We applied MF-ADCCA to analyze the presence and asymmetry of the cross-correlations between the major currency rates and Bitcoin, and the Dow Jones Industrial Average (DJIA), gold price and the oil crude market. We find that multifractality exists in every cross-correlation studied, and there is asymmetry in the cross-correlation exponents under different trend of the WTI, Gold and DJIA. Bitcoin shows a greater multifractal spectra than the other currencies on its cross-correlation with the WTI, the Gold and the DJIA. Bitcoin shows a clearly different relationship with commodities and stock market indices which has to be taken into consideration when investing. This has to do with the years this currency has been traded, the characteristics of cryptocurrencies and its gradual adoption by financial organizations, governments and the general public. (C) 2018 Elsevier Ltd. All rights reserved.