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This lecture covers the foundations of financial economics, focusing on investing in an uncertain world through mean-variance portfolio choice. It discusses valuation under uncertainty, mathematical properties, historical performance of asset classes, and the mean-variance efficient frontier. The lecture also explores optimal mean-variance portfolio choice, efficient frontiers with different asset combinations, and the impact of risk-aversion coefficients. Additionally, it delves into diversification benefits, the distinction between minimum-variance and mean-variance efficient portfolios, and the mathematical characterization of the general case with multiple risky assets. The presentation concludes with the concept of two-fund separation in portfolio optimization.