Lecture 13: Portfolio Management

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-to... YouTube Playlist:    • MIT 18.642 Topics in Mathematics with Appl...   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 portfolios 21:21 Endowment math: perpetual horizon, 5% spending, 3% inflation, and the 8% nominal target 23:29 Endowment strategy menu: bonds, credit, hedge funds, CTAs, stat arb, multi-PM, PE, real assets 25:40 Endowment model mechanics: external managers, active management, benchmarks, manager selection 27:18 Classic portfolio construction problem and why managers reduce assets into risk factors 30:43 Two-asset portfolio theory: weights, variance, correlation cases, and the efficient frontier 35:54 Risk-free assets, capital allocation line, Sharpe ratio, alpha, beta, leverage, and risk parity 40:40 Rebalancing example: diversification only pays if you keep the weights aligned with your assumptions 45:19 Limits of Modern Portfolio Theory: fragile assumptions, artificial constraints, volatility as bad risk 48:50 Gain-loss ratio: expected gain, expected loss, Kelly-style sizing, and downside risk budgeting 52:35 Investment game: using daily gains and losses to evaluate portfolio quality 55:43 Capital market assumptions and why finance is harder than physics: adaptive human behavior 57:12 Crowding behavior: flocking, the Millennium Bridge, bubbles, crashes, panic, and greed 1:00:03 Feedback-loop market model: actions, observations, amplification, reactivity, noise, synchronization 1:05:01 Power laws: wealth, venture returns, city size, networks, and rich-get-richer feedback 1:11:40 Final summary: sizing, rebalancing, expected loss, unreliable assumptions, and super agents 1:14:12 Q&A: taxes, expected loss versus worst-case loss, stop-losses, and hedge fund incentive structure 1:19:19 Investment game wrap-up and possible course directions: trading, research process, or fund-building License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.