📈 economics

The Hierarchy of Factors: How Regime Variables Reset Market Pricing—Evidence from Exhaustive Testing Across 15 Global Equity Markets for a Factor Hierarchy Theory

This paper proposes and empirically validates "Factor Hierarchy Theory" across 15 global equity markets, demonstrating that interest rate spreads act as regime variables that determine the applicable pricing rules, thereby revealing that traditional asset pricing models are merely special cases of a unified field equation rather than parallel factors.

Original authors: Shuiping Tang

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Shuiping Tang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the entire stock market as a giant, chaotic video game where millions of players are trying to guess the score of every single asset. For the last forty years, the "rulebook" for this game has been the same: everyone assumed that all the clues (factors) used to predict prices were sitting on the same level, like ingredients in a smoothie. You'd throw in "value," "momentum," and "size," blend them up, and see which one made the smoothie taste best.

But this paper argues that the rulebook is wrong. It's not a smoothie; it's a video game with two distinct layers.

The Two Layers: Rule-Makers vs. Rule-Executors

The paper proposes a new idea called Factor Hierarchy Theory. It says there are two types of factors, and they don't play by the same rules:

The Rule-Makers (Regime Factors): These are the "game masters." They don't directly tell you the price of a stock. Instead, they decide which set of rules is currently active. Think of them like the weather. If it's sunny, you wear shorts; if it's raining, you wear a raincoat. The weather doesn't be the outfit, but it decides which outfit makes sense. In this paper, the "weather" is the interest rate spread (specifically, the difference between Chinese and U.S. interest rates).
The Rule-Executors (Market Factors): These are the players following the rules. They are the usual suspects like "valuation" (is the stock cheap?) or "momentum" (is the stock going up?). They only work after the Rule-Maker has set the stage.

The Big Mistake: The old theories treated the "weather" (interest rates) and the "outfit" (stock valuation) as if they were just two ingredients in the same smoothie. The paper says this is a massive blind spot. You can't compare the importance of the weather to the importance of the raincoat; one sets the context, and the other acts within it.

The "Dual-Anchor" Switch

The paper uses data from 15 major global equity markets (including the U.S., China, Japan, Germany, and India) spanning from 2002 to 2026 to prove this.

Here's the crazy part they found: The "Rule-Maker" isn't just one country. It's a switch between two anchors: the U.S. and China.

When the interest rate spread is positive (U.S. rates are higher), the U.S. "anchor" takes control, and U.S. rules apply.
When the spread is negative (China's rates are higher), the Chinese "anchor" wakes up and takes control.
The switch happens right around zero.

The paper tested this by looking at 13 out of 15 markets and found that Chinese interest rate signals appeared in the top combinations of factors for almost every single market. Even in the U.S. stock market (S&P 500, NASDAQ, Dow Jones), the top factors were often Chinese interest rate spreads.

How They Proved It (The "Exclusion" Game)

The authors didn't just guess; they played a game of "eliminate the wrong answers" using 12 different testing methods. Here is what they ruled out:

They ruled out that factors are "parallel." If factors were just ingredients in a smoothie, mixing them wouldn't change how they work. But the paper found that when you mix the "Rule-Maker" (interest rates) with the "Rule-Executor" (stock valuation), the result is nearly twice as powerful as just adding them together. The "interaction" is the key.
They ruled out that interest rates are just a "thermometer." A thermometer just measures the temperature; it doesn't cause the heat. The paper used Granger causality tests (a fancy way of checking who moves first) and found that the interest rate spreads often change before the stock market moves. They are the engine, not the thermometer.
They ruled out that old theories are "wrong." This is the most important part. The paper says the old theories (like Fama-French) aren't broken; they are just special cases. They work perfectly fine when the "weather" is stable and the switch doesn't flip. But when the switch flips (the spread changes sign), the old rules stop working, and the new hierarchy takes over.

The Three Weird Switching Modes

The paper discovered that this "switch" doesn't look the same everywhere. It found three distinct modes:

Perfect Symmetric Switch (U.S. Stocks): When the switch flips, the U.S. rules take over completely, and the Chinese rules vanish, and vice versa.
China-Factor Dormancy (A-Shares): When the switch flips to the "negative" side, the Chinese rules go to sleep, but the U.S. rules don't wake up. The market is in a weird "vacuum" state where neither anchor is fully in charge.
Dual-Anchor Coexistence (Nikkei 225): In Japan, both the U.S. and Chinese rules are active at the same time, fighting it out.

The Bottom Line

The paper concludes that for the last forty years, researchers have been looking for the answer in the wrong place. They were looking for a "magic ingredient" that directly prices stocks. But the real secret is structure.

The "Rule-Maker" (interest rate spreads) doesn't price the stock directly. Instead, it tunes the volume of the other factors. It's like a DJ who doesn't play the song but decides which genre of music is playing. When the DJ switches from Hip-Hop to Rock, the same instruments (stocks) sound completely different.

The paper is very confident in this because they tested it against every possible alternative they could think of, including checking if Japanese or German interest rates were the real cause (they weren't, mostly). They found that the "Rule-Maker" logic holds up across 13 out of 15 markets, with the Chinese internal spread appearing in the top models for almost all of them.

So, the next time you hear about a stock factor, ask yourself: Is this the Rule-Maker deciding the game, or just a Rule-Executor playing within the game? The paper says we've been confusing the two for decades.

Technical Summary: The Hierarchy of Factors and Regime Variables in Global Equity Pricing

Problem Statement
The prevailing literature in asset pricing operates under a "forty-year blind spot": the presumption that all pricing factors (e.g., market, size, value, momentum) are parallel entities inserted into a single linear equation. This framework assumes that factor exposure coefficients are stable and that the primary task of research is to compare the magnitude or significance of these coefficients. The paper argues this presumption is fundamentally flawed. It posits that asset pricing factors are not parallel but hierarchical. Specifically, "regime factors" (macro variables like interest rate spreads) do not directly price assets; rather, they determine "which set of rules currently applies." Traditional "market factors" (valuation, momentum) then execute pricing under the rules set by the regime. By placing rule-makers and rule-executors on the same plane, the literature has failed to detect the true pricing mechanism of macro variables, which operate through interaction effects rather than direct linear contributions.

Methodology
The paper employs a rigorous "method of exclusion" across 15 major global equity markets (including Mainland China, the US, Europe, and Asia) using daily data from 2002 to 2026. The research design is built upon a deductive framework derived from the institutional fact that central banks independently set interest rates under a fiat currency system. This leads to a "Unified Field Equation" where a regime variable ( $S_t$ ) determines the weight of pricing functions.

The empirical strategy utilizes a seven-tier progressive testing framework to systematically eliminate alternative hypotheses:

Exhaustive Testing: Traversing all possible single, two, and three-factor combinations (22 candidate factors) to identify optimal models under a Variance Inflation Factor (VIF) < 5 constraint.
Regime-Split Testing: Estimating coefficients separately for positive and negative spread regimes.
Chow Tests: Testing for structural breaks in pricing relationships when the regime variable crosses a critical threshold (zero spread).
Interaction Effect Testing: Regressing returns against regime factors, market factors, and their interaction terms to test if regime factors modulate market factor exposures.
Granger Causality Tests: Determining if regime factors temporally lead market factors (acting as "engines" rather than "thermometers").
Hierarchical Variance Decomposition: Comparing the incremental explanatory power ( $R^2$ ) of direct effects versus interaction effects.
Robustness and Exclusion: Including permutation tests, Newey-West corrections, LASSO regularization, and alternative hypothesis exclusion (controlling for Japanese and German spreads) to ensure findings are not artifacts of specific parameters or noise.

Key Contributions

Factor Hierarchy Theory: The paper proposes a new theoretical framework dividing factors into two tiers: Regime Factors (e.g., China-US yield spreads, internal yield curve slopes) which set the rules, and Market Factors (e.g., valuation percentiles, momentum) which execute pricing. Regime factors indirectly price assets by modulating the exposure coefficients of market factors.
The Unified Field Equation: The paper establishes an axiom system ( $P_t = \Sigma w_i(S_t) \times f_i(X_t^i) + \epsilon_t$ ) that unifies institutional interfaces, dual-anchor switching, and factor hierarchy. It demonstrates that the global asset pricing equation possesses a unified field structure necessitated by the fiat currency system.
Dimensional Reduction of Old Theories: The paper does not overturn existing theories but reduces them to special cases (degenerate forms) of the unified field equation under specific boundary conditions:
- Fama-French: Equivalent to the unified field equation when the number of anchors ( $n$ ) is 1 and the regime variable is constant.
- ICAPM: Equivalent when only one economy's macro conditions enter the equation.
- Portfolio Theory: Equivalent when correlations are assumed stable (i.e., the regime variable is constant).
Discovery of Asymmetric Switching Modes: The research identifies three distinct modes of anchor switching in equity markets:
- Perfect Symmetric Switch: Observed in US markets, where the dominant anchor switches cleanly based on the spread sign.
- China-Factor Dormancy: Observed in A-shares, where the Chinese factor becomes significant in positive spread regimes but enters a "vacuum" state in negative regimes without a US factor takeover.
- Dual-Anchor Coexistence: Observed in the Nikkei 225, where both anchors remain significant across regimes.

Empirical Results

Exhaustive Testing: China-specific factors (internal spreads or the China-US spread) appear in the top 3 optimal factor combinations for 13 out of 15 markets. In 9 markets, the optimal factor is a China factor. The coefficient sign of China's internal spread ( $CN\_slope\_30\_10$ ) remains positive in 79% to 100% of rolling 5-year windows across all markets, rejecting the hypothesis that these are random noise.
Interaction Effects: The interaction between regime factors and market factors is significantly non-zero. Crucially, the incremental $R^2$ from interaction terms is nearly twice that of direct effects (1.78x on average). This confirms that regime factors function by modulating market factor exposures rather than directly explaining returns.
Structural Breaks: Chow tests confirm structural breaks in pricing relationships for 13 out of 15 markets when the spread crosses zero, refuting the assumption of stable factor coefficients.
Causality: Granger causality tests show that regime factors lead market factors in significant proportions (e.g., 38.9% for Nikkei 225), supporting the "engine" hypothesis.
Robustness: The significance of China factors persists even when controlling for Japanese and German spreads, eliminating the alternative hypothesis that China factors are merely proxies for global interest rates.

Significance and Claims
The paper claims to illuminate a methodological blind spot that has persisted for forty years: the confusion of rule-makers with rule-executors. Its significance lies not in discovering a new pricing factor, but in proposing a new theory regarding the organization of factors. By demonstrating that macro factors are hierarchical and operate through interaction effects, the paper explains why macro variables have remained "silent" in traditional linear models.

The work completes a research program (spanning five papers from Tang, 2026a–2026d) that moves from the discovery of the "dual-anchor phenomenon" in commodities and currencies to the construction of a meta-theoretical framework for global asset pricing. The paper asserts that the driving force of scientific progress here is not the discovery of new facts, but the posing of a question that had been overlooked: "What is the relationship among factors?" rather than "Which factor prices assets?" The findings suggest that the old theories are not wrong, but partial, holding true only within specific boundaries where the regime variable is stable.