Lecture 13: Portfolio Management

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MIT 18.642 Topics in Mathematics with Applications in Finance, Fall 2024 Instructor: Jake Xia View the complete course: https://ocw.mit.edu/courses/18-642-topics-in-mathematics-with-applications-in-finance-fall-2024 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP601Q2jo-J_3raNCMMs6Jves This lecture provides a comprehensive overview of portfolio management, focusing on the practical aspects of asset allocation, risk measurement, and investment sizing beyond traditional modern portfolio theory, highlighting its limitations and proposing improved approaches such as gain-loss ratios. It also explores behavioral finance concepts like crowding behavior and power law distributions, emphasizing the importance of dynamic rebalancing and understanding market influences from powerful agents such as governments and large funds. 00:19 Portfolio construction as sizing, objectives, and lecture roadmap 02:54 Class portfolio exercise: objective, horizon, loss tolerance, edge, diversification, sizing 07:52 From market selection to data, signals, models, strategies, allocation, and risk 09:03 Student portfolios: options, VIX, 70/30 bonds-stocks, ETFs, cash, and the post-crypto shift 11:47 Cash, bonds, stocks, indices, private equity, and venture capital on a return-risk map 14:31 Portfolio constraints: return target, volatility, ethics, liquidity, loss tolerance, inflation, alpha 18:12 Asset-liability matching, time horizon, career risk, and personal versus institutional p

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