An analysis of cryptocurrencies conditional cross correlations
Nektarios Aslanidis, Aurelio F. Bariviera, Oscar Martinez-Ibañez
aa r X i v : . [ q -f i n . S T ] F e b An analysis of cryptocurrencies conditional crosscorrelations
Nektarios Aslanidis ∗ , Aurelio F. Bariviera † , and OscarMart´ınez-Iba˜nez ‡ Universitat Rovira i Virgili, Department d’Economia, CREIP, Avinguda Universitat 1, Reus43204, Spain Universitat Rovira i Virgili, Department of Business, Av. Universitat 1, 43204 Reus, Spain
February 28, 2019
Abstract
This letter explores the behavior of conditional correlations amongmain cryptocurrencies, stock and bond indices, and gold, using a gener-alized DCC class model. From a portfolio management point of view,asset correlation is a key metric in order to construct efficient portfolios.We find that: (i) correlations among cryptocurrencies are positive, albeitvarying across time; (ii) correlations with Monero are more stable acrosstime; (iii) correlations between cryptocurrencies and traditional financialassets are negligible.
Almost 10 years ago, triggered by the seminal paper by [Nakamoto, 2009], anew type of financial asset was born. Based on the concept of a distributedledger, blockchain technology is able to validate operations, without the neces-sity of a central trusted authority. The foremost application of blockchain is thevalidation of financial transactions. As a consequence, several assets (self-calledcryptocurrencies) emerged as an alternative to standard fiat money.There is no consensus on the ’currency’ status of the so-called cryptocurren-cies. [Polasik et al., 2015] report an increasing number of businesses and orga-nizations accepting payments in bitcoin, and [Kristoufek, 2015] highlights theusefulness of bitcoin as medium of exchange. However, cryptocurrency volatilityraises doubt about their suitability as a store of value. ∗ [email protected] † [email protected] ‡ [email protected] [Urquhart, 2016] used a set of tests aimed at identifying autocorrelations, unitroots, nonlinearities and long range dependence in Bitcoin returns. The resultsshow evidence of information inefficiency in the Bitcoin market. However, whenthe author splits the sample into two sub-periods, it is found inefficiency is anissue mainly in the first part of the sample. Later, [Nadarajah and Chu, 2017]reexamines the data using power transformations of daily returns, withoutrejecting the null hypothesis of informational efficiency. [Bouri et al., 2017a]2tudy Bitcoin’s return-volatility behavior before and after the severe marketcrash of 2013, and show evidence of serial autocorrelation in Bitcoin returns.[Bouri et al., 2017b] scrutinize hedge and safe haven properties of Bitcoin vis-`a-vis international stock and bond indices and several currencies. The mainfinding is the the Bitcoin proves useful as a diversifier rather than as a hedgeinstrument. Finally, [Balcilar et al., 2017] detect nonlinearities in the return-volume relationship, which allows for return prediction.Furthermore, [Bariviera, 2017] documents that the Bitcoin market exhibitstime-varying information efficiency and persistence in volatility. The policy im-plication here is that the market becomes prone to large swings (either positiveor negative ones). Taking this into account, [Donier and Bouchaud, 2015] studydifferent measures of liquidity as early warning signs of bitcoin market crash.[Dyhrberg, 2016] studies simultaneously Bitcoin, gold and the dollar, usingGARCH models, finding similarities in all three assets. In particular, bitcoinand gold react to the same variables in a GARCH model, and also bitcoin reactsto federal fund rates, as in the case of a fiat currency.One key aspect in portfolio theory, and broadly in financial economics, is thecorrect assessment of correlation returns among different assets. Such metrichas important implications regarding portfolio construction, risk analysis andhedging. [Corbet et al., 2018b] employ the generalized variance decompositionmethodology by [Diebold and Yilmaz, 2012]. They find that three major cryp-tocurencies (Bitcoin, Ripple, Litecoin) are rather isolated from other assets suchas gold, stock or bond indices, offering diversification opportunities to investors.Given the burgeoning literature on this topic, we refer to [Corbet et al., 2018a]and [Smith and Kumar, 2018] for excellent reviews of the empirical literature. Let r t denote an N -dimensional vector time series (zero-mean asset returns)with time-varying conditional covariance matrix: V ar [ r t |ℑ t − ] = E [ r t r ′ t |ℑ t − ] = H t t = 1 , . . . , T (1)where ℑ t − is the information set at time t . The conditional covariancematrix can be decomposed as (see, [Engle, 2002], among others): H t = D t R t D t (2)where D t ≡ diag ( p h ,t , . . . , p h N,t ) is a diagonal matrix with the square rootof the conditional variances on the diagonal. The matrix R t , with the ( i, j )-thelement denoted as ρ ij,t , is the possibly time-varying correlation matrix with ρ ii,t = 1, j = 1 , . . . , N and t = 1 , . . . , T . The standardised returns are denotedby ε t = D − t r t = ( ε t , . . . , ε Nt ) ′ .One of the most frequently used methodologies in capturing the time-varyingstructure of the correlations is the Dynamic Conditional Correlation (DCC)model which assumes that the conditional correlation evolves linearly according3o a simple GARCH (1,1)-type structure ([Engle, 2002]). The DCC frameworkhas become popular among academics and practitioners.In a multivariate framework, the basic DCC may be too restrictive. Inparticular, this model implies that all correlations pairs have the same responseto news and decay parameters. For our application (consisting of 4 assets) weadopt a flexible generalization of the DCC, which allows for correlation-specificnews parameters, while the decay parameter is assumed to be the same acrosscorrelation pairs, in order to keep the model tractable. This generalized DCCmodel, studied initially in [Cappiello et al., 2006] and [Hafner et al., 2006] andlater in [Aslanidis and Casas, 2013], is given by: Q t = ( Q − A ′ QA − βQ ) + A ′ ε t − ε ′ t − A + βQ t − (3) R t = Q ∗− t Q t Q ∗− t (4)where A ≡ diag ( α , . . . , α N ) is parameter diagonal matrix (the implied newsparameters are α i α j for i = j ) and β is the decay parameter. As usual, werescale the quantity Q t in Eq. 4 to obtain a proper correlation matrix, with Q ∗ t being a diagonal matrix composed of the square roots of the diagonal elementsof Q t . So, the basic DCC is obtained as a special case of the generalized DCCif the matrix A is replaced by the scalar α . We use daily price data of four cryptocurrencies, and three traditional finan-cial assets. Cryptocurrencies included in our sample are: Bitcoin (BTC), Dash(DASH), Monero (XMR), and Ripple (XRP). The three traditional assets se-lected are Standard & Poors 500 Composite (SP500), S&P US Treasury bond7-10Y index (BOND), and Gold Bullion LBM (GOLD). Cryptocurrency datawere obtained from https://coinmarketcap.com/, and the other assets data weredownloaded from Eikon Thomsom Reuters. The period under examination goesfrom 21/05/2014 to 27/09/2018. Cryptocurrencies are traded 24 hours a day, 7days a week. However, traditional assets are traded in organized markets, thatare open only during the working week. Therefore we have 1560 observationsfor cryptocurrencies and 1135 observations for the other assets.We show in Table 1 the descriptive statistics of daily logarithmic returnsof both cryptocurrencies and traditional assets. Considering that both typesof assets differ in trading hours, we reduced the dataset of cryptocurrencies tomatch the number of observations and dates of the traditional assets. Therefore,in this table we only considered data from Monday through Friday, and wecomputed the logarithmic return of two consecutive observations. We wouldlike to highlight the enormous difference between the two assets classes. Meanand standard deviation in cryptocurrencies are between 6 to 144 times largerthan traditional assets. 4able 1: Descriptive statistics of daily returns
GOLD S&P500 BOND BTC XRP DASH XRMObservations 1134 1134 1134 1134 1134 1134 1134Mean -0.0079 0.0377 -0.0031 0.2221 0.4506 0.2351 0.3166Median 0.0000 0.0268 0.0000 0.2386 -0.2181 -0.0722 0.0622Std. Dev. 0.8104 0.7744 0.3216 4.5703 8.8985 7.9748 8.6688Min -3.2239 -4.1843 -1.5377 -26.4311 -57.0455 -73.3201 -36.6830Max 4.6184 3.8291 1.3196 27.8435 136.3081 50.0787 69.1884Skewness 0.2312 -0.5831 -0.0559 -0.1335 3.9416 -0.1229 1.3535Kurtosis 5.6593 6.9085 4.0056 8.4510 57.5688 13.6400 12.0729Jarque Bera 344.2570 786.0706 48.3706 1407.3155 143635.1882 5352.0396 4235.7217Probability 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
We compute the dynamic cross correlations, according to Generalized DCC,considering the full dataset. We recall that cryptocurrencies are traded 24/7.Thus, there are no days without trading or weekends. Correlation results foreach correlation pair is displayed in Figure 1.Our study detects several interesting features in the cryptocurrency ecosys-tem. Table 2 displays descriptive statistics of estimated correlations, with themodel estimates being A = diag (0 . , . , . , . β = 0 . α = 0 . . ∗ .
133 = 0 . . ∗ .
133 = 0 . . ∗ .
133 = 0 .
038 for Bitcoin-Monero, Ripple-Monero and Dash-Monero,respectively. The most variable correlation is found between Ripple and Dash,whose correlation spans from +0 .
71 to − . BTC BTC BTC XRP XRP DASHXRP DASH XMR DASH XMR XMR
Mean 0.1912 0.2535 0.3161 0.2035 0.1639 0.2072Median 0.1856 0.2586 0.3073 0.1796 0.1597 0.2065Maximum 0.5740 0.6669 0.6070 0.7151 0.5272 0.5384Minimum -0.1840 -0.1962 -0.0312 -0.5134 -0.1227 -0.2789Std. Dev 0.1216 0.1579 0.0793 0.1862 0.0792 0.0896Skewness 0.1690 -0.0581 0.1220 0.1240 0.0379 -0.2694Kurtosis 3.1208 2.5690 3.5280 3.1768 3.6295 4.6496Jarque-Bera 8.3777 12.9523 21.9910 6.0297 26.1341 195.7463Probability 0.0152 0.0015 0.0000 0.0491 0.0000 0.0000
Our results have important implications for portfolio analysis. An investor,5ho constructs a dynamic hedge portfolio of cryptocurrencies could take intoaccount the stable correlations involving Monero.
In this subsection we compute cryptocurrencies cross correlations against tra-ditional assets such as Standard & Poors 500 Composite (SP500), S&P USTreasury bond 7-10Y index (BOND), and Gold Bullion LBM (GOLD). Takinginto account that the latter assets only trade Monday through Friday, we adaptthe cryptocurrency sample to this restriction. Descriptive statistics of thesecross-correlations are displayed in Table 3 and in Figure 2.Table 3: Descriptive statistics of dynamical cross correlation for cryptocurrency-traditional asset pairs
BTC BTC BTC DASH DASH DASH XMR XMR XMR XRP XRP XRPGOLD S&P500 BOND GOLD S&P500 BOND GOLD S&P500 BOND GOLD S&P500 BONDObservations 1133 1133 1133 1133 1133 1133 1133 1133 1133 1133 1133 1133Mean -0.0114 0.0356 -0.0371 -0.0124 0.0190 -0.0574 0.0064 0.0004 -0.0699 0.0171 0.0029 0.0411Median -0.0113 0.0358 -0.0374 -0.0125 0.0194 -0.0583 0.0064 0.0005 -0.0710 0.0172 0.0032 0.0420Std. Dev. 0.0054 0.0145 0.0117 0.0003 0.0022 0.0042 0.0002 0.0001 0.0051 0.0084 0.0204 0.0160Min -0.0446 -0.0368 -0.1237 -0.0128 0.0091 -0.0646 0.0052 -0.0001 -0.0787 -0.0256 -0.0857 -0.0377Max 0.0147 0.1599 0.0198 -0.0102 0.0225 -0.0312 0.0066 0.0006 -0.0384 0.0525 0.1233 0.1748Skewness -0.4068 0.5391 -0.5775 2.5126 -1.0930 1.4827 -2.4022 -1.4505 1.4843 -0.3647 0.3775 0.5953Kurtosis 7.9148 11.7318 8.7038 13.2251 4.5691 6.8779 11.9654 8.6414 6.8898 5.9921 6.2472 12.5905Jarque Bera 1171.6081 3654.2501 1598.8186 6127.8613 341.8345 1125.0357 4884.2173 1899.7223 1130.3363 447.7655 524.6903 4409.0356
We summarize our findings in the correlation matrix displayed in Table 4.We detect three correlation groups. The first group is a well known correlationstocks, bonds and commodities. The second group correspond to cryptocur-rencies cross correlations. We detect that this market is positively correlated.Finally, the third group correspond to very low correlations between one cryp-tocurrency and one traditional asset. We verify, using an alternative methodol-ogy, the findings by [Corbet et al., 2018b], in the sense that the cryptocurrenciesreturns are not connected to main financial markets. We also detect that, corre-lation of traditional assets against Monero are even closer to zero than againstother cryptocurrencies. This result could mean that Monero behavior is differ-ent from other cryptocurrencies, in the same way as we detected previously thatcryptocurrency correlations against Monero are more stable through time.However, we believe that this market could not be attractive for diversifica-tion pursposes. The reason is that, cryptocurrencies’ mean return and stardarddeviation are between 1 and 2 orders of magnitude larger than the other tradi-tional assets. As a consequence, a small portion of cryptocurrency, will dominatethe stochastic dynamic of the whole portfolio.
Our empirical study detects that cryptocurrencies exhibit similar mean corre-lation among them ( ≈ . .
31 and a minimum of 0 . −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 B i t c o i n − D as h correlation ( a ) −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 B i t c o i n − M on e r o correlation ( b ) −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 B i t c o i n − R i pp l e correlation ( c ) −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 D as h − M on e r o correlation ( d ) −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 R i pp l e − D as h correlation ( e ) −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 R i pp l e − M on e r o correlation ( f ) F i g u r e : C r y p t o c u rr e n c i e s p a i r w i s ec o rr e l a t i o n s
015 2016 2017 2018 − . − . − . . . . . Date c o rr e l a t i on BTC−GOLD DASH−GOLD XMR−GOLD XRP−GOLD (a) − . − . − . . . . . Date c o rr e l a t i on BTC−S&P500 DASH−S&P500 XMR−S&P500 XRP−S&P500 (b) − . − . − . . . . . Date c o rr e l a t i on BTC−BOND DASH−BOND XMR−BOND XRP−BOND (c)
Figure 2: Cryptocurrencies and traditional assets pairwise correlations8able 4: Correlation matrix. Cross correlation for cryptocurrencies’ pairs arecomputed for the full sample. Cross correlation for cryptocurrency-traditionalasset pairs are computed for the reduced sample, corresponding to stock andbonds trading week.
BTC DASH XMR XRP GOLD S&P500 BONDBTC 1.0000 0.2535 0.3161 0.1912 -0.0114 0.0356 -0.0371DASH 1.0000 0.2072 0.2035 -0.0124 0.0190 -0.0574XMR 1.0000 0.1639 0.0064 0.0004 -0.0699XRP 1.0000 0.0171 0.0029 0.0411GOLD 1.0000 -0.1023 0.2815S&P500 1.0000 -0.3466BOND 1.0000 a result, those pairs generate more stable correlation across time. The otherpairs exhibit large variations, from ≈ − .
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