*2.7. Cross-Correlations between Cryptocurrencies and Other Markets*

Recently, BTC and ETH have been found to be significantly coupled to the traditional financial markets during the period covering the COVID-19 pandemic and the bear market of 2022 [55]. This result has essential practical implications in risk management as cryptocurrencies cannot serve as hedging assets [92]. It differs from earlier findings that, before 2020, the cryptocurrency market was detached from the traditional markets [47,52,93,94], but, at the same time, it remains in agreement with the observations that COVID-19 changed the safe-haven paradigm and contributed to the correlation of major cryptocurrencies with traditional risk assets [53,95–98]. So far, only the most capitalized cryptocurrencies have been studied [55], and this is why cryptocurrencies with smaller capitalization were also studied here.

The time series of log-returns of 70 cryptocurrencies and 22 traditional financial instruments were collected from Dukascopy platform [99]. Among the latter, there are contracts for difference (CFDs) representing the returns of 12 fiat currencies (AUD, CAD, CHF, CNH, EUR, GBP, JPY, MXN, NOK, NZD, PLN, and ZAR), 4 commodities (WTI crude oil (CL), high-grade copper (HG), silver (XAG), and gold (XAU)), 4 US stock market indices (Nasdaq 100 (NQ100), S&P500, Down Jones Industrial Average (DJI), and Russell 2000 (RUSSEL)), the main German stock index DAX 40 (DAX), and the Japanese Nikkei 225 (NIKKEI). All these instruments except for the non-US stock indices were expressed in USD. Their quotes cover a period from 1 January 2020 to 30 December 2022. The quotes were recorded over the trading hours, i.e., from Sunday 22:00 to Friday 20:15 UTC, with a break between 20:15 and 22:00 UTC each trading day. In order to assess the cross-correlations, the cryptocurrency time series were synchronized with those from Dukascopy. Crosscorrelations were quantified by *ρRR <sup>q</sup>* (*s*).

Figure 11 shows the *q*-dependent detrended cross-correlation matrix **C***q*(*s*) entries for the inter-market pairs consisting of a cryptocurrency and a traditional asset. The first observation is that the maximum available values of the matrix entries do not exceed *ρRR <sup>q</sup>* (*s*) = 0.25, which makes them much smaller than in the case of the inner crosscorrelation among the cryptocurrencies. This is an expected effect because markets are typically more tightly coupled inside than outside. Among the strongest cross-correlations, one can point out the coupling of BTC and ETH with the American stock market indices (*ρRR <sup>q</sup>* (*s*) > 0.2 and with NIKKEI and DAX (0.15 < *ρRR <sup>q</sup>* (*s*) < 0.2). Considerably weaker yet still prominent are the cross-correlations between several other cryptocurrencies, such as XRP, ADA, LTC, LINK, VET, ETC, EOS, ATOM, and BCH on one side and the American indices (0.15 < *ρRR <sup>q</sup>* (*s*) < 0.2). The relations between cryptocurrencies and fiat currencies remain moderate, with the AUD, CAD, and NZD being the relatively strongest (0.1 < *ρRR <sup>q</sup>* (*s*) < 0.15). Contrary to this, the cryptocurrencies are the most decoupled from JPY, CHF, gold (XAU), and crude oil (CL). A general observation is that the less liquid a cryptocurrency is, the weaker its cross-correlation with traditional instruments. Here again, DOGE is somewhat of an exception and has a weaker cross-correlation than its trading frequency and capitalization would imply. However, it should be noted that the values collected in Figure 11 correspond to the shortest available scale of *s* = 10 min. How these values refer to the maximum cross-correlations for longer scales is documented in Figure 12. Here, the cross-correlation between the selected cryptocurrencies and their sets grouped according to the average inter-transaction time (Groups I–III) and NASDAQ 100 is presented. This particular choice of the traditional index was motivated by the fact that the cryptocurrency market is strongly cross-correlated with it [55]. Indeed, for much longer *s*, the values of *ρRR <sup>q</sup>* (*s*) grow significantly and even reach some saturation level resembling the Epps effect for *s* > 500 min, with the average values of *ρRR <sup>q</sup>* (*s*) in Groups I-III oscillating around 0.4 (for a given scale, *ρRR <sup>q</sup>* (*s*) decreases systematically with an increasing *δt*). The cryptocurrencies that are the most cross-correlated with NASDAQ 100, i.e., BTC and ETH, have maximum values of *ρRR <sup>q</sup>* (*s*) > 0.5.

**Figure 11.** The *q*-dependent detrended cross-correlation matrix entries *ρ ij <sup>q</sup>* (*s*) calculated from time series of log-returns representing selected cryptocurrencies and selected traditional financial instruments with *q* = 1 and *s* = 10 min. Cryptocurrencies have been sorted according to the average inter-transaction time *δt* in increasing order (top to bottom). The color coding scheme, which differs from the one in Figure 9, is shown on the right.

**Figure 12.** The *q*-dependent detrended cross-correlation coefficient *ρRR <sup>q</sup>* (*s*) calculated for the pairs of log-return time series consisting of NASDAQ 100 and a cryptocurrency (BTC, ETH, DOGE, FUN, PERL, or WAN) or a group of cryptocurrencies characterized by average inter-transaction time from a specific range: *δt* < 1*s* (Group I, red), 1*s* ≤ *δt* < 2*s* (Group II, blue), and *δt* ≥ 2*s* (Group III, green).
