Using the example of the COVID-19 global crisis (2020), we prove the low effectiveness of the existing approach to managing the financial risks of investments based on commercial investments. For this, we performed an applied quantitative study based on the statistics from the World Bank for 2020 and the Forbes Global 2000 ranking in 2021, using as an example 17 developing countries with lower-middle and upper-middle incomes from different regions of the world. As an alternative, we suggest a new approach for managing the financial risks of investments, which is based on corporate social responsibility. It implies the placement of long-term, large-scale investments in social and ecological innovations based on the mechanism of public-private partnership. We substantiated the high effectiveness and advantages of the new approach. The new approach to financial risk management amid a crisis was more effective (in comparison with the existing approach) for businesses (ensures higher return on investments, allows avoiding losses), the government (contributes more to economic growth, the probability of which achievement is higher), and for society (supports SDGs to a larger extent and contributes to sustainable development). This paper contributes to the development of the Theory of Investments (Neo-Keynesianism) and fills a gap in the literature, bridging the gap between the Theory of Investments and the Theory of Sustainable Development—outlining the perspectives of the simultaneous overcoming of economic crises and supporting sustainable development during the management of financial investment risks based on corporate social responsibility.