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As a first step to assess the financial risks associated with biodiversity loss, this paper develops a method to evaluate the exposure of the financial system to biodiversity-related - physical or transition - shocks. We apply it to the security portfolio held by French financial institutions at the end of 2019. Employing the ENCORE database, we assess physical risks by examining how the firms that issued the securities in the portfolio depend on ecosystem services to produce. Our results indicate that they significantly depend on water-related ecosystem services and that 42% of the value of securities held by French financial institutions were issued by firms highly or very highly dependent on at least one ecosystem service. Using the Global Biodiversity Score tool, we assess transition risks by quantifying the biodiversity footprint of the security portfolio and of the firms that issued the securities. We find that the portfolio footprint is equivalent to the loss of 130,000km2 of pristine nature and that 38.5% of the portfolio value comes from firms belonging to sectors in the top 10% of biodiversity footprints. This offers new methodological tools to address the relationship between finance and biodiversity from a financial stability perspective. [ABSTRACT FROM AUTHOR]