Stock Convexity
For the past 56 years, we have been told that stock prices rise and fall on a straight line. They do not. Some stocks rise faster than they fall, convex. Some fall faster than they rise, concave. Across every major crisis since 2001, high convexity stocks recovered faster than the index, and no existing model predicted it, until now.
Wall Street is built on Beta and CAPM, both derived from historical stock prices. The Predictive Convexity Score (PCS) is built on the two numbers that actually run a business, revenue and earnings. In empirical tests, PCS explains the crisis behavior that Beta and CAPM cannot. In those same tests, portfolios built on PCS have outperformed the index.
Revenue and Earnings Predict What Price History Cannot
Revenue and earnings growth actually describe whether a company is winning or losing. Beta and CAPM only look backward at a stock's own price history relative to the market.
During a market crash, selling is indiscriminate. There is no logic or efficiency. Everyone gets hit regardless of business quality. But the recovery isn't indiscriminate; capital flows back selectively to companies that kept revenue and earnings growing through the downturn. That pattern holds not only across 18 major market events, but during normal markets as well.
Beta Flagged the Wrong Stock
Nike's beta sat near 1.0, unremarkable by any conventional measure. Its Predictive Convexity Score (PCS) told a different story, collapsing from Tier 1 to Tier 4 as the stock fell 38%. NVIDIA's beta sits at 2.17, more than twice the market's sensitivity, the number that is supposed to mean risk. Its PCS peaked at 61.77, the highest ever recorded in this dataset, and it has held Tier 1 for six straight quarters since. Beta called the ordinary stock safe and the extraordinary one dangerous. It had both backward.
Positive Convexity (Convex)
Strong revenue and earnings growth bend a stock's return curve in the investor's favor. These stocks recover faster on the way back. A portfolio that ignores this is not actually diversified.
PCS > 2.0, Tier 1 & Tier 2 stocksNegative Convexity (Concave)
Declining revenue and earnings bend the curve against the investor. These stocks recover more slowly, if they recover at all. Concentrate on these names, and diversification does not protect you; it just spreads the damage evenly.
PCS < 0, Tier 4 stocksTwo Interconnected Tools
Measure and quantify equity convexity.
Stock Convexity™
The foundational discovery. Stock Convexity measures how nonlinear and asymmetric a stock's return behavior really is relative to the market, the exact thing beta and CAPM assume away.
Predictive Convexity Score™
The measurement tool. PCS scores every stock on trailing revenue growth and adjusted earnings growth together, then sorts the results into four tiers of convexity.
Full-Window Performance
Every product built on PCS, measured against its benchmark over the same seven-year window, 2019-08-01 to 2026-07-09. This is what the disclosed construction would have produced over that window, capital appreciation only, no dividend reinvestment, a data availability constraint, not a choice.
Hypothetical, backtested results. No client account held these positions. Price returns only: no dividends, fees, or transaction costs are modeled. See full disclosures below.
| Product | Cumulative | CAGR | Sharpe | Max Drawdown |
|---|---|---|---|---|
| PCS 500 | +188.63% | +16.51% | 0.627 | -32.67% |
| PCS ESG 500 | +194.52% | +16.85% | 0.636 | -32.30% |
| PCS 100 | +344.17% | +23.98% | 0.801 | -35.58% |
| PCS ARE | +335.21% | +23.61% | 0.779 | -35.63% |
| SPY (benchmark) | +154.83% | +14.43% | 0.552 | -34.10% |
| QQQ, actual ETF (PCS 100 benchmark) | +280.37% | +21.24% | 0.727 | -35.62% |
Over the past 5 and 10 years, 88.96% and 85.59% of active large-cap funds underperformed the S&P 500, respectively. The table above shows what happens when you measure the difference rather than guessing at it: all four PCS portfolios are ahead of their benchmark. The tier is not a label. It is the one piece of information that beta was never built to give you.
Source: SPIVA U.S. Scorecard, Year-End 2025, S&P Dow Jones Indices, data as of Dec. 31, 2025, All Large-Cap Funds vs. S&P 500, 5-year and 10-year periods.
Modern Portfolio Theory Has Blind Spots
Stock Convexity weakens beta
Beta assumes a linear, symmetric relationship between a stock and the market. Stock Convexity demonstrates that this relationship is nonlinear and asymmetric. A stock with positive convexity outperforms in up markets by more than it underperforms in down markets. Beta flattens it out.
Diversification without considering Stock Convexity is incomplete
Modern Portfolio Theory holds that diversification reduces risk because correlations are less than one. But if individual stocks have different convexity profiles, a portfolio of stocks with negative convexity does not diversify away the concavity; it concentrates it. Thirty stocks, all with negative SC, still underperform asymmetrically in downturns.
PCS captures what factor models compress
Companies that grow revenue and earnings together are rewarded more than the sum of the two alone. Linear factor models, including Fama-French and the q-factor model, can't capture that by construction. PCS does.
Beta's size measures sensitivity, not quality.
Beta's sign shows which way a stock tends to move with the market, but its size, its absolute value, only measures how much. It says nothing about whether that sensitivity comes from a business getting stronger or falling apart. NVIDIA's beta sits at 2.17, more than twice the market's sensitivity. That same sensitivity produced the best compounding run in this dataset. A high beta can mean extraordinary, or it can mean dangerous; beta alone cannot tell you which.
Every factor still comes from price.
Modern Portfolio Theory has been extended many times, with more factors, more dimensions. However, every one of them, beta, size, value, momentum, is still derived from historical price and return data. None of them start from what the business actually produces. PCS does.
A beta-driven rule cuts both ways and gets both wrong. It trims Tier 1 and 2 names for being volatile when that volatility is compounding growth, and it holds or adds to Tier 3 and 4 names for being calm when that calm is often just a business running out of momentum.
Two Case Studies
Nike, Visa, and NVIDIA across 27 quarters. Three stocks, three growth profiles, one framework.
Milligan, M. & Milligan, N. (2026). "Revenue and Earnings Growth as Predictors of Asymmetric Equity Behavior During Market Crises." SSRN Working Paper. Available at: papers.ssrn.com/abstract=6463861
JEL Codes: G10, G11, G12, G14
All products deliver ticker and tier classification only, never portfolio weights, position sizing, or trade recommendations. Neither Michael Milligan nor Nina Milligan, CFP®, is a registered investment adviser or holds a securities license, and nothing on this site constitutes investment advice.
All performance shown is hypothetical and backtested, not the record of an actual managed account. No portfolio described here was actually traded with client money. Past performance does not predict future results.