ABSTRACT This paper discusses whether the Bitcoin exchange-traded fund (ETF), which tracks the value of Bitcoin, improves equity portfolios, by using a robust portfolio performance analysis. The equity portfolio is represented by an ETF that tracks the Standard & Poor’s 500. We use data from a turbulent investment period within the coronavirus pandemic, to study the diversification benefits of Bitcoin. We compare the performances of diverse portfolios composed of both ETFs, which include 40 classical dynamic volatility model-based portfolios and 900 score-driven portfolios. For the score-driven portfolios, the dynamic association is modelled by score-driven Clayton, rotated Clayton, Gumbel, rotated Gumbel and Student’s t copulas. We compare portfolio strategies using the model confidence set test. We find that score-driven portfolios outperform classical volatility model-based portfolios and the equity portfolio. Our results may provide suggestions for cryptocurrency investors on portfolio optimization and may also have policy implications for regulators and policymakers.