Got crypto? : evidence from Markowitz, Kataoka, and conditional value-at-risk models

Should we include cryptocurrency in risky portfolio investing? Bitcoin, given its status as the leader of cryptocurrencies and a speculative asset due to its non-dividend-paying trait and high volatility as well as high returns, poses an interesting question whether it can also be beneficial in a portfolio of risky assets. In order to find an answer, we revisit the conventional dual objective of minimizing risk and maximizing expected return for risky assets. Various models are tested to analyze the risk-return trade-off of risky portfolios including Bitcoin. Given an initial budget for a finite portfolio, the cumulative filtration yields the expected return and the covariance matrix. With the addition of Bitcoin, we compare the performance of the portfolio generated from the optimization models and technical analysis. The main implications are follows: (1) risk tolerance and diversification constraints are the key factors in portfolio optimization; (2) including cryptocurrency enhances portfolio returns; and (3) the Markowitz model (Kataoka’s and conditional value-at-risk models) recommends to fully weigh (unload) Bitcoin in (from) the portfolio.