Abstract: Drawing upon Bitcoin, Ripple and Litecoin as the research objects, this paper uses the multifractal portfolio model to research the portfolio investment of cryptocurrency and further studies the difference of portfolio effect between bull market and bear market. Return, risk and Sharpe ratio are used to perform in-sample forecasting and out-of-sample effect test analysis on the investment portfolio. The empirical results show that: in different periods, each cryptocurrency and the pair of cryptocurrencies exhibit scaling effects and multifractal characteristics, and the characteristics of long memory are stronger during the bull market. During the full-sample, bull-market and bear-market periods, the multifractal portfolio model can significantly decentralize risks compared with the traditional portfolio model under different volatility and time scales, and the effective boundary of the multifractal portfolio moves significantly to the left during the bull and bear market periods. Further research shows that the multifractal portfolio model can achieve the optimal portfolio effect in both bull and bear market under the appropriate scale q.

Key words: cryptocurrency, portfolio, fractal, bull and bear market