Jake Xia teaches this session of MIT's 18.642, Topics in Mathematics with Applications in Finance, on how portfolios actually get built beyond textbook modern portfolio theory. He walks through sizing, objectives, and constraints using a class portfolio exercise, then maps cash, bonds, stocks, private equity, and venture capital on a return-risk grid. A long stretch covers endowment management: perpetual time horizons, 5% spending rules, 3% inflation assumptions, and the resulting 8% nominal return target, plus the endowment model's reliance on external managers and benchmarks. The lecture closes with two-asset portfolio theory, working through portfolio weights, correlation cases, and the efficient frontier. Along the way Xia flags limitations of mean-variance optimization and points toward alternatives like gain-loss ratios, crowding behavior, and power law return distributions, treating markets as shaped by large agents such as governments and big funds rather than idealized efficient participants.