All rights reserved Abstract: This study aims to determine which auxiliary asset – S&P500, SHCOMP, the U.S. 10Y bond, gold, Brent or corn, in combination with Bitcoin has the best downside risk- minimizing performances. Six portfolios are constructed via an optimal DCC-GARCH model, while for downside risk measures, we use parametric and semiparametric Value- at-Risk and Conditional Value-at-Risk. All selected auxiliary assets have very low dynamic correlation with Bitcoin, which classifies them as good diversifiers. According to parametric results, S&P500 has the best downside risk-minimizing output, while SHCOMP and gold take second and third place. However, when higher moments of portfolios are taken into account, the results change significantly. Due to very high kurtosis and negative skewness, portfolio with S&P500 has among the worst semiparametric downside risk results. On the other hand, SHCOMP index and gold have relatively favourable third and fourth moments’ characteristics, which pushes them to the first and second place of the best auxiliary assets when modified downside risk measures are at stake. We also calculate Sharpe ratio, which suggests that portfolio with gold has by far the best return/risk characteristics. Živkov, Dejan Manić, Slavica Đurašković, Jasmina Viduka, Dejan https://phaidrabg.bg.ac.rs/o:29523 doi:10.32065/CJEF.2021.02.04 ISSN: 0015-1920 info:eu-repo/semantics/article application/pdf 1390991 bytes Finance a Uver: Czech Journal of Economics and Finance 71(2) Keywords: Bitcoin, parametric and semiparametric downside risk measures, DCC-GARCH Measuring Downside Risk in Portfolios with Bitcoin eng 2021