Financial and commodity markets around the world have tumbled due to the global outbreak of COVID-19, also known as SARS-COV-2. The total number of confirmed cases and deaths has reached a staggering amount of 8,546,919 and 456,726 (2010-06-20, 1815 hours Beijing time), respectively. The Dow Jones and the S&P 500 had suffered as much as a 30% decline in values, and recorded the worst single day point drop in the history during March, 2020. Moreover, the markets in Asia, Europe, UK, and Australia also recorded similar declines (Zhang et al., 2020) . Due to the unprecedented low demand and unavailability of further storage capacity, oil crossed all the lower limits and recorded a negative price for May, 2020 futures, which couldn't have been imagined a few weeks ago (Sharif et al., 2020) . Unemployment is at a historic high in most of the world economies and creating multiple social and psychological issues (Kawohl & Nordt, 2020) . Such turmoil is once in a while kind of thing to be observed in the modern history. Figure 1 shows the daily addition in new COVID-19 infections and deaths worldwide till June 16, 2020.
The search for safe assets during such an uncertain and disastrous market situation is a natural desire for the most of the investors. One of the many forms of such safe assets may include digital cryptocurrencies as proposed by several studies (Shahzad et al., 2019; Urquhart and Zhang, 2019; Mnif et al., 2020) . Where all traditional financial assets seemed to lose value freely, a lot of investors were watching closely the behavior of these digital cryptocurrencies, especially the Bitcoin during this stressful period. Cryptocurrencies which started merely as a peer-to-peer payment system have emerged as an important asset class recently (Chaim and Laurini 2019; Corbet et al., 2019) . These assets have gained a lot of investors' attention recently due to the huge returns provided since its inception merely a decade ago. The unprecedented gains provided by these assets and a huge increase in their demand has attracted the attention of the scholars also. The number of studies trying to model this market's pricing mechanism, volatility, and bubbles is ever increasing in order to improve the understanding related to the crypto-assets (Chu et al., 2017; Fry & Cheah, 2016; Shen et al., 2019) . As Bitcoin and other cryptocurrencies are emerging as an important asset class generally, and as a hedging and diversification instrument specifically, it is important to know that how this asset class behaves in the times of extreme and varying stress, and how much is it useful for hedging against the traditional equity markets. The recent pandemic of COVID-19 provides us an opportunity to examine and evaluate the behavior of cryptocurrencies in extremely stressful periods.
The paper currency is being considered as a means of spreading contagious viruses due to changing hands frequently in a pandemic situation like we are facing recently.
The need for a contactless payment system and replacement of the paper money is never felt more before now. However, the lack of regulatory control and a possible major digital hack are only a few among the many concerns associated with the wide-spread usage of such forms of digital payments (Corbet et al. , 2020a .
Pertaining to the high complexity associated with the operational mechanism of this market, it is difficult to assess the market efficiency with confidence. A recent study points towards a possible management of the Bitcoin-Tether market from a few very highly influential nodes in the trading system/network. Consistent and predictable patterns of trading in the Bitcoin and Tether issuance are identified by this research published in the most prestigious journal of finance (Griffin & Shams, 2020 ). Yet another concern is its ability to cope with an unseen and uncertain situation, like a rapid decline in trust or market failures that may lead to a complete collapse of the prices in the absence of a centralized regulatory system (Fry, 2018) . Table 1 shows the top 10 cryptocurrencies worldwide according to the market capitalization.
A lot of people used to think of Bitcoin as a hedge against the Bearish market J o u r n a l P r e -p r o o f Journal Pre-proof scenarios (Dyhrberg, 2016) . It proved to be so in some cases but not this time (Conlon et al., 2020; Conlon and McGee 2020; Ji et al., 2020; Maniff et al., 2020) . During the early stages of the COVID-19 spread, Bitcoin seem to have performed like a hedge but soon after that, it fell more in value as compared to the other assets 1 .
According to some recent studies, the Bitcoin's association with the traditional equity markets is not symmetric (Gajardo et al., 2018) . Additionally, there are differences in the correlations exhibited by the intra-market characteristics also in case of different cryptocurrencies (Aste, 2019; Czapliński & Nazmutdinova, 2019) . So, it can reasonably be inferred that the crypto-currency market may exhibit a non-linear and asymmetric association with the COVID-19 outbreak too. While several recent studies have discussed the impact of COVID-19 on the crypto-currency markets worldwide (Conlon et al., 2020; Corbet et al., 2020b; Lahmiri & Bekiros, 2020) , most of these authors ignored the possibility of an asymmetric nature of such an association, as revealed in earlier studies related to the cryptocurrencies (Baur and Dimpfl, 2018) .
Hence, it is very much possible that the small and the large changes in the COVID-19 intensity (infections and deaths) may affect the returns of the digital cryptocurrencies differently, at various quantiles of its returns. Additionally, most of these studies focus on Bitcoin only, ignoring the dynamics of other cryptocurrencies which form a considerable portion of the overall market now. So, we attempt to fill this research gap by examining the asymmetric nexus between COVID-19 outbreak and the cryptocurrencies' returns. For this purpose, we investigate how the daily addition in confirmed cases of COVID-19 worldwide (pandemic intensity) affect the daily returns in the cryptocurrency market, specifically the top ten currencies according to the market capitalization, using the QQR approach. Additionally, we have employed an alternative proxy also for the pandemic intensity (the daily number of new deaths) to increase the robustness of our results. In this way, we plan to uncover not only the 1 During the early and mid of the March 2020, it recorded a decline of more than 50% in value, moved in tandem with the traditional financial assets' prices (https://www.cnbc.com/2020/03/13/bitcoin-loses-half-of-its-value-in-two-day-plunge.html).
J o u r n a l P r e -p r o o f Journal Pre-proof asymmetric impact of various quantiles of COVID-19 on cryptocurrencies' returns but also consider the variation in this influence over the Bearish (prior low level returns) and the Bullish (prior high level returns) market scenarios of these cryptocurrencies. Figure 2 shows the time trend of daily returns of the top 10 cryptocurrencies from January 1, 2020 to June 15, 2020. A steep decline in the values of all currencies is visible during March, and then the varying speed of recoveries.
The recent decision of the Peoples' Bank of China to test-launch its digital RMB in three cities at a limited level also adds to the significance of our study 2 . This step of the Chinese government is an indication that the future may belong to the cryptocurrencies and that paper money may be replaced gradually by the digital currency. The seriousness of this policy can be judged from the inclusion of more cities recently, to this pilot program 3 . Although the Chinese digital currency will be centrally-managed as compared to the decentralized system of today's cryptocurrencies, still both of these are the kinds of digital currencies and expected to possess certain similar features. In the wake of growing use and importance of the digital currencies, it is imperative that the literature on this market be enriched to enhance the understanding of its dynamics during the varying/volatile market conditions, especially the extreme events. Hence any study related to the behavior of digital cryptocurrencies, especially during a crisis like a pandemic, should be of great value and significance for the policymakers, investors, and regulators alike. Our study contributes to the existing literature on the association between COVID-19 and cryptocurrencies in three ways. Firstly, we identify how the major cryptocurrencies' returns respond to the changing severity of the pandemic overall. Secondly, we check for any differences in the pattern of this association following small and large changes in the severity of the pandemic given low, middle, and high levels of prior returns of cryptocurrencies (asymmetric nature of the relationship). Finally, we identify the differences in the responses of the top cryptocurrencies to the pandemic intensity.
In this section, we have presented a background and overview of our topic, and the next section consists of the theoretical development. The third section defines data and econometric methodology used in this study. The fourth section presents results and discussions whereas the last section concludes our paper.
The recent pandemic of COVID-19 is a form of an extreme stress test for the global markets. As this pandemic has caused havoc in the equity and commodity markets around the world through negative returns, increased uncertainty, and higher volatility, cryptocurrency markets are also affected as a result of this contagion. It is hard to find an example of similar financial markets' response in the modern history (Zhang et al., 2020; Ashraf, 2020; Baker et al., 2020) . Periods of extreme financial stress can cause spillover effects in the cryptocurrency markets (Ji et al., 2019) . A recent study suggests that the direction of contagion in case of financial disasters is from traditional to crypto-markets, and investors avoid crypto-assets in the times of extreme stress (Matkovskyy & Jalan, 2019) . Stress in the global financial markets can cause significant changes in the upper and the lower distributions of the cryptocurrencies such as Bitcoin, exhibited by the copula-based quantile models (Bouri et al., 2018b) . A study on 973 types of cryptocurrencies and 30 different indices finds that the safe-haven feature of the cryptocurrencies is market and region specific (performs better as a safe haven in developed markets), and its hedging capacity is very limited . During the early days of pandemic, Bitcoin showed a high correlation with the equity markets and dropped in value in tandem with the other financial markets due to the lack of demand for risky assets in a highly uncertain situation 4 . Additionally, cryptocurrencies are found to overreact 4 The DJIA dropped 9.99% in value in a matter of few hours which was the biggest single-day drop since 1987.
J o u r n a l P r e -p r o o f Journal Pre-proof against the negative news more profoundly when compared with the traditional equities' behavior (Borgards & Czudaj, 2020) .
On the other hands, a number of studies find that the behavior of cryptocurrencies is different as compared with the traditional assets including equities, commodities, and currencies, and investors' enthusiasm driven by the extreme news and events (both positive and negative) causes an increase in the crypto-markets' returns (Liu & Tsyvinski, 2018; Rognone et al., 2020) . In the wake of conflicting evidence on the behavior of cryptocurrencies, it is interesting to examine how these assets perform during the recent pandemic which is an extremely rare event with unprecedented characteristics.
Some researchers have attempted to document the impact of this outbreak on the Bitcoin returns and found that it performed poorly during this situation, and showed a high correlation with the equity markets (Conlon & McGee, 2020) . Some of them even compare it to the gold and conclude that the Bitcoin is not the so-called digital gold (Klein et al., 2018; Conlon & McGee, 2020) . Gold once again came out as a triumphant when it came to a natural hedge against the market disasters like the current pandemic . Some sane voices advised the people not to expect too much from Bitcoin in this regard, and treat it as a hedge against fiat money and not the huge market falls and failures (Ali et al., 2020) .
Where everyone seems to curse the Bitcoin and call it a complete failure during the recent market turmoil, only a few if any have paid an attention to the detailed analysis of the situation. According to a study, the relationship of Bitcoin returns with the US stock markets is not symmetric, and only specific market conditions related to the S&P and the Bitcoin show co-movements (Bouri et al., 2017) . Similarly, another study reports that non-linear methodologies extract the asymmetric impact of positive The Bitcoin followed the course and recorded a decline of more than 50% in value till 17 th of March, 2020.
https://cointelegraph.com/news/crypto-traders-explain-what-caused-the-bitcoin-price-plunge-to-3-000.
Journal Pre-proof and negative news more efficiently in case of cryptocurrency markets (Katsiampa et al., 2019; Bouri et al., 2018a) . The volatility in the cryptocurrency market exhibits a different asymmetry as compared to the equity markets, and shows more sensitivity to the positive as compared to the negative shocks, induced by the noise traders (Baur & Dimpfl, 2018) . Bouri et al., (2018a) suggest the use of non-traditional and non-linear techniques to study the behavior of Bitcoin for unraveling the hidden characteristics and patterns.
With such guide from the literature, it is interesting to investigate if the recent COVID-19 outbreak has an asymmetric impact on the returns of the top cryptocurrencies. For instance, the small and large increments in the severity of the pandemic may affect the market for cryptocurrencies differently not only in its entirety but also in the case of Bearish and Bullish scenarios. For this purpose, we have employed a recently developed technique, the QQR regression to study the asymmetric association between our variables of interest (Sim & Zhou, 2015) . This technique has already been used in the financial studies related to the Bitcoin returns and oil market prices (Bouri et al., 2017) . The top ten currencies according to the market capitalization represent the major portion of the cryptocurrencies' market, and remaining currencies are highly correlated with these assets leading to the contagion like effects among them (Yi et al., 2018; Bouri et al., 2019a; Bouri et al., 2019b; Katsiampa et al., 2019) .
We have collected daily prices of the top ten cryptocurrencies according to the market capitalization from an online source (https://coinmarketcap.com/) and calculated the daily returns manually and converted into the logarithmic values (log differences). All values are stationary at the first differences. The data about daily additions in the active cases of COVID-19 worldwide (severity of the pandemic) is collected from the J o u r n a l P r e -p r o o f website designed by the Johns Hopkins University for the purpose. The series is divided by 100 after converting into log values. Such a transformation is supported by the literature (Gan & Xu, 2019) , and the proponents of the QQR methodology advise the normalization of the values in this case (Sim & Zhou, 2015) . The Sample period comprises of daily observations starting from January 1, 2020 and ending on June 15, 2020 (146 observations). Additionally, we use the "daily addition in number of deaths due to COVID-19" as an alternative proxy for the severity of the pandemic to check for the robustness of our results. This data is also collected from the website of the Johns Hopkins University.
We have employed the QQR (Quantile-on-Quantile Regression) technique developed by Sim and Zhou (2015) recently. This technique has already been used effectively in the numerous studies related to economics and finance, to check the asymmetric nexus between the variables of interest (Bouri et al., 2017; . The main advantage of this technique is to capture the association at different quantiles of the both variables. In this way, we can know how the upper, lower, and middle quantiles of COVID-19 affect the upper, lower, and middle quantiles of the cryptocurrencies' returns differently. Moreover, we can divide the whole distribution of variables of interest in varying numbers of quantiles according to our requirements.
In this section, we briefly highlight the basic importance and the characteristics of Sim and Zhou (2015) , quantile-on-quantile regression method, which is structured to explore the asymmetric connection between COVID-19 and world's top ten cryptocurrencies' returns here. The QQR is a general form of standard quantile regression technique. This novel econometric method allows us to investigate how the quantiles of an independent variable impact the conditional quantiles of the dependent variable. The QQR method is implemented with a combination of the non-parametric J o u r n a l P r e -p r o o f Journal Pre-proof estimation and quantile regression.
Firstly, Koenker & Bassett, (1978) develop the quantile regression that determines how the regressor (independent variable) affect the conditional quantiles of the regressand (dependent variable). Secondly, quantile regression is a modified version of the classical linear regression approach. In line with the ordinary least square (OLS), quantile regression determines the effect of regressor on regressand at the lower, middle, and top quantile distributions. Thirdly, the local linear regression model is proposed by Stone (1977) and Cleveland (1979) that classifies the local effects of the specific quantiles of the regressor on the fitted regressand. Furthermore, one of the many advantages of the local linear regression method over the non-parametric method is to overwhelm the situation of the "curse of dimensionality."
Hence, the combination of these two methodologies helps us to understand the linkages between the quantiles of regressor and the regressand and then provides more profound information than the conventional regression approaches, such as ordinary least square and/or quantile regression.
The current study aims to apply the QQR method to capture the quantiles' impact of COVID-19 daily cases on the quantiles of cryptocurrencies' returns (BTC, ETH, XRP, BCH, BSV, LTC, BNB, EOS, ADA, and CRO). In this direction, the nonparametric quantile regression is defined below.
Where Crypto t explains a given cryptocurrency's returns (BTC, ETH, XRP, BCH, BSV, LTC, BNB, EOS, ADA, and CRO) in period t, the COVID19 t is the daily new confirmed cases globally in period t, is the ℎ quantile of the conditional distribution of Crypto t, and is a quantile error term for which ℎ quantile is equal to zero, '   (.) is a feature that is an unidentified function since we do not assume a prior hypothesis about the form of connection between COVID19 t and Crypto t .
The quantile regression is an efficient approach as it considers the variations in effects of COVID19 t at different points of the Crypto t distribution. However, the quantile regression cannot extract the entire nature of dependency between the regressor and the regressand. Specifically, it is unable to analyze the asymmetric nature of the small and the huge positive shocks of COVID19 t that can affect the Crypto t differently .
Therefore, the novel QQR approach has been proposed by Sim and Zhou (2015) that can derive the dependency relationship more profoundly between COVID19 t and Crypto t .
For studying the linkages between ℎ quantile of Crypto t and τth quantile of 
Where '   signifies the partial derivative of 
Where   (.) shows quantile loss function and K(.) the Gaussian kernel function in both the minimization problems as minimal weighting criterion to improve the estimation efficiency.
Finally, when applying a non-parametric estimation, bandwidth selection is important.
A higher bandwidth provides us low variances but greater bias in the results, while a lower bandwidth produces unbiased estimates with high variances. Following Sim and Zhou (2015), the current research is based on a bandwidth parameter of h = 0.05. the Jarque-Bera test shows the abnormality in the data distribution, which further advocates the use of the QQR approach in such a scenario . The unit root tests of ADF (Augmented Dickey-Fuller) and ZA (Zivot and Andrews, 2002) show that all the variables are non-stationary at levels but turn into stationary at the first differences. The structural break test is applied following Ahmed et al., (2019) to check a single break-in-time which is 17 th and 18 th of March for most of the currencies, while 6 th April for the COVID-19 cases, and 18 th April for the deaths.
As evident from Figure Figure 4 presents the results from QQR regression between the numbers of daily new COVID-19 cases worldwide and daily returns of the top ten cryptocurrencies in the world according to the market capitalization.
The vertical bars on the right side of the 3D graphs show the scale, direction, and magnitude of the beta coefficients. The x, y, and z-axis show the quantiles of COVID-19, the quantiles of cryptocurrencies, and the beta coefficients, respectively.
The coefficient values and the relationship between variables move from lower and negative to the higher and positive, respectively as the color shifts from blue (downward) to red (upward). As the colored bar is scaled which also shows the numerical values associated with the different colors for the coefficients, we have not If we report all matrices, it requires additional ten tables which consumes a lot of space and is not efficient as those coefficients are already represented by the colored 3D graphs included above. 
The QQR methodology can be thought of as an approach that disintegrates the estimates from a standard quantile regression, making it possible for the specific estimates to be observed for varying quantiles of the independent variable. In our study, the QQR model is used for regressing the th  quantiles of the cryptocurrencies' returns on τth quantiles of COVID19; hence, the parameters will be indexed here by both  and τ. Thus, the QQR method contains more localized information regarding J o u r n a l P r e -p r o o f the COVID19-cryptocurrencies link than the standard quantile regression (if used).
Such an association is perceived to be potentially heterogeneous by the QQR approach, across different quantiles of cryptocurrencies' returns and COVID-19. Because of the presence of such an inherent property of decomposition in the QQR method, it should be possible to employ the QQR estimates to recover the standard quantile regression estimates (Sim & Zhou 2015; Shahzad et al., 2017) . More specifically, the parameters of quantile regression, only indexed by  , should be generated through averaging the QQR parameters along τ. The slope coefficient for the quantile regression model that measures the impact of COVID-19 on the quantiles of cryptocurrencies' returns, and is denoted by 1 () , can be obtained through the following equation:
Where S=19 is the number of quantiles, τ = [0.05, 0.10, ..., 0.95], considered here in this study.
So, a simple way of observing the validity of the QQR approach should be to compare the parameters estimated through the quantile regression with the τ-averaged QQR parameters. Figure 5 shows the plot of estimates from the quantile regression and the averaged QQR approach towards the slope coefficient, measuring the effect of COVID-19 on returns of the top 10 cryptocurrencies. The graphs generated in Figure 5 
To increase the robustness of our results, we further apply the same econometric technique between cryptocurrencies' returns and COVID-19 related deaths instead of infections, following other studies on COVID-19 . Resulting graphs for QQR and robustness are reported in Figure 6 and Figure 7 correspondingly.
No obvious differences are observed between the graphs reported above (for COVID-19 related infections, Figure 4 and Figure 5 ) and these from figure 6 and figure 7 (for COVID-19 related deaths).
By thinking logically, and referring to the recent literature on the COVID-19 and cryptocurrencies, we are unable to find any third variable which might affect the COVID-19 and cryptocurrencies' returns simultaneously, and cause a spurious relationship resultantly (distort the true relationship among our variables). The only variable that can be thought to have an effect on both of COVID-19 and cryptocurrencies' returns is the "weather". A number of recent articles have discussed the role of weather in causing/reducing the COVID-19 cases Shahzad et al., 2020) . At the same time, weather has the potential to cause changes in investors' moods, which in turn may affect their investment behavior. In this way, weather cannot directly affect the cryptocurrencies returns, and can only influence this market through a behavioral variable, like mood which has no known/obvious link to cause the COVID-19. Investors' mood cannot cause more/less COVID-19 cases.
Additionally, the impact of weather on the market returns of cryptocurrencies may be feeble/negligible only. Reverse causality is also not an expected phenomenon in our case as increase/decrease in cryptocurrencies' returns in no way can cause increase/decrease in the cases or deaths related to COVID-19.
J o u r n a l P r e -p r o o f
This study attempts to explore the impact of COVID-19 outbreak on the returns of top 10 cryptocurrencies in the world according to the market capitalization. To check how the small and the large increments in the pandemic intensity affect the returns of these currencies differently, conditional on the various quantiles of given returns, we have employed QQR (Quantile-on-Quantile Regression) approach which is suitable for this purpose. Results reveal that the association between the COVID-19 and the cryptocurrencies' returns is not symmetric and varies in magnitude and direction at the different quantiles of both variables. These findings are similar to the earlier results where cryptocurrency market is found to behave in a non-linear fashion with the Global Financial Stress Index . Apart from this, although the overall trend in the cryptocurrencies market is the same for all currencies, still there are differences in these assets' responses to the changes in the COVID-19 intensity.
This result is similar to another recent study, and could not be revealed through traditional linear, or standard quantile regression techniques alone (Conlon et al., 2020) .
Furthermore, in combating the negative impacts of COVID-19 on financial markets, and serving as an alternative investment tool in the times of stress, panic and uncertainty, BTC, Ethereum, ADA and CRO performed better as compared with the other currencies. This finding is contrary to an earlier study of Conlon and McGee (2020) that branded Bitcoin as a failure in this pandemic, and is in line with Huynh et al., (2020) who find Bitcoin as a better hedge as compared to other cryptocurrencies due to its independence.
Most of the other cryptocurrencies in our sample posted positive gains in response to the small additions in the COVID-19 cases. Such a behavior shows the ability of these assets to absorb small external shocks and perform as a hedge during the limited market-turmoil conditions. Further, this phenomenon reveals that a selective and J o u r n a l P r e -p r o o f cautious approach needs to be adopted in case of diversifying with cryptocurrencies against systematic risks of a global nature, such as the recent pandemic.
The intensity of the COVID-19 pandemic as measured by the daily new cases/deaths can also be regarded as a global market stress due to its wide scale devastation in terms of lockdowns, deaths, panic, fear, psychological distress and uncertainty in the absence of any vaccine or a sound cure. In this way, our results also correspond to another study by . They examined the quantile causality and extreme right and left tail dependencies between Bitcoin and Global Financial Stress Index, and concluded that the lower and the higher quantiles of Bitcoins' returns were dependent on the GFSI against a limited dependency between the middle quantiles.
Our results are robust to the use of alternative proxy for the severity of the pandemic (daily addition in death). These results have important implications for the investors, especially in understanding the behavior of cryptocurrencies in the times of huge stress/disaster, such as a pandemic, and making informed investment decisions.
Regulators and governments may benefit from this research to formulate policies for stabilizing this market, reducing its high volatility, and enhancing the investors' confidence there. 
The impact of COVID-19 daily new cases on Cryptocurrencies 