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 with 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. This finding has significant implications, including questioning the starting point of the Black & Litterman (1992) model, which is widely used in asset allocation and assumes that the CAPM equilibrium provides a neutral starting point for estimating expected risk premia. However, this assumption may not hold in a multi-currency environment, potentially rendering the model less effective