Inconsistency of the Capital Asset Pricing Model in a Multi‐Currency Environment

The capital asset pricing model (CAPM) is a widely adopted model in asset pricing theory and portfolio construction because of its intuitive nature. One of its main conclusions is that there exists a global market portfolio that each rational investor should hold in proportion to the risk-free asset. In this paper, we demonstrate theoretically and through an example that the CAPM cannot hold in a multi-currency environment. This is because it produces different market risk premia depending on the investor's base currency unless each exchange rate is uncorrelated with the asset prices in the portfolio.