As an investor, volatility plays an important role in decision making. It is defined as the rate at which a security’s price increases or decreases, i.e., shows pricing behaviour during a definite span of time. A high volatility will lead to high risk. Thus, it becomes critical to determine the volatility and the risk-return trade-off among investments. This paper tries to document the volatility and risk-return trade-off of four prominent crypto-currencies (Bitcoin, Ethereum, Binance and Ripple), based on market-capitalization. For analysis, closing prices of cryptocurrencies had been accumulated through secondary method for 365 days, starting from 1st March 2022 and ending on 28th February 2023. Standard Deviation and Kurtosis, used together for volatility and risk assessment, documented that Bitcoin had the highest volatility and risk associated with expected returns. Regression, for assessing the impact of volatility in BTC price on others, derived that ETH had a strong, but not very strong, bivariate relationship with BTC, among all the pairs. Durbin Watson (DW) concluded that there was no auto- correlation in the prices of crypto-currencies, i.e., previous day’s price does not play significant role in today’s price. For risk-return trade-off, Coefficient of Variation (CoV) had been applied. It determined that Ethereum had the highest ratio indicating its non-suitability to a conservative investor because of having the lowest returns as compared to risks involved; while Binance had the lowest Coefficient of Variation (CoV) depicting lower risk and maximum return among all.

Crypto-currency that has recently been in limelight, is a virtual or digital form of currency that uses block chain technology for transactions. As the name suggests, it is hidden or secret money, having no physical value [1]. It has evolved as a virtual medium of exchange platform which uses internet for transactions [2]. Since its inception, it has been fascinating for many investors, especially who are risk takers [3]. They choose crypto-currencies, over others, because of its capacity to generate high returns [4]. But, as a saying goes, every coin has two faces, same is with crypto-market. Although it has the capability to generate higher returns [5], it involves huge risks too, due to its volatile nature. As an investor, volatility plays an important role in decision making. The term volatility, in layman language, can be defined as the probability of unexpected or sudden change. Technically, it can be defined as the rate at which a security’s price increases or decreases, i.e., shows pricing behaviour during a definite span of time; meaning price can vary dramatically over a short duration in either direction. The rate of volatility and risk involved are interconnected. Volatility is directly proportional to risk, i.e., a higher volatility will lead to higher risk, resulting greater probability of incurring losses. Thus, it becomes crucial to determine the dispersion of returns, i.e., to determine whether expected return is worth the volatility involved. For this purpose, there are several methods: GARCH model, beta coefficients, option pricing model, standard variations (SD), kurtosis tail risk, coefficient of variation (CoV), etc. This paper aims to document the volatility of crypto-currency. For this, four crypto-currencies have been considered, having prominent market-capitalization. These are Bitcoin (BTC), Ethereum (ETH), Binance (BNB) and Ripple (XRP). For analysis, closing prices of cryptocurrencies have been accumulated through secondary method of data collection. The data have been gathered from secondary sources such as websites: investing.com, coinmarketcap.com, published reports of IMF or OECD. Data of past one year, i.e., from 1st March 2022 to 28th February 2023, have been taken into consideration for the analysis. Objectives are the core ingredients of any study. Without these, a paper loses its direction.

Following are the research objectives of this paper.

1. To measure the volatility and risk of cryptocurrencies
2. To measure the trade-off between risk and return of cryptocurrencies
3. To determine the impact of volatility of Bitcoin prices on other cryptocurrencies

Literature Gap

Table 1: The following table shows the background of the related literature.

Table 2: Descriptive Analysis.

Table 4: Regression.

Studies on inter-cryptocurrencies performance comparison are still smaller in number. This paper tries to fill the gap by analysing the performance of four prominent cryptocurrencies based on market-capitalization, which are Bitcoin (BTC), Ethereum (ETH), Binance (BNB) and Ripple (XRP). Along with these, this paper tries to analyse bivariate relationship of Bitcoin, being most dominant, with other selected cryptocurrencies.

Secondary method has been used for collection of data on closing prices of selected crypto- currencies. The prices are in dollars ($). Daily analysis has been done, i.e., the data being collected and analysed for 365 days, starting from 1st March 2022 to 28th February 2023. For the set objectives, following tools and methods have been used: SPSS - Descriptive Analysis, Regression analysis and Durbin Watson Excel - Coefficient of Variance (CoV). Descriptive analysis (SD and Kurtosis) has been used to measure the volatility and risk involved in cryptocurrencies and similarly, Coefficient of Variation (CoV) for risk-return trade off: lower ratio, better trade-off; and Regression for impact of volatility in BTC price on others. Durbin Watson (DW) is used to predict the direction of price movement or variation (result range between 0to4) of any security. According to Rule of Thumb, if there is positive auto-correlation (DW<2), it indicates that previous day’s price has a positive impact on today’s price, i.e., increase in previous day’s price will increase today’s price and vice-versa. If the auto-correlation is negative (DW>2), increase in previous day’s price will result in decline in today’s price and vice-versa. No auto-correlation (DW = 0) means previous day’s price does not affect today’s price. But in order to test the significance level, a standard DW table is used. In this paper, the significance level for the two hypotheses was determined at .01 and .05 level.

Standard Deviation (SD) is a statistical tool which is used to measure the volatility. It ascertains the proliferation of asset’s price from its mean (average) price. While Kurtosis determines how often prices move dramatically. It is useful only when interpretated with SD. A higher SD and a lower kurtosis indicate higher volatility thus more risk involved. From Table 1, it can be observed that Bitcoin has the highest SD and a lower kurtosis, indicating highest volatility resulting in higher risk. Ethereum has high SD and high Kurtosis. Along with the risk factor, an investor would also like to determine whether expected return is worth the volatility involved. Coefficient of Variance (CoV), the ratio of standard deviation (SD) and mean, is used to determine the trade-off between the degree of risk involved and returns. The lower the ratio, the better will be the trade-off, i.e., lower CoV means favourable trade-off between risk and return. Table 2 depicts the CoV of four selected cryptocurrencies. Ethereum, followed by Bitcoin, has the highest ratio indicating its non-suitability to a conservative investor. Binance has the lowest CoV depicting lower risk and maximum return, i.e., return is approximately 5.5 times more than the risk involved, which is highest as compared to other cryptocurrencies. Ethereum has the lowest returns as compared to risks involved: 2.7 times return generating capacity.

H01: There is no impact of volatility of Bitcoin prices on other cryptocurrencies

H11: There is an impact of volatility of Bitcoin prices on other cryptocurrencies

H02: There is no first-order auto-correlation

H12: There is a first-order auto-correlation

Simple linear regression (SLR), also known as Bivariate Analysis, was applied to test the null hypothesis H01 in order to know the impact of price volatility in Bitcoin (BTC) on other cryptocurrencies under consideration, i.e., Ethereum (ETH), Ripple (XRP) and Binance (BNB). The analysis was done separately, keeping independent variable (BTC price) same, and then regression was applied, first on ETH, followed by BNB and XRP. The result can be visualised in Table 3. R closer to 1 signifies a strong strength of linear relationship. The impact on prices of other cryptocurrencies, caused due to variation (volatility) in BTC price, can be explained by R2. From Table 3 it can be concluded that volatility in BTC price significantly (p < .01 & p < .05) affected the prices of other cryptocurrencies. Hence, null hypothesis (H01) was rejected and alternate hypothesis (H11) was accepted: There is an impact of volatility of Bitcoin prices on other cryptocurrencies. Durbin Watson (DW) analysis was also done to test the presence of auto-correlation (serial- correlation). Auto-correlation is used to measure relationship between current value and past values of a variable. According to Rule of Thumb, from Table 3, it can be inferred that there is no auto-correlation. But, in order to test null hypothesis H02, upper (U) and lower (L) limits, at significance level of .01 and .05, were determined through a standard DW table. If dU < d < (4 – dU), then null hypothesis (H02) should be accepted, and if d < dL, alternate (H12) should be, accepted. From the Table 3, is can be documented that alternate hypothesis was rejected and null hypothesis was accepted at .01 and .05 significance level: There is no first-order auto- correlation [dU < d < (4 – dU)].

The data was analysed and interpreted based on the set objectives. To measure the risk, resulting from volatility, standard deviation (SD) and kurtosis were used. Bitcoin had the highest SD and lowest kurtosis indicating maximal fluctuations in the prices and thus in returns too. In order to determine the trade-off between risk and return, Coefficient of Variance (CoV) had been used. It analysed whether it was worthy to take risk or not. Binance had the lowest risk-return ratio among others, indicating its suitability for risk-averse investors, i.e., maximum return of 5.5 times to the risk involved. Binance is then followed by XRP and BTC, while ETH has the lowest return generating capacity in comparison to risk. Simple Linear Regression was applied to test the impact of volatility in prices of Bitcoin (BTC) on other selected cryptocurrencies, which are Ethereum (ETH), Binance (BNB) and Ripple (XRP). The analysis concluded that there was an impact of price volatility on other cryptocurrencies. But while there was not a very strong bivariate relationship among the crypto-currencies, ETH had a strong bivariate relationship with BTC, among all the pairs, indicating that the two currencies have the highest market capitalization and that they have a strong bivariate relationship. The impact of volatility in BTC price on XRP price is lowest, indicating only 55% of changes in XRP can be explained by BTC price changes. Durbin Watson (DW) analysis showed no auto- correlation, i.e., there was no serial correlation. It means that there was no impact of previous day’s price on today’s price.

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