Twitter.
In other words, exposing the direction of the underlying jumps of Bitcoin prices seems less sensitive to Twitter (than Google Trends) for stable periods, which however becomes a significant related factor under high uncertainty. Similarly, the jump spillovers exposed by Google Trends are confirmed the entire period, acting as information demand source for investors who are looking opportunities in the Bitcoin market to diversify or speculate through their portfolio. Overall, our analysis suggests that media attention might have an advantage as a source of information demand over the Bitcoin prices. Information demand is positively related to the degree of risk aversion of a market agent; however, increasing risk aversion does not always increase the value of information. Moscarini and Smith (2002) argue that information demand is a decreasing function of the informational content of a signal; when a stress event occurs,
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ACCEPTED MANUSCRIPT the uncertainty with respect to its consequences is greater and agents demand more information.
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Generally, in similar empirical exercises, the uncertainty about which factors to model is high; to a certain extent and in case such factors can be observed or inferred, this uncertainty might be reduced. Recent research has shown that investors are taking a breather from Bitcoin and looking at alternative cryptocurrencies such as Ethereum, Ripple, Litecoin, Stellar and Dash (Ji et al., 2018). Our method can be applied to any of these cryptocurrencies with a sufficient data availability. However, the results would satisfy other cryptocurrencies in a similar manner, conditional to their degree of demand. In this setting, information demand and supply would affect similarly Bitcoin and Litecoin that are in the centre of the cryptocurrency market, Ripple and Ethereum are affected mostly from negative-return shocks, whereas Ethereum and Dash would exhibit very weak effect via positive returns. In the case of volatility spillovers, Bitcoin, Litecoin, and Dash would be the most influential, suggesting their use for hedging and diversification opportunities in the cryptocurrency market.
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Finally, media attention can be an important informative signal for herding; an intuitive result based on our results that bitcoin tweets reflect information supply and Google searches information demand. A signal from Twitter may be associated with an unexpected information supply peak reflecting bitcoin market information while a signal in Google searches indicates a dip and sudden resurgence of interest in bitcoin-related information, which can be used by investors to form strategies. Nevertheless, our analysis points to a relative disadvantage of using media attention of social networks, which is the trade-off between accuracy and priority. This downplays the importance of strong and relevant exogenous and latent factors in determining the direction of underlying volatility spillovers on Bitcoin prices.
5. Conclusion
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This letter uses a dual exponential compound process as a momentum factor in a jump diffusion model to expose the effect of media attention in social networks, namely Twitter and Google Trends, on Bitcoin prices. We illustrate the number, the direction and the intensity of jumps derived from media networks of social networks on Bitcoin prices. We suggest that media networks have only a partial influence on Bitcoin prices, which is greater on periods with higher uncertainty, also acting as information demand sources in some cases. References
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Bohme, R., Christin, N., Edelman, B., Moore, T., 2015. Bitcoin: Economics, Technology, and Governance. Journal of Economic Perspectives, 29, 213–238. Da, Z., Engelberg, J., Gao, P., 2014. The sum of all fears: Investor sentiment and asset prices. Review of Financial Studies, 28, 1–32. Dastgir, S., Demir, E., Downing, G., Gozgor, G., Lau, C. K. M., 2019. The causal relationship between Bitcoin attention and Bitcoin returns: Evidence from the Copula-based Granger causality test. Finance Research Letters, 28, 160-164. Dwyer, G.P., 2015. The economics of Bitcoin and similar private digital currencies. Journal of Financial Stability, 17, 81–91. Dyhrberg, H., 2016. Bitcoin, gold and the dollar-A GARCH volatility analysis. Finance Research Letters, 16, 85–92.
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ACCEPTED MANUSCRIPT Fry, J., Eng-Tuck C., 2016. Negative bubbles and shocks in cryptocurrency markets. International Review of Financial Analysis, 47, 343–352. Hendrickson, J.R., Luther, W.J., 2017. Banning bitcoin. Journal of Economic Behavior & Organization, 141, 188–195. Ji, Q., Bouri, E., Lau, C.K.M., Roubaud, D., 2018. Dynamic connectedness and integration in cryptocurrency markets. International Review of Financial Analysis, (in press), https://doi.org/10.1016/j.irfa.2018.12.002. Kim, T., 2017. On the transaction cost of Bitcoin. Finance Research Letters, 23, 300–305.
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Kou, S.G., Wang, H., 2004. Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192. Kou, S.G., 2002. A Jump-Diffusion Model for Option Pricing. Management Science, 48, 1086-1101. Lee, D., 2015. Handbook of Digital Currency: Bitcoin, Innovation, Financial Instruments, and Big Data. London: Academic Press. 1–135.
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Moscarini, G. and Smith, L., 2002. The law of large demand for information. Econometrica, 70, 2351–2366. Nakamoto, S., 2008. Bitcoin: A Peer-To-Peer Electronic Cash System available at: https://bitcoin.org/bitcoin.pdf. Nisar, T.M., Yeung, M., 2018. Twitter as a tool for forecasting stock market movements: A short-window event study. Journal of Finance and Data Science, 4, 101–119.
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Ron, D., Shamir, A., 2013. Quantitative Analysis of the Full Bitcoin Transaction Graph. Financial Cryptography and Data Security, 13, 6–24.
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Media Attention and Bitcoin Prices Dionisis Philippas , Hatem Rjiba , Khaled Guesmi , Stephane Goutte ´ PII: DOI: Reference:
S1544-6123(19)30055-8 https://doi.org/10.1016/j.frl.2019.03.031 FRL 1138
To appear in:
Finance Research Letters
Received date: Revised date: Accepted date:
16 January 2019 22 March 2019 24 March 2019
Please cite this article as: Dionisis Philippas , Hatem Rjiba , Khaled Guesmi , Stephane Goutte , Media Attention and Bitcoin Prices, Finance Research Letters (2019), doi: ´ https://doi.org/10.1016/j.frl.2019.03.031
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Highlights
We use dual process diffusion model to identify jumps attributed to informative signals derived from Twitter and Google Trends on Bitcoin prices. The signals justify a sentimental appetite for information demand.
AC
CE
PT
ED
M
AN US
CR IP T
1
ACCEPTED MANUSCRIPT
Media Attention and Bitcoin Prices
Dionisis Philippas ESSCA School of Management, France [email protected]
CR IP T
Hatem Rjiba ESSCA School of Management, France [email protected]
Khaled Guesmi Ipag Business School, France & Telfer School of Management, University of Ottawa, Canada [email protected]
M
AN US
Stéphane Goutte University Paris 8, LED, France & Paris School of Business, PSB, Paris, France [email protected]
Abstract
ED
We present a dual process diffusion model to examine whether Bitcoin prices behave with jumps attributed to informative signals derived from Twitter and Google Trends. The empirical results indicate that Bitcoin prices are partially driven by a momentum on media attention in social networks, justifying a sentimental appetite for information demand.
AC
CE
PT
Keywords: bitcoin, twitter, google trends, jump diffusion JEL classification: G11, G15, C15
2
ACCEPTED MANUSCRIPT 1. Introduction Bitcoin is a widely accepted payment system, among the so-called cryptocurrencies, first introduced by Nakamoto (2008). This letter examines the jump intensity of Bitcoin prices, partially attributed to increasing media attention in social networks.
CR IP T
Over the last decade that Bitcoin has been traded, many alterations have taken place from exchanges to the likelihood of closure. Nevertheless, the Bitcoin has unique default benefits and properties by its structure. It is fully decentralized and depends on a sophisticated cryptographic protocol that it is difficult to counterfeit (Ron and Shamir, 2013; Dwyer, 2015). It also has the benefits of security and anonymity for investors because banks, governments, or organizations do not issue it. Thus, there is no central authority guaranteeing it or having control over it, thereby shifting the market to become more monopolistically competitive (Bohme et al., 2015). Finally, Bitcoin exchanges have been closely linked with the performance of hedge funds (Lee, 2015); therefore, it can be assumed that along with the increasing daily transactions, the performance of the exchanges increases, which is measured by whether the exchange is still trading or not.
AN US
Due to the extensive trading of Bitcoin from investors over the last years, there is a considerable amount of media attention along with a mounting interest in the literature on Bitcoin electronic transactions, costs and inefficiencies, (see Fry et al., 2016; Dyhrberg, 2016; Hendrickson et al., 2017; Kim, 2017; Dastgir et al., 2019). In this letter, we empirically examine to what extent the increasing media attention in social networks may have an effect on jumps of Bitcoin prices.
PT
ED
M
We employ the jump diffusion model of Kou (2002) focused on jump's intensity of Bitcoin prices, which is conditional on the momentum of informative signals, as a dual compound exponential process in the time domain, derived from the volume of corresponding hashtags on Twitter and attention on Google Trends. We emphasize on the daily jumps' effects, mostly because Bitcoin is a short-term horizon trading asset from retailers, thus potentially been affected to a degree by the direction of social networks momentum. Our analysis reveals that media attention in social networks, i.e. Twitter and Google Trends, are partial drivers to sentimental on Bitcoin prices, despite some overlapping expected influence between them. This evidence is more extensive during periods of higher uncertainty, highlighting that underlying reflected media attention has greater spillover effect on Bitcoin prices due to uncertainty. Nevertheless, we argue that investors partially consider media attention in social networks as oriented information demand source concerning Bitcoin prices.
CE
We believe our insights might be useful to a larger body of research, when defining the relationship between media coverage and Bitcoin prices.
2. Data
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Our data come from Bloomberg and span the period from January 1st 2016 to May 28th 2018. The sample includes daily price levels of Bitcoin (hereafter BTC) and, alternatively for robustness, the daily levels of Bitcoin to USD rate (hereafter XBTUSD). We compute daily returns, using the 1st log differences. Our proxies for media attention flows in social networks are derived from the Google Trends and Twitter. Both are quantitative data that capture the queries of interest using search keywords or hashtags, whereas users are connected to the same network of public information with full access and no costs. We use in Google Trends and Twitter1 the terms "bitcoin" and "btc" as search keyword and hashtag, respectively, to avoid arbitrariness and assure the reliability of our analysis building a market portfolio of 1
Recent studies have pointed out the link between financial markets and sentimental analysis derived from Google Trends and Twitter (see among others, Da et al., 2014; Nisar and Yeung, 2018). Google Trends data can be derived from: https://trends.google.com/trends/?geo=US. Twitter data is derived from: https://bitinfocharts.com/comparison/tweets-btc.html.
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ACCEPTED MANUSCRIPT information source on Bitcoin. We label the media coverage indices derived for our analysis as “google” and “tweets”. Our time span covers some major economic and market stress events occurred where Bitcoin prices have experienced high variations (see Figure 1 with triggered events in note). Within a highly connected financial system, domestic determined stress events can have global consequences. Figure 1. Bitcoin prices versus Google Trend and Twitter 25000
180 Tweets
20000
160
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BTC Price
140 120
15000
100 80
10000
60
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5000
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40 20 0
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Note: This figure presents the Bitcoin prices along with the media attention flows of “google” and “tweets”. Google Trends data represents the number of searches for the specific query "bitcoin", divided by the total number of queries at that time cell and scaled to the highest value for the requested period so that the highest value of the sample is 100. Twitter data represents the volume for hashtag "btc" (in thousands). The timespan is rich enough to include many of the most significant economic and financial stress events as long as social and political events that have affected the global financial industry, including events originating in the US, Europe, and elsewhere. We can recount: the Brexit referendum (June 2016), the US presidential election (November 2016), the terrorist attacks (e.g. in Paris, London, etc.), the North Korea’s missile tests (July 2017), Theresa May’s Snap General Election (June 2017), Catalonia General Election vote (December 2017), the Venezuela crisis, the ultra-low bond yields (2016-2017), the return of OPEC as deal boosts the oil price (November 2016), the China’s debt pile (2018), the U.S Tax Reform Bill (December 2017), and so on.
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We perform a preliminary analysis for the bitcoin prices and we calculate the descriptive statistics, the tabulations for the mean, the standard deviation, the skewness and kurtosis over the total sample period. Finally, we implement the Granger causality approach building on a bivariate VARX framework, as a comparative analysis. Table 1 presents the results. We observe that although the majority of the bitcoin prices are below the value of $5000, the range of bitcoin values is wide while the normality exhibits different from zero skewness and excess kurtosis, for all intervals (panel B of Table 1), indicating sensitivity and variations of the prices. The results of panel C in Table 1 indicate that google index appears as a major volatility source for both Bitcoin indices (price and currency rate), but only episodically for tweets index. Google search engine is a major influencer when searching information for much more users than Twitter and, therefore, media attention influence is stronger in the case of Google.
Table 1. Preliminary analysis Panel A. Descriptive statistics
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Mean
Maximum
Minimum
Std. dev.
Skewness
Kurtosis
Bitcoin 3518.578 19114.20 364.330 4204.971 1.4936 4.4313 prices Note: The table reports the mean, the standard deviation, the maximum and minimum values, the skewness and the kurtosis for the bitcoin prices over the sample period.
Panel B. Tabulations of descriptive statistics Interval
Tabulation of mean
Tabulation of
Tabulation of skewness
Tabulation of kurtosis
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Std. dev. [0, 5000) 1301.823 1174.297 1.566 4.297 465 [5000, 10000) 7879.727 1199.222 -0.330 2.177 103 [10000, 15000) 11826.76 1610.272 0.795 2.138 43 [15000, 20000) 16715.11 1071.503 0.424 2.608 17 All 3518.578 4204.971 1.493 4.432 628 Note: The table reports the tabulation of the means, the standard deviations, the skewness and the kurtosis for the bitcoin prices over the sample period. The first column shows the interval values while the next column show the tabulations of mean, standard deviation, skewness and kurtosis, along with the number of corresponding observation by interval.
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Panel C. Granger causality
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→ (causes) XBTUSD BTC Tweets Google XBTUSD → Yes No Yes BTC→ No No Yes Tweets → Yes No No Google → Yes Yes Yes Note: Label “Yes” (“No”) indicates whenever we cannot (can) reject the existence of Granger causality, using 5% as a threshold level.
3. Empirical design
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Consider an informative signal introduced into a market for all market investors. Each investor has an initial asset value 𝑉0 and she should incorporate the signal to her individual investment strategy, given her priority and urgent. This asset value would change over time as the result of the volume of information arrival (random or scheduled, public or private) and the value of the volume of information arrival (evaluation). This change should be illustrated in a time-varying continuous model conditional to the effect of the value of new information arrivals.
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The volume of information arrivals and the evaluation of aggregate information arrived in time 𝑡 for any investor are unknown. Therefore, we can’t really know what an investor actually observes and how this observation is evaluated (modeled). We can only assume that on aggregate level, the market value is perfectly observed for any time cell, representing the aggregate value of information arrival for all investors in the market. Let assume a Levy process to model the asset value, which is a stochastic process defined on the probability space (Ω, ℜ, 𝑃), allowing diffusion with jumps, when the asset value changes in every time cell, using the formulation (Kou, 2002): 𝑉𝑡 = 𝑉0 exp(𝑋𝑡 ) 𝑤𝑖𝑡ℎ 𝑉0 > 0
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where, 𝑉0 is the initial value of the asset and 𝑋𝑡 = {𝑋𝑡 }𝑡≥0 is a jumping diffusion process, defined as: 𝑁𝑡
𝑋𝑡 = 𝛾𝑡 + 𝜎𝑊𝑡 + ∑ 𝑦𝑡
(2)
𝑡=1
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1 𝑉𝑡 = 𝑉0 𝑒𝑥𝑝 [(𝛾 − 𝜎 2 ) 𝑡 + 𝜎𝑊𝑡 ] ∏ 𝑒𝑥𝑝(𝑦𝑡 ) 2
(3)
𝑡=1
In this study, we assume that 𝑦 is a dual exponential jumping diffusion process: 𝑓(𝑦) = 𝑝𝜆+ exp(−𝜆+ 𝑦𝑖 ) 𝐼𝑋>0 + (1 − 𝑝)𝜆− exp(−𝜆− 𝑦𝑖 ) 𝐼𝑋<0
(4)
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where, 𝑝 is the probability of positive jump, 𝜆+ 𝑜𝑟 𝜆− is the size of the jump (positive or negative) and duality refers to the fact that information can be either adopted with a jump or not. In this setting, the mean and standard deviation of the dual diffusion process are: 𝑝 1−𝑝 𝐸(𝑋𝑡 ) = 𝑡 (𝛾 + ( + )) 𝜆+ 𝜆−
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(5)
𝑝 1−𝑝 𝑣𝑎𝑟(𝑋𝑡 ) = 𝑡 (𝜎 2 + ( + )) 𝜆+ 𝜆−
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There are two interesting properties using the dual exponential jumping diffusion process. First, it has the leptokurtic feature of the jump size distribution, which is inherited by the return distribution. The second unique feature is the less memory property, which explains why the closed-form solutions (or approximations) for various pricing problems, are feasible under the exponential jumps-diffusion model, while it seems difficult for many other models, including the normal jump-diffusion model (Kou, 2004). Finally, all sources of randomness, size of the jumps, 𝑊𝑡 and 𝑁𝑡 are mutual independent.
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The asset value depends exponentially on the linear trend, the variance of diffusion of informative signal, the probability of adoption and the size of the jumps. If the diffusion of informative signal is limited during time (𝑝 → 0) then the asset value is influenced by two parameters: the negative jump and its size. This means that media attention is causing bigger negative jumps to Bitcoin prices so informative signals may curtail Bitcoin prices. If the diffusion is spreading from the start time point (𝑝 → 1), the asset value is influenced by two parameters: the positive jump and its size. This means that the greater the positive momentum is the greater the positive jump is and thereby the asset value increases.
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Finally, we can write the effect of jump diffusion on an asset price whose price is normally dictated by Brownian drift as a simple form of equation (3) conditional to equation (4), as: 𝑟𝑡 = 𝜇 + 𝜀𝑡 + 𝐼𝑡,𝑋 𝑢𝑡
(6)
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where 𝑟𝑡 is the log return, 𝜇 is the mean drift, 𝜀𝑡 is the diffusion, 𝐼𝑡,𝑋 is the dual exponential function, and 𝑢𝑡 is the value of the jump. 4. Empirical results Table 2 summarizes the main results of our analysis and reveals the casual relationship between Bitcoin prices and media attention in social networks that might provide a narrative consistent with the stress events observed during the time spanning. First, the results show that the number of jumps for both social networks are almost half of the days across the time spanning in our sample. This can be consider as robust volatile sources for Bitcoin prices (also Bitcoin to USD rate). Moreover, we observe that the percentage of positive jump values is less than the negative one, thereby indicating that higher uncertainty reflected in social
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BTC and Google
XTBUSD and Tweets
XTBUSD and Google
325
297
307
332
Positive jumps (average)
0.52%
0.50%
0.47%
0.57%
Negative jumps (average)
-0.81%
-0.74%
Diffusion (average)
-0.35%
-0.55%
Jump value (average)
-0.29%
-0.24%
Prices’ variation conditional to jump (average)
-63.034
-38.469
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Jumps
-0.78%
-0.35%
-0.55%
-0.16%
-0.21%
-28.623
-35.165
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-0.63%
Note: This table presents a summary of the average values of our empirical results for Bitcoin prices and Bitcoin to USD rate. The first row shows the number of jumps out of 627 observations in total, for each informative social network, i.e. Twitter and Google Trends. The second and the third rows show the values (percentages) of positive and negative values of jumps, respectively. The next row shows the average rate of diffusion and the fifth row shows the average rate of jump value. Finally, the last row shows the price values’ variation (in absolute values) on average.
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In this setting, the results converge to the first main conclusion that media attention in social networks is volatile source for Bitcoin prices during the time spanning; however, this can be only episodically, which is visually illustrated in comparing bar charts in Figure 2 as our second main result. We observe that during high variations of Bitcoin prices (i.e. starting 2017 onwards as noted in Figure 1), the unidirectional influences from media attention in social networks are greater, where negative jumps have a clearly more significant influences being exposed within the jump approach. In particular, we see several significant spillover effects identified for Twitter mainly after July 2017 and Google Trends across all the period, on Bitcoin prices. This indicates that Twitter is mostly an instantly related momentum factor, which are captured by the model, bringing influences based on debates when commenting current situation but not entirely working as a source of information demand.
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Figure 2. Bitcoin prices and Google Trend and Twitter jumps
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Note: This figure presents the Bitcoin prices’ variations along with the “google” and “tweets” jumps, distinguished of positive and negative jumps. The red bars correspond to negative jumps, the blue bars correspond to positive jumps of media attention flow, and the grey bars correspond to Bitcoin prices’ variations. Google Trends and Twitter.
In other words, exposing the direction of the underlying jumps of Bitcoin prices seems less sensitive to Twitter (than Google Trends) for stable periods, which however becomes a significant related factor under high uncertainty. Similarly, the jump spillovers exposed by Google Trends are confirmed the entire period, acting as information demand source for investors who are looking opportunities in the Bitcoin market to diversify or speculate through their portfolio. Overall, our analysis suggests that media attention might have an advantage as a source of information demand over the Bitcoin prices. Information demand is positively related to the degree of risk aversion of a market agent; however, increasing risk aversion does not always increase the value of information. Moscarini and Smith (2002) argue that information demand is a decreasing function of the informational content of a signal; when a stress event occurs,
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Generally, in similar empirical exercises, the uncertainty about which factors to model is high; to a certain extent and in case such factors can be observed or inferred, this uncertainty might be reduced. Recent research has shown that investors are taking a breather from Bitcoin and looking at alternative cryptocurrencies such as Ethereum, Ripple, Litecoin, Stellar and Dash (Ji et al., 2018). Our method can be applied to any of these cryptocurrencies with a sufficient data availability. However, the results would satisfy other cryptocurrencies in a similar manner, conditional to their degree of demand. In this setting, information demand and supply would affect similarly Bitcoin and Litecoin that are in the centre of the cryptocurrency market, Ripple and Ethereum are affected mostly from negative-return shocks, whereas Ethereum and Dash would exhibit very weak effect via positive returns. In the case of volatility spillovers, Bitcoin, Litecoin, and Dash would be the most influential, suggesting their use for hedging and diversification opportunities in the cryptocurrency market.
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Finally, media attention can be an important informative signal for herding; an intuitive result based on our results that bitcoin tweets reflect information supply and Google searches information demand. A signal from Twitter may be associated with an unexpected information supply peak reflecting bitcoin market information while a signal in Google searches indicates a dip and sudden resurgence of interest in bitcoin-related information, which can be used by investors to form strategies. Nevertheless, our analysis points to a relative disadvantage of using media attention of social networks, which is the trade-off between accuracy and priority. This downplays the importance of strong and relevant exogenous and latent factors in determining the direction of underlying volatility spillovers on Bitcoin prices.
5. Conclusion
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This letter uses a dual exponential compound process as a momentum factor in a jump diffusion model to expose the effect of media attention in social networks, namely Twitter and Google Trends, on Bitcoin prices. We illustrate the number, the direction and the intensity of jumps derived from media networks of social networks on Bitcoin prices. We suggest that media networks have only a partial influence on Bitcoin prices, which is greater on periods with higher uncertainty, also acting as information demand sources in some cases. References
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Bohme, R., Christin, N., Edelman, B., Moore, T., 2015. Bitcoin: Economics, Technology, and Governance. Journal of Economic Perspectives, 29, 213–238. Da, Z., Engelberg, J., Gao, P., 2014. The sum of all fears: Investor sentiment and asset prices. Review of Financial Studies, 28, 1–32. Dastgir, S., Demir, E., Downing, G., Gozgor, G., Lau, C. K. M., 2019. The causal relationship between Bitcoin attention and Bitcoin returns: Evidence from the Copula-based Granger causality test. Finance Research Letters, 28, 160-164. Dwyer, G.P., 2015. The economics of Bitcoin and similar private digital currencies. Journal of Financial Stability, 17, 81–91. Dyhrberg, H., 2016. Bitcoin, gold and the dollar-A GARCH volatility analysis. Finance Research Letters, 16, 85–92.
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ACCEPTED MANUSCRIPT Fry, J., Eng-Tuck C., 2016. Negative bubbles and shocks in cryptocurrency markets. International Review of Financial Analysis, 47, 343–352. Hendrickson, J.R., Luther, W.J., 2017. Banning bitcoin. Journal of Economic Behavior & Organization, 141, 188–195. Ji, Q., Bouri, E., Lau, C.K.M., Roubaud, D., 2018. Dynamic connectedness and integration in cryptocurrency markets. International Review of Financial Analysis, (in press), https://doi.org/10.1016/j.irfa.2018.12.002. Kim, T., 2017. On the transaction cost of Bitcoin. Finance Research Letters, 23, 300–305.
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Kou, S.G., Wang, H., 2004. Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192. Kou, S.G., 2002. A Jump-Diffusion Model for Option Pricing. Management Science, 48, 1086-1101. Lee, D., 2015. Handbook of Digital Currency: Bitcoin, Innovation, Financial Instruments, and Big Data. London: Academic Press. 1–135.
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Moscarini, G. and Smith, L., 2002. The law of large demand for information. Econometrica, 70, 2351–2366. Nakamoto, S., 2008. Bitcoin: A Peer-To-Peer Electronic Cash System available at: https://bitcoin.org/bitcoin.pdf. Nisar, T.M., Yeung, M., 2018. Twitter as a tool for forecasting stock market movements: A short-window event study. Journal of Finance and Data Science, 4, 101–119.
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Ron, D., Shamir, A., 2013. Quantitative Analysis of the Full Bitcoin Transaction Graph. Financial Cryptography and Data Security, 13, 6–24.
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