A case study of the Trading Invariance Principle on Cryptocurrency

Abstract

In the traditional financial markets, much research has been done and relations derived to understand the inner workings of them. In particular, the "trading invariance principle" defines a particular relationship between key variables that links the trading activity with the price variability. The trading activity is defined as the number of trades N, while the price variability is described by the variables: the traded volume V, the asset price P, the squared volatility \(\sigma^{2}\), the cost of trading C, and the bid-ask spread S. By primarily using dimensional analysis, Benzaquen et al. and Pohl et al. derives the 3/2-law N\(^{3/2}\) \(\sim\) \(\sigma\)PV/C, which is tested on NASDAQ stock data and is shown to hold fairly well. In addition, Kyle and Obizhaeva derived a relation, coined the ``KO Trading Invariance Principle" in Benzaquen et al., via dimensional analysis as well, which is in the form I = \(\sigma\)PV / N\(^{3/2}\) and notably does not use the variables: cost of trading (C) or bid-ask spread (S). The focus of this paper is to build off of this 3/2-law and the "KO Trading Invariance Principle" and examine how well cryptocurrencies would adhere to it. As the nature of the cryptocurrency markets is very different from that of the traditional markets, the motivation lies in seeing if the trading invariance principle is universal to even the relatively new cryptocurrency markets. Because the data for cost of trading (C) and bid-ask spread (S) is not available, only the ``KO Trading Invariance Principle" is empirically tested. The empirical tests are performed on the top 47 highest adjusted volume cryptocurrencies according to CoinMarketCap, excluding stablecoins as they are not representative of the usual characteristics that cryptocurrency present.