Crix Or Evaluating Blockchain Based Currencies

Simon Trimborn
Humboldt-Universitat zu Berlin

Wolfgang K. Hardle
Humboldt University of Berlin – Institute for Statistics and Econometrics; Humboldt University of Berlin – Center for Applied Statistics and Economics (CASE)

June 15, 2016

SFB 649 Discussion Paper 2016-021, Economic Risk, Berlin


The S&P500 or DAX30 are important benchmarks for the financial industry. The first mimics the performance of the major US on the NYSE, AMEX and NASDAQ, while the second does the same for the German Prime Share sector. These and other indices describe different compositions of certain segments of the financial markets. It is surprising, though, to see that emerging e-coins have not been mapped into an index yet because with cryptos like Bitcoin, a new kind of asset of great public interest has arisen. One difficulty is that data sources are scarce and an effort has to be made to collect data with the necessary frequency. Another one is buried in the construction of indices. Usually, the index provider decides on a fixed number of index constituents which will represent the market segment. It is a huge challenge to set this fixed number and develop the rules to find the constituents, especially since markets change and this has to be taken into account. For volatile markets like the crypto market, having a fixed number of index constituents is an even stronger constraint since the liquidity changes very frequently. A method relying on the AIC is proposed to quickly react to market changes and therefore enable us to create an index, referred to as CRIX, for the cryptocurrency market. For further investigation of the new methodology, an application to the German and Mexican stock markets is provided. The results show that this methodology provides a more accurate benchmark compared to the DAX and IPC, the current market indices for Germany and Mexico.

Crix Or Evaluating Blockchain Based Currencies – Introduction

More and more companies have started offering digital payment systems. Smartphones have evolved into a digital wallet, so that it seems like we are about to enter the era of digital finance. In fact we are already inside a digital economy. The market for e-x (x = “finance,” “money,” “book,” you name it . . . ) has not only picked up enormous momentum but has become standard for driving innovative activities in the global economy. A few clicks at y and payment at z brings our purchase to location w. Own-currencies for the digital market were therefore just a matter of time. The idea of the Nobel Laureate Hayek, see Hayek (1990), of letting companies offer concurrent currencies seemed for a long time scarcely probable, but the invention of the Blockchain has made it possible to bring his vision to life. Cryptocurrencies (abbr. cryptos) have surfaced and opened up an angle towards this new level of economic interaction. Since the appearance of bitcoins, several new cryptos have spread through the Web and offered new ways of proliferation. Even states accept them as legal payment method or part of economic interaction. E.g., the USA classifies cryptocurrencies as commodities, Kawa (2015), and lately Japan announced that they accept them as a legal currency, EconoTimes (2016). Obviously, the crypto market is fanning out and shows clear signs of acceptance and deepening liquidity, so that a closer look at its general moves and dynamics is called for.

The technical aspects behind cryptocurrencies have been reviewed by several researchers. For a well written technical survey, see Tschorsch and Scheuermann (2015). The transaction graph of Bitcoin, the Blockchain, has received much attention too, see e.g. Ron and Shamir (2013) and Reid and Harrigan (2013). Even the economics of the Bitcoin has been studied, e.g. Kristoufek (2014). To our knowledge, the development of the entire cryptocurrency market has not been studied so far, only subsamples have been taken into account. Additionally, a reliable benchmark for this market is still missing. We will contribute to this area of research by designing a market index (benchmark) which will enable each interested party to study the performance of the crypto market or single cryptos. First, the term benchmark has to be defined for the crypto market: Definition 1. A benchmark for the crypto market is a market measure which consists of a selection of representative cryptos.

Blockchain Based Currencies
Blockchain Based Currencies

Usually index providers construct their indices, which should be constructed in terms of Definition 1, with a fixed number of index constituents, see e.g. FTSE (2016), S&P (2014) and Deutsche Boerse AG (2013). But markets change which should cause the chosen number of index constituents to be altered too. While trying to mimic the movements of an innovative market like the crypto market, one is confronted with a frequently changing market structure. This calls for a dynamic structure of the benchmark, especially for the number of constituents. The StrataQuant index family, see NYSE (2015), alters the number of constituents in each sector index dependent on their affiliation with a certain sector and membership in the Russell1000 index. But the benchmark for the crypto market won’t have a parent index since it is meant to be the leading index. Therefore an independent approach is necessary. In addition to reacting to changes in the market structure, a dynamic methodology is necessary to help circumvent arbitrary rules like maximal weighting rules, MEXBOL (2013), which will preserve the diversity of an index at any time. For the crypto market what results is CRIX: a CRyptocurrency IndeX,, which fulfills the requirement of having a dynamic structure by relying on statistical time series techniques, namely the AIC.

This paper is structured as follows. Section 2 introduces the topic and reviews the basics of index construction. In Section 3 the method for dynamic index construction is described and Section 4 introduces the remaining rules for the CRIX family. Section 5 describes the applied indices before their performance is tested in Section 6. In Sections 7 and 8 the new method is applied to the German and Mexican stock markets to test the performance of the methodology against existing indices. The codes used to obtain the results in this paper are available via

Blockchain Based Currencies
Blockchain Based Currencies

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