The economic impact of the COVID-19 pandemic is still an ongoing topic, broadly analysed and discussed in many studies. Recent articles state that sustainable assets can offer return volatility resilience during demand shock events and, in some cases, provide higher returns than their unsustainable counterparts. We set out to test such claims in our own controlled study. This paper is written from the perspective of a portfolio manager and examines four main variables: share/token prices, log returns, volatility, and trading volumes in a difference-indifference statistical regression in order to compare the performance of sustainable and unsustainable portfolios in the context of the market shock suffered on March 11, 2020. We are using both a traditional asset, stocks, and a non-traditional asset, cryptocurrencies, therefore analysing a total of four investment portfolios. The present study aims to help fill in a gap in the current literature regarding the extension of the flight-to-quality theory to sustainable and unsustainable assets, treating sustainable stocks and cryptocurrencies as our safer assets and unsustainable stocks and cryptocurrencies as our riskier assets. Method results uncover that, on the surface, a sustainable equity portfolio does indeed seem to have lower return volatility and less negative average returns post-WHO announcement compared to an unsustainable equity portfolio, but a deeper statistical analysis indicates that a high ESG score is not the main factor influencing such performance. Sustainable cryptocurrency portfolio results uncover a different picture of significantly lower average returns and higher return volatility post-event compared to the unsustainable crypto portfolio. However, the PoS sustainability factor is not the main suspect in the poor performance indicated by the statistical analysis. The flight-to-quality cannot be extended to sustainable assets due to the lack of significant evidence and the performance dynamics of the average returns. Our analysis finds that the sustainability factor alone does not provide a benefit to portfolio managers and investors in the context of equity and alternative asset classes. This paper contributes empirical evidence to the green finance theory and puts forward relevant advice for investment policy statement consideration.