MIT 18.642 Topics in Mathematics with Applications in Finance, Fall 2024
Instructor: Jake Xia
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
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