SUPTECH WORKSHOP III
Are cryptocurrencies connected to forex? A quantile
cross-spectral approach
·SUPTECH WORKSHOP III ·Are cryptocurrencies connected to forex? A quantile cross-spectral approach 1 / 17
Introduction Related literature
Related literature
Connectedness among asset classes is important (i) for
investors, as portfolio selection and its performance are
associated with the dependence structure of portfolio
components, and (ii) for policy makers, because if
information is transmitted across assets, policy decisions
will likely have cross-market influence (Ciner et al., 2013)
Baur and Lucey (2010) suggested distinguishing between
diversifiers, hedges and safe havens.
The literature on safe haven currencies is relatively rich
(Ranaldo and Söderlind, 2010; Habib and Stracca, 2012;
Menkhoff et al., 2012).
The literature on the safe haven properties (connectedness)
of cryptocurrencies is still rather sparse (Yermack, 2015;
Bouri et al., 2017a,b; Kurka, 2017; Corbet et al., 2018; Ciaian
et al., 2018).
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Introduction Related literature
Three main conclusions can be drawn:
The general consensus in empirical research (although many
studies so far are in the form of a working paper) is that
Bitcoin returns are not closely related to returns on any
other asset classes.
Most of the studies on cryptocurrencies utilized Bitcoin as a
benchmark, which is understandable considering its
dominant role in the field. All existing 1500 cryptocurrencies
have a market capitalization of 536 billion as of the end of
January 2018, while the top 20 cryptocurrencies yield a
market capitalization of more than 463 billion (almost 180
billion of which is a share of Bitcoin).
Bitcoin has the longest history, so most of the studies so far
have neglected other cryptocurrencies given the limited
number of observations.
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Data and methodology Data description
Data coverage (vs USD)
Forex: Euro (EUR), Japanese Yen (JPY), British Pound (GBP),
Swiss Franc (CHF), Canadian Dollar (CAD), and Chinese
Yuan (CNY).
Cryptocurrencies: Bitcoin (BTC), Ether (ETH), Ripple (XRP),
Litecoin (LTC), Stellar Lumens (XLM), and NEM (XEM).
Daily data from 1 September 2015 to 29 December 2017
(607 obs).
Closing prices are recorded at 00:00 Greenwich Mean Time.
Continuous returns.
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Data and methodology Data description
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Data and methodology Methodology at-a-glance
Methodology at-a-glance:
Standard Pearson’s correlations.
DMCA (detrended moving-average cross-correlation
analysis) coefficient proposed by Kristoufek (2014).
Quantile cross-spectral approach proposed by Baruník and
Kley (2019).
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Data and methodology DMCA
Detrended moving-average
cross-correlation analysis
Fluctuation functions Fx,DMA and Fy,DMA are defined as:
F2
x,DMA(λ) =
1
T −λ +1
T−θ(λ−1)
∑
i= λ−θ(λ−1)
(Xt − ˜Xt,λ )2
F2
y,DMA(λ) =
1
T −λ +1
T−θ(λ−1)
∑
i= λ−θ(λ−1)
(Yt − ˜Yt,λ )2
where λ is the moving-average window length, and θ is a
factor of moving-average type (forward, centered and
backward), which for the purpose of Kristoufek’s (2014)
ρ(DMCA)(λ) coefficient is set to 0.5 (centered one).
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Data and methodology DMCA
Detrended moving-average
cross-correlation analysis
He and Chen (2011) proposed DMCA as a combination of
detrended cross-correlation analysis (DCCA) and DMA. The
bivariate fluctuation is defined as:
F2
DMCA(λ) =
1
T −λ +1
T−θ(λ−1)
∑
i= λ−θ(λ−1)
(Xt − ˜Xt,λ )(Yt − ˜Yt,λ )
The DMCA coefficient (actually bounded in [–1, 1]) is then
defined as (Kristoufek, 2014):
ρ(DMCA)(λ) =
F2
DMCA(λ)
Fx,DMA(λ)Fy,DMA(λ)
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Data and methodology Quantile coherency
Quantile coherency
Baruník and Kley’s (2019) recently proposed quantity - quantile
coherency - is a measure of the dynamic dependence of the
two processes of (Xt,j1) and (Xt,j2), defined as:
ℜj1,j2
(ω,τ1,τ2) =
f j1,j2(ω,τ1,τ2)
(f j1,j1(ω,τ1,τ1)f j2,j2(ω,τ2,τ2))1/2
where for every j ∈ 1,2,...d and τ ∈ [0,1], f j1,j2, f j1,j1 and
f j2,j2 are quantile cross-spectral, and the quantile spectral
densities of processes Xt,j1, and Xt,j2, respectively, are
obtained from the Fourier transform of the matrix of quantile
cross-covariance kernels Γk (τ1,τ2) := (γj1,j2
k (τ1,τ2))j1,j2=1,2,...,d ,
where
γj1,j2
k (τ1,τ2) := Cov I Xt+k,j1
≤ qj1(τ1) ,I Xt,j2 ≤ qj2(τ2)
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Data and methodology Quantile coherency
Quantile coherency
For continuous cases, this measure corresponds to the difference
in the copula of (Xt+k,j1 ,Xt,j2 ) and the independence copula.
Thus, by letting k vary, we can obtain important information
about the serial dependence; by choosing j1 = j2, we can obtain
important information about the cross-sectional dependence. In
the frequency domain, this yields the so-called matrix of quantile
cross-spectral density kernels:
f(ω,τ1,τ2) := f j1,j2 (ω,τ1,τ2)
j1,j2=1,2,...,d
where
f j1,j2 (ω,τ1,τ2) := (2π)−1
∞
∑
k=−∞
γj1,j2
k (τ1,τ2)e−ikω
Quantile coherency is estimated via the smoothed quantile
cross-periodograms. We will extract quantile coherency matrices
for three percentiles (0.05, 0.50, 0.95) and all their combinations.
Moreover, three frequencies are considered: short-term (2 days),
mid-term (22 days), and long-term (250 days).·SUPTECH WORKSHOP III ·Are cryptocurrencies connected to forex? A quantile cross-spectral approach 10 / 17
Results Standard Pearson’s correlations
Standard correlations
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Results DMCA coefficients
DMCA coefficients
Table 2 Detrended moving-average cross-correlation analysis
EUR JPY GBP CHF CAD CNY BTC ETH XRP LTC XLM XEM
EUR 1 0.381 0.513 0.816 0.358 0.336 -0.051 -0.063 0.036 -0.027 -0.013 -0.012
JPY 0.415 1 0.041 0.486 0.126 0.142 -0.066 -0.016 0.012 -0.086 0.005 -0.061
GBP 0.486 0.034 1 0.409 0.386 0.284 -0.158 -0.108 0.042 -0.105 -0.073 -0.079
CHF 0.822 0.517 0.382 1 0.346 0.270 -0.104 -0.031 0.034 -0.037 -0.010 -0.060
CAD 0.319 0.111 0.369 0.312 1 0.236 -0.108 -0.028 0.022 0.005 -0.009 -0.002
CNY 0.335 0.172 0.241 0.270 0.234 1 -0.098 -0.037 -0.001 0.004 -0.004 -0.050
BTC -0.037 -0.053 -0.120 -0.059 -0.099 -0.085 1 0.263 0.152 0.469 0.220 0.254
ETH -0.031 0.023 -0.076 -0.009 -0.024 -0.013 0.289 1 0.073 0.260 0.146 0.054
XRP 0.048 0.032 0.027 0.053 0.021 0.013 0.170 0.126 1 0.220 0.522 0.150
LTC -0.017 -0.064 -0.070 -0.029 -0.001 0.027 0.488 0.257 0.251 1 0.266 0.242
XLM 0.004 0.003 -0.046 -0.005 0.007 0.028 0.248 0.165 0.534 0.319 1 0.334
XEM 0.009 -0.040 -0.059 -0.041 -0.022 -0.041 0.259 0.105 0.211 0.270 0.354 1
Note: Coefficients under the diagonal correspond to the moving-average window length λ = 2, and those above the diagonal
correspond to λ = 5.
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Results Quantile coherency
Quantile coherency (short-term)
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Results Quantile coherency
Quantile coherency (short-term - extreme
negative returns)
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Results Quantile coherency
Quantile coherency (mid-term)
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Results Quantile coherency
Quantile coherency (long-term)
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Results Conclusions
Concluding remarks
General public tends to view all cryptocurrencies as a
single entity, there are significant differences between
them.
On average, correlations among cryptos and forex are
close to zero – in line with the previous research (Yermack,
2015; Bouri et al., 2017a; Bouri et al., 2017b; Corbet et al.,
2018).
However, the intra-group dependencies are positive in the
lower extreme quantiles, while inter-group dependencies
are negative.
The connection between cryptocurrencies is not as strong
as is widely believed.
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