#  Arbitrage impact on the relationship between XRP price and correlation
tensor spectra of transaction networks

Abhijit Chakraborty 1,2,∔ and Yuichi Ikeda1,† Currently at the Department of
Humanities and Social Sciences, Indian Institute of Science Education and
Research Tirupati, Tirupati 517619, India.1 Kyoto University1 Kyoto University
Graduate School of Advanced Integrated Studies in Human Survivability Graduate
School of Advanced Integrated Studies in Human Survivability Kyoto Kyoto
606-8306 606-8306 Japan
2RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program Japan
2RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program Saitama
Saitama 351-0198 351-0198 Japan Japan $\dotplus$<EMAIL_ADDRESS>
${\dagger}$<EMAIL_ADDRESS>
###### Abstract

The increasing use of cryptoassets for international remittances has proven to
be faster and more cost-effective, particularly for migrants without access to
traditional banking. However, the inherent volatility of cryptoasset prices,
independent of blockchain-based remittance mechanisms, introduces potential
risks during periods of high volatility. This study investigates the intricate
dynamics between XRP price fluctuations across diverse crypto exchanges and
the correlation of the largest singular values of the correlation tensor of
XRP transaction networks. Particularly, we show the impact of arbitrage
opportunities across different crypto exchanges on the relationship between
XRP price and correlation tensor spectra of transaction networks. Distinct
periods, non-bubble and bubble, showcase different characteristics in XRP
price fluctuations. Establishing a connection between XRP price and
transaction networks, we compute correlation tensors and singular values,
emphasizing the significance of the largest singular value. Comparisons with
reshuffled and Gaussian random correlation tensors validate the uniqueness of
the empirical tensor. A set of simulated weekly XRP prices, resembling
arbitrage opportunities across various crypto exchanges, further confirms the
robustness of our findings. It reveals a pronounced anti-correlation during
bubble periods and a non-significant correlation during non-bubble periods
with the largest singular value, irrespective of price fluctuations across
different crypto exchanges.

cryptoassets, price fluctuation, correlation tensor, singular values

##  1 Introduction

In recent years, cryptoassets have become widely used as an essential means of
international remittances [1, 2]. For example, when migrants transfer money
earned from working in the destination country to family members in the
country of origin, international remittances using cryptoassets are faster and
cheaper than the traditional method of transferring money via banks. In
particular, for migrants who do not have bank accounts in their economically
developing countries of origin, international remittances using cryptoassets
are the only practical way to send money. However, the prices of cryptoassets
are more volatile than fiat currency at times, and international remittances
during periods of high price volatility are said to be risky [3]. The price of
cryptoassets is independent of the blockchain-based remittance mechanism for
cryptoassets. The price is determined when fiat currency and cryptoassets are
exchanged on cryptoasset exchanges.

The price of a cryptoasset generally varies from exchange to exchange, as well
as the point in time when the cryptoasset is exchanged for fiat currency.
Concerning differences in the price of cryptoassets at different points in
time, if cryptoassets are purchased and remitted abroad to family members in
the country of origin when the price of cryptoassets is low, and if
cryptoassets can be sold when the price of cryptoassets is high, the family
members in the country of origin can obtain more economic value. On the other
hand, concerning the price difference between exchanges, if cryptoassets are
purchased on an exchange where the price of cryptoassets is low and remitted
abroad to family members in the country of origin, and cryptoassets are sold
on an exchange where the price of cryptoassets is high, the family members in
the country of origin can obtain more economic value. This is referred as an
arbitrage.

The application of Random Matrix Theory (RMT) [4, 5, 6] has become a prevalent
approach in the analysis of financial time series data, encompassing domains
like stock prices [7, 8, 9], foreign exchange rate [10, 11], and other
macroeconomic indicators. Recently, we utilized random matrix theory to study
crypto transaction networks [12, 13, 14, 15, 16]. Specifically, our method
[12, 13] involving correlation tensor spectra provides a crucial understanding
of the relationship between XRP price and the largest singular value. Our
previous work [12, 13] found that the largest singular value of the
correlation tensor for the transaction networks and the price of cryptoassets
(on a particular exchange) shows a significant negative correlation. Using
this negative correlation may, therefore, reduce the risk of price volatility
of cryptoassets at different points in time. However, no attention has so far
been paid to the impact of exchanges on the price difference of cryptoassets.
If the price difference by exchange is more significant than the difference by
point in time, then the negative correlation described above would have no
practical significance.

In this paper, we first examine the time series of the price of the
cryptoasset XRP on representative exchanges to determine the magnitude of the
price differences by the exchange. It then examines the correlation between
the first singular value of the correlation tensor of the transaction network
and the price, considering the exchange-specific price differences obtained
from the actual price time series. Statistical tests test the significance of
the correlation. This study aims to answer whether the negative correlations
between the largest singular value of the correlation tensor for the
transaction networks and the prices of cryptoassets obtained in our previous
studies are statistically significant when considering the differences in
prices between exchanges.

The paper is organized as follows. We describe our data in Section 2. In
Section 3 we provide a brief description of our methods. Following that,
Section 4 presents a comprehensive discussion of the results obtained from our
investigation. Finally, in Section 5, we share concluding observations.

##  2 Data

We collect XRP daily close price data from nine different crypto exchanges.
The typical 24-hour trade volume on these crypto exchanges is tabulated in
Table 1. It is important to note that among the nine exchanges, Bittrex and
FTX are currently not operational. We additionally present the monthly volumes
across three leading cryptoasset exchanges in Fig. 8.

XRP transaction data is collected from the Ripple API. We construct weekly
networks of users’ wallets from the transactional data by aggregating the XRP
transaction volume for a week between pairs of wallets. It is noteworthy that
the weekly transaction networks are weighted and directed in nature. XRP
wallets serve as the nodes, and a weighted directed link represents the total
XRP transferred from a source wallet to a destination wallet in a week.

Table 1: Crypto exchanges in terms of 24 hour volume on February7, 2024, according to analytics website Coinranking. Exchange | 24h Volume ( billion USD)
---|---
Binance | 11.20
OKX | 1.39
Huboi | 1.20
Kraken | 0.85
Bitstamp | 0.19
Bitfinex | 0.18
Exmo | 0.03
Bittrex | -
FTX | -

##  3 Methods

We provide a concise overview of our methodology in the following subsections.

###  3.1 Network embedding

Network embedding is a technique in machine learning that transforms nodes in
a network into low-dimensional vectors, capturing the structural and
relational information of the graph. We employed the node2vec algorithm [17]
to embed each weekly weighted directed network into a $D$-dimensional space.
Setting the return parameter $p$ and in-out parameter $q$ both to 1 in the
algorithm signifies the use of unbiased random walks. Consequently, every node
in the networks is represented by a $D$-dimensional vector, denoted as
$V_{i}^{\alpha}$, where $i$ and $j$ are node indices, and $\alpha$ and $\beta$
are components in the $D$-dimensional space. This algorithm encodes both local
community structure and global network topology in the learned node
embeddings.

###  3.2 Correlation tensor

Utilizing the correlation tensor method and its diagonalization through double
Singular Value Decomposition (SVD) offers valuable insights into crypto
transaction systems. [12, 13, 14]. In the weekly XRP transaction networks, we
consider $N$ nodes conducting at least one weekly transaction during the
investigated period, categorizing them as regular nodes. Each regular node
within the embedding space is presented as a time series of $D$-dimensional
vectors, indicated as $V_{i}^{\alpha}(t)$. Here, $i$ varies from $1$ to $N$,
$t$ spans from $1$ to $T$, and $\alpha$ ranges from $1$ to $D$. The
correlation tensor among components of regular nodes is expressed as:

$M_{ij}^{\alpha\beta}(t)=\frac{1}{2\Delta T}\sum\limits_{t^{\prime}=t-\Delta
T}^{t+\Delta
T}\frac{[V_{i}^{\alpha}(t^{\prime})-\overline{V_{i}^{\alpha}}][V_{j}^{\beta}(t^{\prime})-\overline{V_{j}^{\beta}}]}{\sigma_{V_{i}^{\alpha}}\sigma_{V_{j}^{\beta}}},$
(1)

In this equation, we compute the sum across five weekly networks at times
$t^{\prime}=\\{t-2,t-1,t,t+1,t+2\\}$ within a time window of $(2\Delta T+1)$,
where $\Delta T=2$ for our analysis. The terms $\overline{V_{i}^{\alpha}}$ and
$\sigma_{V_{i}^{\alpha}}$ denote the mean and standard deviation of
$V_{i}^{\alpha}$ over a time window of $(2\Delta T+1)=5$ weekly networks at
times $\\{t-2,t-1,t,t+1,t+2\\}$. It’s crucial to acknowledge that a smaller
$\Delta T$ introduces more noise into the correlation tensor. However, opting
for a larger $\Delta T$ is not feasible due to the detailed temporal evolution
of the networks. In this analysis, we adopt a dimensionality of $D=32$. The
influence of the correlation tensor on window size $(2\Delta T+1)$ and
dimension $D$ is elaborated in [12].

###  3.3 Double singular value decomposition

To get the spectrum of the correlation tensor, we employ a double SVD approach
as outlined below:

We consecutively diagonalize $M_{ij}^{\alpha\beta}$ through a bi-unitary
transformation, or SVD, first in terms of the $(ij)$-index and subsequently
the $(\alpha\beta)$-index. In the initial step, we represent
$M_{ij}^{\alpha\beta}$ as a sum of matrices using the SVD technique.

$M_{ij}^{\alpha\beta}=\sum\limits_{k=1}^{N}L_{ik}^{\alpha\beta}\sigma_{k}^{\alpha\beta}R_{kj}^{\alpha\beta}.$
(2)

In the subsequent stage, we proceed to decompose each singular value
$\sigma_{k}^{\alpha\beta}$ into a sum of matrices, employing the SVD method:

$\sigma_{k}^{\alpha\beta}=\sum\limits_{\gamma=1}^{D}\mathcal{L}_{k}^{\alpha\gamma}\rho_{k}^{\gamma}\mathcal{R}_{k}^{\gamma\beta}.$
(3)

Finally, substituting Eq. 3 into Eq. 2, we get the following expression for
$M_{ij}^{\alpha\beta}$:

$M_{ij}^{\alpha\beta}=\sum\limits_{k=1}^{N}\sum\limits_{\gamma=1}^{D}\rho_{k}^{\gamma}(L_{ik}^{\alpha\beta}R_{kj}^{\alpha\beta})(\mathcal{L}_{k}^{\alpha\gamma}\mathcal{R}_{k}^{\gamma\beta}).$
(4)

where $\rho_{k}^{\gamma}$ denotes the $N\times D$ generalized singular values,
characterized by being both real and positive, due to all elements of the
correlation tensor, $M$ is real.

Figure 1: The daily XRP prices at Huboi (HTX) crypto exchange. The four
vertical lines represent the following dates: A) January 6, 2020; B) November
1, 2020; C) February 1, 2021; and D) August 1, 2021.

##  4 Results

We show the daily XRP prices from January 18, 2018, to January 22, 2024, at
the Huobi exchange in Fig. 1. The graph illustrates a considerable fluctuation
in XRP prices, ranging from 0.136 USD to 1.838 USD during this timeframe.
Vertical lines on the Fig. mark specific dates: A) January 6, 2020; B)
November 1, 2020; C) February 1, 2021; and D) August 1, 2021. In this study,
our primary focus lies on the periods AB and CD. These two phases exhibit
distinct characteristics regarding XRP price fluctuations. Notably, the XRP
price remained relatively stable during period AB. In contrast, period CD
showcases a notable surge and decline in XRP prices. We label CD as the
”bubble period” and AB as the ”non-bubble period” for XRP prices.

We examine how the XRP price varies among different crypto exchanges in Fig.
2. We have considered daily XRP prices from nine crypto exchanges, which are
listed in Table 1. Considering these nine crypto exchanges, we calculated the
daily mean XRP price, $\langle{\rm XRP/USD}\rangle$ (daily), shown in Fig. 2
(a) for the period AD. The daily fluctuation in XRP price among the exchanges
is measured by the standard deviation $\sigma$. The fluctuation in the daily
XRP price among the crypto exchanges is illustrated in Fig. 2 (b). The
fluctuation in the daily XRP price among the crypto exchanges was very low
during the first ten months of 2020. However, we observed a high fluctuation,
even up to $5\%$, beyond the first ten months of 2020. We calculated the
weekly XRP price, $\langle{\rm XRP/USD}\rangle$ (weekly), for a particular
crypto exchange by averaging the daily XRP price over seven days. The mean
$\langle{\rm XRP/USD}\rangle$ (weekly) and standard deviation $\sigma$
(weekly) in the weekly XRP price among the crypto exchanges are shown in Fig.
3 (a) and (b), respectively. The fluctuations are relatively low for weekly
XRP prices, as expected.

Figure 2: Mean daily XRP prices, $\langle{\rm XRP/USD}\rangle$ (daily) and
fluctuation $\sigma$ (daily) over nine different crypto exchanges.  Figure 3:
Mean weekly XRP prices, $\langle{\rm XRP/USD}\rangle$ (weekly) and fluctuation
$\sigma$ (weekly) over nine different crypto exchanges.  Figure 4:  Singular
value examination of correlation tensors from April 5 to 11, 2021. (a)
Comparative analysis of singular values, $\rho_{k}^{1}$, for the empirical
correlation tensor (depicted by black filled circles) and the reshuffled
correlation tensor (represented by red filled triangles) across all $k$
values. (b) Exploration of singular values, $\rho_{k}^{\gamma}$, for the
empirical correlation tensor and the reshuffled correlation tensor,
encompassing all $k$ values with $\gamma>1$. (c) Simulated singular values,
$\rho_{k}^{1}$, for the Gaussian random correlation tensor (illustrated as
green open squares), accompanied by the corresponding analytic curve from Eq.
5 (solid purple line). (d) Examination of simulated singular values,
$\rho_{k}^{\gamma}$, for the Gaussian random correlation tensor, considering
all values of $k$ with $\gamma>1$.

To establish a connection between the XRP price and the XRP transaction
network, we compute the correlation tensor among the components of the regular
nodes, denoted as $N$. This process is detailed in the Method section. The
number of regular nodes is determined to be 465 and 753 for the time periods
AB and CD, respectively. Focusing on the regular nodes during period CD, we
compute the correlation tensor $M_{ij}^{\alpha\beta}(t)$ for the week $t=$
April 5-11, 2021. The correlation tensor contains a total of $N\times N\times
D\times D$ elements. Extracting essential insights from this tensor involves
diagonalizing it through a technique known as double SVD, as detailed in
Method section. The double SVD is an extension of the standard SVD, typically
employed for matrices. By applying double SVD to the weekly correlation
tensor, $M_{ij}^{\alpha\beta}(t)$, we derive the singular values denoted as
$\rho_{k}^{\gamma}(t)$.

Determining the significance of the empirical correlation tensor requires
comparing it with the reshuffled correlation tensor. To construct the
reshuffled correlation tensor, we perform a reshuffling of the components
within the time window $(2\Delta T+1)$ for the embedded regular node vector
$V_{i}^{\alpha}$. Utilizing these reshuffled embedded regular node vectors, we
compute the reshuffled correlation tensor according to Eq. 1. Furthermore, we
simulate singular values of a Gaussian random correlation tensor utilizing
random matrix theory [6, 18, 19, 20, 21]. The elements of the Gaussian
correlation tensor, denoted as $G_{ij}^{\alpha\beta}$, are drawn from a
Gaussian distribution with a mean of zero and a standard deviation of
$\sigma_{G}=0.5$, where $(i,j=1,\ldots,N)$ and $(\alpha,\beta=1,\ldots,D)$. We
opt for $\sigma_{G}=0.5$ to align with the standard deviation of our empirical
correlation tensor.

The probability distribution function for the largest singular values of the
Gaussian random correlation tensor, denoted as $(\tilde{\rho}_{k}^{1})$ for
all $k$, is expressed as [13]:

$P(\tilde{\rho}_{k}^{1})=\frac{1}{\pi\sigma_{G}^{2}}\sqrt{(\tilde{\rho}_{1}^{1})^{2}-(\tilde{\rho}_{k}^{1})^{2}}.$
(5)

Here, the largest singular value is given by
$\tilde{\rho}_{1}^{1}=2\sigma_{G}D\sqrt{N}$ for $k=1$.

Figure 5: Comparison of the mean simulated weekly XRP prices, $\langle{\rm
XRP/USD(t)}\rangle$(simulated) with the mean correlation coefficient, $\langle
r(t)\rangle$ , depicting the relationship between the mean simulated weekly
XRP prices, $\langle{\rm XRP/USD(t)}\rangle$(simulated) and the largest
singular value $\rho_{1}^{1}(t-1)$. A moving window of 9 weeks is applied for
two distinct periods: (a) AB, covering January 6, 2020, to November 1, 2020,
and (b) CD, ranging from February 1, 2021, to August 1, 2021. The black curves
illustrate the mean simulated weekly XRP prices, $\langle{\rm
XRP/USD(t)}\rangle$(simulated). The blue curves, marked with green and red
triangles, represent the mean correlation coefficient, $\langle r(t)\rangle$,
with green triangles denoting significant correlations (p-value $<0.05$) and
red triangles indicating no significant correlations (p-value $>0.05$). The
two lower panels display the corresponding p-values for Pearson correlations.
Dotted grey vertical lines delineate the weekly windows.

Fig.4 (a) displays the singular values $\rho_{k}^{\gamma}$ for all $k\in[1,N]$
and $\gamma=1$, along with the singular values for the reshuffled correlation
tensor. Notably, only the largest singular value $\rho_{1}^{1}$ for the
empirical correlation tensor surpasses the largest singular value of the
reshuffled correlation tensor.

We extend this comparison to other singular values $\rho_{k}^{\gamma}$ for all
$k\in[1,2,3,\dots,N]$ and $\gamma\in[2,3,4,\dots,D]$ in Fig.4 (b). Here, we
observe that several singular values of the empirical correlation tensor
surpass the largest singular values of the reshuffled correlation tensor,
although these singular values are notably smaller than $\rho_{1}^{1}$.
Consequently, their contribution to the correlation tensor is relatively
minor.

Additionally, we compare the empirical singular values with those of the
Gaussian random correlation tensor, where the elements are drawn from a normal
distribution. The singular values $\tilde{\rho}_{k}^{1}$ of the Gaussian
random correlation tensor follows Eq. 5. In Fig.4(c), the simulated singular
values, $\tilde{\rho}_{k}^{1}$, of the Gaussian correlation tensor exhibit a
smooth fit with the analytical curve provided by Eq.5. Fig.4 (d) presents the
spectrum, $\tilde{\rho}_{k}^{\gamma}$, of the Gaussian random correlation
tensor across all $k$ values, where $\gamma$ ranges from 2 to $D$. It is
evident that the singular values of the Gaussian correlation tensors are much
smaller than those of the empirical and reshuffled correlation tensors. The
singular values of the reshuffled correlation tensor tend to approach those of
the Gaussian correlation tensor when the time window $\Delta T$ becomes
significantly larger than $N$ [12]. While we present results specifically for
the week April 5-11, 2021, it is worth noting that these findings remain
qualitatively consistent for any other week.

We generate a set of $1000$ time series representing weekly XRP prices,
denoted as ${\rm XRP/USD}(t)$ (simulated). These time series are simulated
from Gaussian distributions characterized by the mean $\langle{\rm
XRP/USD}\rangle$ (weekly) and the standard deviation $\sigma(t)$ (weekly). To
assess the relationship between the simulated weekly XRP prices and the
largest singular value $\rho_{1}^{1}(t-1)$, we employ the Pearson correlation
coefficient. Specifically, we calculate the correlation within a moving time
window of length $9$ weeks. The Pearson’s correlation coefficient, denoted as
$r(t)$, is defined as follows:

$r(t)=\frac{1}{2\Delta\tau}\sum\limits_{t^{\prime}=t-\Delta\tau}^{t+\Delta\tau}\frac{[y(t^{\prime})-\langle
y\rangle][\rho_{1}^{1}(t^{\prime}-1)-\langle\rho_{1}^{1}\rangle]}{\sigma_{y}\sigma_{\rho_{1}^{1}}},$
(6)

where the variable $y$ corresponds to ${\rm XRP/USD}(t)$ (simulated), and we
have chosen $\Delta\tau=4$. Herein, the symbols $\sigma$ and
$\langle\cdot\rangle$ denote the standard deviation and mean, respectively, of
the quantities within the temporal span of $(2\Delta\tau+1)$ weeks.

Figure 6: (a) Distribution of correlation coefficients between the largest
singular value $\rho_{1}^{1}(t-1)$ and simulated $1000$ weekly XRP Price times
series $XRP/USD(t)$ for the week, $t=$April $12-18,2021$. (b)Distribution of
associated p-values.  Figure 7: (a) Distribution of correlation coefficients
between the largest singular value $\rho_{1}^{1}(t-1)$ and simulated $1000$
weekly XRP Price times series $XRP/USD(t)$ for the week, $t=$April $27$ \- May
$3,2020$. (b)Distribution of associated p-values.

We calculate mean correlation coefficient $\langle r(t)\rangle$ over $1000$
simulated set of weekly XRP prices, ${\rm XRP/USD}(t)$ (simulated). The mean
simulated weekly XRP prices are represented as $\langle{\rm
XRP/USD}(t)\rangle$ (simulated). We investigate the temporal correlation
separately for two different periods, AB and CD. The temporal variation of the
mean correlation coefficient $\langle r(t)\rangle$ between the simulated
weekly XRP prices, ${\rm XRP/USD}(t)$ (simulated), and the largest singular
values $\rho_{1}^{1}(t-1)$ of the weekly correlation tensors is shown along
with the mean simulated weekly XRP prices, $\langle{\rm XRP/USD}(t)\rangle$
(simulated), in Fig. 5. The anti correlation is high and significant during
the period CD. The anti correlation mostly non-significant during the period
AB. This reflects the fact that the formation of a large bubble in the XRP
price is indicated by a strong anti correlation with the largest singular
value. The findings underscore the impact of XRP price fluctuations across
various exchanges. Specifically, the largest singular value, $\rho_{1}^{1}$,
demonstrates a pronounced and meaningful average negative correlation during
the bubble period. Conversely, during non-bubble periods, the average
correlation is observed to be non-significant.

Our analysis extends to a more detailed exploration of the correlation
coefficients with each simulated weekly XRP price time series, ${\rm
XRP/USD}(t)$ (simulated). Specifically, we focus on two distinct weeks, namely
$t_{1}$ and $t_{2}$, each chosen from distinct periods - $t_{1}$ from April
12-18, 2021, falling within the bubble period CD, and $t_{2}$ from April 27-
May 3, 2020, situated within the non-bubble period $AB$. In Fig. 6, we present
the distributions of correlation coefficients, $r(t)$, along with associated
p-values between the largest singular value $\rho_{1}^{1}(t-1)$ and a
simulated set of 1000 weekly XRP Price time series, ${\rm XRP/USD}(t)$
(simulated), for the week $t=t_{1}$. Notably, all correlation coefficients
$r(t)$ exhibit a highly negative and statistically significant pattern.
Conversely, in Fig. 7, we illustrate the distributions of correlation
coefficients $r(t)$ and corresponding p-values for the same analysis conducted
for the week $t=t_{2}$. Remarkably, all correlation coefficients $r(t)$ in
this case are observed to be non-significant. These findings provide
additional affirmation that our results remain consistent across each
simulated time series. This underscores the notion that price fluctuations
across various crypto exchanges do not exert any significant influence on our
conclusions. This phenomenon can be attributed to the minimal price variations
of XRP across various trading exchanges, leading to limited arbitrage
opportunities. Notably, the p-values associated with the correlation between
the largest singular value of the correlation tensor and the price reveal that
this correlation remains significant even when accounting for the price
differentials of XRP across diverse exchanges, particularly during the bubble
period.

##  5 Conclusions

We have examined the impact of XRP price fluctuations across different crypto
exchanges on the correlation between the largest singular values of the
correlation tensor of XRP transaction networks and the XRP price. For this
purpose, we have collected XRP price data from nine different crypto
exchanges. We have displayed the daily and weekly prices and their
fluctuations over a period of approximately 1.5 years. To uncover the
correlation between price and XRP transaction networks, we have calculated the
singular values of correlation tensor spectra. Comparing this with a
reshuffled correlation tensor, we found that only the largest singular value
is significant.

To capture the price impact of fluctuations, we have generated a set of 1000
simulated weekly XRP price time series from a Gaussian distribution with an
identical mean and standard deviation as empirical XRP prices. We have found
that irrespective of XRP price fluctuations at crypto exchanges, the largest
singular value shows a strong, significant anti-correlation during the bubble
period and a non-significant correlation during the non-bubble period with the
XRP price. Our simulated weekly XRP price mirrors the potential arbitrage
opportunities present across various cryptocurrency exchanges. Upon
examination of correlation coefficients and p-values between the largest
singular value and these time series, it becomes evident that arbitrage exerts
a non-significant impact. This can be attributed to the relatively low
arbitrage opportunities across diverse cryptocurrency exchanges.

##  Appendix A Cryptoassets monthly exchange volume

We illustrate the monthly spot market volume across three prominent
cryptoasset exchanges from January 2020 to August 2020 in Fig. 8. It visually
demonstrates the evolution of Binance as it ascends to become the largest
crypto exchange during this period.

Figure 8: Monthly spot market volumes across three major cryptoasset exchanges
from https://www.theblock.co/data/crypto-markets/spot.

##  Appendix B Data sources:

  * •

Binance: https://www.investing.com/crypto/xrp/xrp-btc-historical-data

  * •

OKX: https://www.investing.com/crypto/xrp/xrp-usd-historical-data

  * •

Huboi: https://www.investing.com/crypto/xrp/xrp-usd-historical-
data?cid=1058260

  * •

Kraken: https://www.marketwatch.com/investing/cryptocurrency/xrpusd

  * •

Bitstamp: https://www.CryptoDataDownload.com

  * •

Bitfinex: https://www.CryptoDataDownload.com

  * •

Exmo: https://www.CryptoDataDownload.com

  * •

Bittrex: https://www.CryptoDataDownload.com

  * •

FTX: https://www.CryptoDataDownload.com

  * •

Transaction networks: https://xrpl.org/data-api.html#payment-objects.

## Acknowledgements

We express our gratitude to Tetsuo Hatsuda for his valuable comments on our
manuscript. YI acknowledges the financial support received from the Ripple
Impact Fund (Grant Number: 2022-247584) for partial support to this work.

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