The cryptocurrency market is unique on many levels: Very volatile, frequently changing market structure, emerging and vanishing of cryptocurrencies on a daily level. Following its development became a difficult task with the success of cryptocurrencies (CCs) other than Bitcoin. For fiat currency markets, the IMF offers the index SDR and, prior to the EUR, the ECU existed, which was an index representing the development of European currencies. Index providers decide on a fixed number of index constituents which will represent the market segment. It is a challenge to fix a number and develop rules for the constituents in view of the market changes. In the frequently changing CC market, this challenge is even more severe. 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. CRIX is chosen by model selection such that it represents the market well to enable each interested party studying economic questions in this market and to invest into the market. The diversified nature of the CC market makes the inclusion of altcoins in the index product critical to improve tracking performance. We have shown that assigning optimal weights to altcoins helps to reduce the tracking errors of a CC portfolio, despite the fact that their market cap is much smaller relative to Bitcoin. The codes used here are available via www.quantlet.de .

Cryptocurrencies have left the dark side of the finance universe and become an object of study for asset and portfolio management. Since they have low liquidity compared to traditional assets, one needs to take into account liquidity issues when adding them to a portfolio. We propose a Liquidity Bounded Risk-return Optimization (LIBRO) approach, which is a combination of risk-return portfolio optimization under liquidity constraints. Cryptocurrencies are included in portfolios formed with stocks of the S&P 100, US Bonds, and commodities. We illustrate the importance of the liquidity constraints in an in-sample and out-of-sample study. LIBRO improves the weight optimization in the sense that it only adds cryptocurrencies in tradable amounts depending on the intended investment amount. The returns greatly increase compared to portfolios consisting only of traditional assets. We show that including cryptocurrencies in a portfolio can indeed improve its risk–return trade-off.

Cryptocurrencies (CCs) have risen rapidly in market capitalization over the last years. Despite striking price volatility, their high average returns have drawn attention to CCs as alternative investment assets for portfolio and risk management. We investigate the utility gains for different types of investors when they consider cryptocurrencies as an addition to their portfolio of traditional assets. We consider risk-averse, return-seeking as well as diversification-preferring investors who trade along different allocation frequencies, namely daily, weekly or monthly. Out-ofsample performance and diversification benefits are studied for the most popular portfolio-construction rules, including mean-variance optimization, risk-parity, and maximum-diversification strategies, as well as combined strategies. To account for low liquidity in CC markets, we incorporate liquidity constraints via the LIBRO method. Our results show that CCs can improve the risk-return profile of portfolios. In particular, a maximum-diversification strategy (maximizing the

Public interest, explosive returns, and diversification opportunities gave stimulus to the adoption of traditional financial tools to crypto-currencies.While the CRIX index offered the first scientifically-backed proxy to the cryptomarket (analogous to S&P 500), the introduction of Bitcoin futures by Cboe became the milestone in the creation of the derivatives market for cryptocurrencies. Following the intuition of the "fear index" VIX for the American stock market, the VCRIX volatility index was created to capture the investor expectations about the crypto-currency ecosystem. VCRIX is built based on CRIX and offers a forecast for the mean annualized volatility of the next 30 days, re-estimated daily. The model was back-tested for its forecasting power, resulting in low MSE performance and further examined by the simulation of VIX (resulting in a correlation of 78% between the actual VIX and VIX * Financial support from NUS FRC grant R-155-000-199-114 "Augmented machine learning and network analysis with applications to cryptocurrencies and blockchains" and IRTG 1792 "High Dimensional Non Stationary Time Series", Humboldt-Universität zu Berlin is gratefully acknowledged.† kolesnal[at]hu-berlin.de ‡ simon.trimborn[at]nus.edu.sg § haerdle[at]hu-berlin.de 1 estimated with the VCRIX model). VCRIX provides forecasting functionality and serves as a proxy for the investors' expectations in the absence of the developed derivatives market. These features provide enhanced decision making capacities for market monitoring, trading strategies, and potentially option pricing.