Small Portfolio Construction with Cryptocurrencies

In this paper, we describe and apply different models of portfolio construction in the selection between a small number of big-cap cryptocurrencies. Our purpose is to select the minimum riskiness between cryptocurrencies, comparing different risk measures and maximum diversification. We build our models without the constraints of the expected returns. Without relying on expected returns, we have the same condition on the comparison between them. Cryptocurrencies are not common stock or other assets indexed in the market but it is interesting to study how diversification can significantly improve investment performance. We first give the methodology to use high-frequency observation data, in the numeral approximation especially in the novel application of the Risk parity models, used with different risk measures we can achieve a very good result, from the position of gaining and variation. Since Risk parity models divide the weights of the asset in equal risk contribution proportion, it is suggested to use a small number of cryptocurrencies, otherwise their performance will be close to the uniform portfolio. To the traditional Mean Variance model, and the alternative, Expected shortfall/Conditional Value at Risk, we use three versions of Risk Parity with two different risk measures and a naive risk parity. The uniform portfolio is used as a benchmark for selection comparison with the other portfolio models. We give the conditions for the Risk Parity with the Expected shortfall/Conditional Value at Risk (CVaR) to guarantee convergence with the numerical approximation. In the end, we study the tradeoff between each model and which is more suitable for a small cryptocurrency portfolio.