mit18 642 f24 lec13
This lecture provides a comprehensive overview of portfolio management for the MIT 18.642 course. It begins by framing portfolio construction as a decision‑making process that balances return objectives, loss tolerance, and an investor’s edge, and outlines the layers of choices from market selection to risk management. The endowment model is presented, highlighting internal vs. external managers, benchmark considerations, liquidity constraints, and the challenges of predicting manager performance. Classic two‑asset portfolio theory is derived, covering return and volatility formulas, special cases of correlation, the capital allocation line, leverage, and the critical role of periodic rebalancing. The instructor then critiques Modern Portfolio Theory, arguing that volatility and the Sharpe ratio inadequately capture risk, especially skewness, and that mean‑variance optimization suffers from instability and over‑constrained solutions. A new sizing metric based on Expected Gain (G) and Expected Loss (L) – the GL ratio – is introduced as a replacement for Sharpe, with an associated optimization problem akin to the Kelly criterion. The lecture shifts to behavioral dynamics, modeling crowd interaction through agent‑based differential equations, defining an order parameter to measure synchronization, and showing how reactive agents can generate bubbles and power‑law distributions of wealth and influence. Simulations illustrate tipping points when external forces amplify crowd reactions. The session concludes with practical takeaways, an investment game assignment, and a broader view of market and strategy categories. Throughout, the material blends theoretical derivations, empirical observations, and the instructor’s own research papers.
Topics
Foundations of Portfolio Construction – Objectives, Loss Tolerance, and Edge
Defines the core questions investors must answer: desired return, acceptable drawdown, and unique advantage, and introduces the hierarchy of decisions from market selection to sizing.
Endowment Model – Structure, Benchmarks, and Liquidity Constraints
Describes how endowments allocate capital across internal and external managers, balance absolute vs. relative returns, manage liquidity, and confront the difficulty of forecasting manager skill.
Classic Two‑Asset Portfolio Theory – Formulas, Correlation Cases, and Leverage
Derives portfolio return and variance for two assets, explores special correlation scenarios (ρ=1,0,−1), introduces the capital allocation line, Sharpe ratio, and the effect of borrowing on risk/return.
Rebalancing as the “Free Lunch” of Diversification
Shows through a numerical example how periodic rebalancing captures volatility decay and improves cumulative returns compared to a static allocation.
Limitations of Modern Portfolio Theory (MPT)
Critiques MPT on three fronts: volatility ignores skew, Sharpe inherits this flaw, and mean‑variance optimization yields unstable, overly constrained solutions.
GL Ratio – Expected Gain over Expected Loss as a New Sizing Metric
Introduces the (G‑L)/(G+L) ratio, explains its bounded range, links it to the Kelly criterion, and formulates an optimization problem to maximize portfolio GL ratio.
Agent‑Based Crowd Behavior Modeling – Synchronization Loop and Order Parameter
Presents differential equations for agent actions, external forces, and observations; defines an order parameter R(t) to quantify collective synchronization.
Power‑Law Emergence from Heterogeneous Agents
Explains why wealth, city size, and other social phenomena follow power‑law distributions, attributing it to heterogeneous agent influence and rich‑get‑richer dynamics.