"This paper proposes a new tractable approach to solving asset allocation problems in situations with a large number of risky assets which pose problems for standard numerical approaches. Investor preferences are assumed to be defined over moments of the wealth distribution such as its skewness and kurtosis. Time-variations in investment opportunities are represented by a flexible regime switching process. We develop analytical methods that only require solving a small set of difference equations and can be applied even in the presence of large numbers of risky assets. We find evidence of two distinct bull and bear states in the joint distribution of equity returns in five major regions with correlations that are much higher in the bear state. Ignoring regimes, an unhedged US investor's optimal portfolio is strongly diversified internationally. The presence of regimes in the return distribution leads to a large increase in the investor's optimal holdings of US stocks as does the introduction of predictability in returns from a short US interest rate. Our paper therefore offers a rational explanation of the strong home bias observed in US investors' asset allocation, based on regime switching, skew and kurtosis preferences and predictability from the short US interest rate"--Federal Reserve Bank of St. Louis web site.