An Incomplete Multi-Currency Equilibrium Model with Heterogeneous Time Preferences and Subjective Beliefs

For global multi-asset fund managers, reflecting their macroeconomic views in the prediction of expected interest rates across countries, exchange rates, and equity prices in a manner consistent with economic theory is challenging. The existing literature has yet to provide an established multi-currency model that is flexible enough to incorporate such views into the prediction of future asset price dynamics. To address this problem, this paper proposes a novel multi-currency incomplete market model in which agents in each country have logarithmic utility but differ in their time references and subjective beliefs, within a market equilibrium framework, namely, supply and demand equilibrium. With only a few exogenous inputs, such as each country’s output process and agents’ preference parameters, the model endogenously determines equilibrium interest rates, exchange rates, and stock prices, along with optimal consumption and portfolios. Thus, the model enables us to (i) flexibly incorporate cross-country differences in investors’ time preferences and macroeconomic outlooks, and (ii) examine how these differences affect equilibrium interest rates and asset prices, including stock prices and exchange rates. Moreover, by applying the particle filtering method within a state-space framework based on the two-country, two-currency version of the model to Japanese and U.S. market data (equity index futures, short-term interest rates, and the exchange rate), the model not only fits the observed dynamics of equity indices, short rates, and the exchange rate, but also effectively estimates the dynamics of home-country biases and latent economic factors, which can be utilized in making investment decisions in asset management practice.