The Stock Convexity Papers
Four working papers, most recent first. All four are posted on SSRN and open for anyone to read.
Predictive Convexity Score: A Longitudinal Case Study of Nike, NVIDIA, and Visa (2020 to 2026), September 2026 Update
Tracks the Predictive Convexity Score of three stocks, Nike (Tier 4), NVIDIA (Tier 1), and Visa (Tier 3), from Q4 2019 through the most recently reported quarter. This update focuses on Nike as a case study in beta and CAPM's blind spot: a beta near 1.0 implies a stock should move in line with the market, yet Nike fell roughly 77% from its 2021 peak and was removed from the S&P 100 in September 2026, while PCS flagged the deterioration seven consecutive quarters ahead of it.
Read on SSRNBeyond Beta: Stock Convexity and the Convexity Gap
The most complete version of the research to date, built on 60 years of empirical data. Extends the original crisis-based finding into a full account of why beta and CAPM misprice convex and concave stocks, and what it costs active managers who do not account for this.
Read on SSRNThe Convexity Gap: How the S&P 500 Preserves Convexity and How Active Managers Can Too
Examines why the majority of active large-cap managers underperform the S&P 500 over the long run, and argues that portfolio constraints, position limits, rebalancing mandates, and style box rules work against natural convexity rather than for it.
Read on SSRNRevenue and Earnings Growth as Predictors of Asymmetric Equity Behavior During Market Crises
The original finding. Across three major market crises since 2001, high growth stocks consistently fell less and recovered faster than the S&P 500, an asymmetry that beta cannot explain. Introduces the Predictive Convexity Score as the measure behind it.
Read on SSRNNeither Michael Milligan nor Nina Milligan, CFP®, is a registered investment adviser or holds a securities license, and nothing on this page constitutes investment advice.