This chapter analyzes the consistency between the standard asset pricing model and actual return data from an asset allocation perspective. Modern portfolio theory such as Capital Asset Pricing Model (CAPM) implies that it is optimal for all investors to hold a portfolio of risky assets with the same composition as the market portfolio. Therefore, most general investment advice recommends buying mutual funds or exchange-traded funds (ETFs) that tracks market indices as a first step. However, there is always noise and parameter uncertainty in the information about expected returns and covariance investors use when making investment decisions. Honda models the optimizing behavior of investors in the presence of such uncertainty by introducing the concept of ‘ambiguity aversion’ and examines its validity using Japanese and US stock market data. His approach has been relatively successful with US data; however, analyses using Japanese data have been somewhat disappointing. Honda’s chapter also serves as an excellent introduction to the vast amount of academic research on two important topics, “model uncertainty” in finance and “ambiguity aversion” in microeconomic theory. In his comments to Honda, “Challenges and Solutions for the Estimation of the Ambiguity Aversion,” Hideyuki Takamizawa offers suggestions for improving the fit to Japanese data, as well as other potential applications of the concept of ambiguity aversion.