A new method for building optimal investment portfolios using particle filtering was developed. By estimating expected returns and volatilities of assets through a Monte Carlo filter, the method significantly enhances the performance of mean-variance portfolios. State variables related to expected returns and asymmetric volatilities were introduced to predict asset returns accurately. The estimated portfolios outperformed other common portfolio strategies like risk parity and minimum variance portfolios. The method also considers transaction costs and constraints on short selling, allowing for a diverse portfolio including Japanese and U.S. REITs, bonds, and equities. Evaluation based on returns, Sharpe ratios, Sortino ratios, and maximum drawdowns confirmed the effectiveness of the approach.