By: Tsahi Halyo

Many have been drawn to Ethereum trading by its promise of getting rich quickly but is that promise legitimate or just a product of a “bubble” styled craze?

Given the rapid rise in cryptocurrency prices and their extreme volatility, interest has grown in understanding cryptocurrencies price behavior. This article examines the short term price fluctuations of the second largest cryptocurrency, Ethereum, and through such explains the pitfalls of daytrading that currency.

Before we delve into short term Ethereum price behavior a few points must be touched. Firstly, a cryptocurrency generally has little intrinsic value. Traditional currencies, which are minted by nations, derive their value through the necessity of paying one’s taxes through them and their ability to be used as a medium of exchange. Stocks depend on the company’s performance and commodities have intrinsic value. Unlike those mentioned before, a cryptocurrency almost completely derives its value from speculative behavior. The little intrinsic value it does possess is usually derived either through its use in illicit Dark Web transactions or, in the case of Ethereum, through the use of Smart Contracts, those being contracts that use Ethereum to ensure payment. The fact that cryptocurrency prices are mostly derived from speculative behavior leaves them extremely sensitive to swings in public opinion, some of which reinforce themselves in a positive feedback loop in order to create massive price shifts. While examples of bubble-like price increases are plentiful (consider that one year ago Ethereum was worth less than $15 whereas now it’s worth more than $900), that isn’t to say that examples of large price decreases can’t be found. Recently, the price of Bitcoin dropped more than 20% after the South Korean government announced that it would ban cryptocurrency trading.

Secondly, as a result of this extreme volatility; long term predictions are difficult. The sensitivity of the price to its initial conditions, meaning that any minor deviation from the initial conditions quickly snowballs into a far larger deviation when employed for predictions, renders accurate long term prediction futile. This is comparable in some ways to the behavior of the weather. No model can predict whether it will be rainy or sunny on a specific day a year from now. This chaotic behavior bars precise long term measurements. The only prediction we can make is that the crypto-bubble will eventually pop. We don’t know when this will occur; however, due to the nature of Ethereum’s rapid rise in a manner reminiscent of other bubbles it is assumed that it will pop just like the others did.

Thirdly, it is important to note that cryptocurrency prices are moderately correlated. The correlation coefficient for percent changes in Bitcoin price vs percent changes in Ethereum price is r=0.46 with a p value of approximately 1 x 10^-68. This means that a downturn for Ethereum likely reflects a downturn for Bitcoin and vice versa.

Ethereum price changes every 6 hours were recorded over a ten month period. All comments made henceforth concern price changes with that resolution. The short window ensures that the prices remain roughly the same as they were six hours prior. To normalize the price changes for their magnitude, the analysis was conducted on percent price changes (this meaning that the analysis checked if there was a 1% increase in price not a $9 increase in price). The analysis found that the percent price changes follow a Cauchy distribution with location 0.0025 and scale factor 0.014. A variable will have a Cauchy distribution if said variable is the ratio of two Normal random variables. The location of the distribution is the location of the spike and the scale factor is equal to half the size of the interquartile range.

The graph to the left shows the normalized distribution of percent price changes. The red line shows the Cauchy distribution and the blue rectangles are the raw data. Unfortunately, the Cauchy distribution is one of the statistical distributions that lends itself least to analysis. Its cumulative distribution function (the function that returns the probability of a value less than the input occurring) is given by

in which x_0 is the location and gamma is the scale. This function however results in the distribution to having any moments, a specific quantitative measure. The n^{th }moment of a distribution is defined by in which f(x) is the probability density function and c is the axis the moment is to be evaluated about. If c is 0, the first moment is the mean; if c is the mean, then the second moment is the variance. Since this integral is undefined for the Cauchy distribution’s density function the distribution doesn’t have a mean or a variance. Its mode is the axis of symmetry and the range between -γ and γ covers 50% of the occurrences.

Despite this lack of several key statistical properties, conclusions can be drawn given that Ethereum’s short term price behavior is well described by a Cauchy distribution. Firstly, the distribution of percent price changes has fat tails This corresponds to the large shifts in price that occur far more often than a Gaussian distribution would predict. This behavior can perhaps be understood as a result of the speculative nature of Ethereum trading and the positive feedback effect people have an price changes. This allows large shifts in price to happen more regularly since a minor sell-off can quickly escalate into a panic and a surge in a buying can lead to tulip-craze level increases in prices. Under a Gaussian regime, the large changes in price observed lie more than ten standard deviations away from the mean. This would mean that the probability of large price shifts occurring would be less than that of being struck by lightning thrice after having won the lottery; something which is clearly not the case.

In short, Ethereum trading is little more than a technologically “cool” way of betting. Given that short term price shifts have a nearly equal chance of increasing or decreasing means that betting on Ethereum is similar to betting on a coin toss. This effect combined with its tendency to reinforce price changes through a positive feedback mechanism allows for large price changes. Finally, the chaotic nature of Ethereum price changes renders long term prediction moot. Many people have made thousands off the Ethereum bubble and their gains have prompted many to test their skills in investing in the market. Unfortunately the data shows that being an Ethereum investor is nothing more than being a glorified gambler.