Baryonic Beta Dynamics: Splitting the Atom of Systematic Risk

76 Pages Posted: 1 Sep 2016 Last revised: 19 Sep 2016

James Ming Chen

Michigan State University - College of Law

Date Written: August 31, 2016


Despite the rise of multi-factor models emphasizing value, firm size, and momentum, beta remains the primary measure of risk in asset pricing. Designed to define systematic risk, net of idiosyncratic risk that can be neutralized through diversification, beta combines a measure of volatility with a measure of correlation.

Much of the frustration with beta stems from the failure to disaggregate beta’s discrete components. Conventional beta is often treated as if it were “atomic” in the original Greek sense: uncut and indivisible.

This article rehabilitates beta by splitting the atom of systematic risk. Particle physics provides a fruitful framework for evaluating discrete components of financial risk. Quantum chromodynamics (QCD) focuses on six flavors of quarks in three matched pairs: up/down, charm/strange, and top/bottom. Baryons are subatomic particles consisting of three quarks. They include protons and neutrons, which account for most of the mass of the visible universe.

By analogy to the Standard Model’s three generations of matter and the three-way interaction of quarks under QCD, I divide beta as the fundamental unit of systematic financial risk into three matching pairs of “baryonic” components:

1. Up and down on either side of mean returns
2. Relative volatility (σ) and correlation (ρ) between asset-specific and market-wide returns
3. “Bad” cash-flow beta versus “good” discount-rate beta

The resulting econophysics of beta explains three of the most significant anomalies and puzzles in mathematical finance:

1. Abnormal returns on value and small-cap stocks within the Fama-French three-factor model
2. The low-volatility anomaly, also known as Bowman’s paradox
3. The equity premium puzzle

Remarkably, baryonic beta provides persuasive explanations for all of these anomalies strictly on the basis of fuller mathematical specification of a two-moment capital asset pricing model.

Suggested Citation

Chen, James Ming, Baryonic Beta Dynamics: Splitting the Atom of Systematic Risk (August 31, 2016). Available at SSRN: or

James Ming Chen (Contact Author)

Michigan State University - College of Law ( email )

318 Law College Building
East Lansing, MI 48824-1300
United States

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