Saturday, 25 March 2017: 12:10
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, the 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. I seek to rehabilitate beta by splitting the atom of systematic risk. Particle physics provides a fruitful framework for evaluating the discrete components of financial risk. Quantum chromodynamics 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, I divide beta as the fundamental unit of systematic financial risk into three matching pairs of “baryonic” components:
The upside and downside of mean returns
Relative volatility (σ) and correlation (ρ) between asset-specific and market-wide returns
“Bad” cash-flow beta versus “good” discount-rate beta
The resulting econophysics of beta explains no fewer than three of the most significant anomalies and puzzles in mathematical finance:
Abnormal returns on value and small-cap stocks within the Fama-French three-factor model
The low-volatility anomaly, also known as Bowman’s paradox
The equity premium puzzle
Remarkably, this “baryonic” model of 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. Moreover, this model’s three-way analysis of systematic risk connects the mechanics of mathematical finance with phenomena usually attributed to behavioral influences on capital markets. Perceptions of risk on either side of expected returns animate many theories of behavioral economics, including generalized higher-moment capital asset pricing, prospect theory, SP/A theory, and behavioral portfolio theory. Adding consideration of volatility and correlation and of the distinct cash flow and discount rate components of systematic risk, harmonizes mathematical finance with labor markets, human capital, and macroeconomics.