2017 | Book

# Econophysics and Capital Asset Pricing

## Splitting the Atom of Systematic Risk

Author: Dr. James Ming Chen

Publisher: Springer International Publishing

Book Series: Quantitative Perspectives on Behavioral Economics and Finance

2017 | Book

Author: Dr. James Ming Chen

Publisher: Springer International Publishing

Book Series: Quantitative Perspectives on Behavioral Economics and Finance

This book rehabilitates beta as a definition of systemic risk by using particle physics to evaluate discrete components of financial risk. Much of the frustration with beta stems from the failure to disaggregate its discrete components; conventional beta is often treated as if it were "atomic" in the original Greek sense: uncut and indivisible. By analogy to the Standard Model of particle physics theory's three generations of matter and the three-way interaction of quarks, Chen divides beta as the fundamental unit of systemic financial risk into three matching pairs of "baryonic" components. The resulting econophysics of beta explains no fewer than three of the most significant anomalies and puzzles in mathematical finance. Moreover, the model's three-way analysis of systemic risk connects the mechanics of mathematical finance with phenomena usually attributed to behavioral influences on capital markets. 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.

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Abstract

The conventional capital asset pricing model remains the dominant paradigm among financial practitioners, if not among scholars of finance. The preferred academic approach—Fama and French’s three-factor model—assigns greater weight to book-to-market ratios and firm size as factors affecting the cross-section of stock returns. In order to rehabilitate the CAPM and its near cousin, the efficient market hypothesis, this book proposes to bifurcate beta (the CAPM’s basic measure of systematic risk) along three vectors: either side of mean returns, relative volatility versus correlation, and cash-flow versus discount-rate effects. These three divisions in beta correspond to the three generations of quarks and leptons in the Standard Model of particle physics.

Abstract

Traditional measures of volatility, variance, and beta assign equal weight to the upside and downside components of these measures of systematic risk. Such symmetry reflects neither actual market conditions nor investors’ behavioral reactions to abnormal financial events. Single-sided versions of all of these measures better reflect the state of markets and their likely interpretation by investors on either side of mean returns. As a bonus, single-sided volatility is related to the traditional double-sided volatility through the Pythagorean theorem. That relationship facilitates the application of trigonometry to mathematical finance.

Abstract

Beta is a composite measure. It reports not only the ratio of asset-specific volatility to market-wide volatility, but also the correlation between asset-specific and market-wide prices or returns. Closer examination of these components of beta, especially in conjunction with single-sided definitions of semideviation, semivariance, and semicovariance, reveals parameters indicating changes in relative volatility and correlation tightening. The behavioral implications of these competing components of beta correspond to the psychological distinction between fast, System 1 instinct and slow, System 2 thought.

Abstract

This chapter takes a closer look at the volatility-specific component of beta. Some financial practitioners have advocated the use of relative volatility, standing alone, as a risk measure. This decision would eliminate the correlation component and its insights into the diversification value of financial portfolios. For its part, volatility is asymmetrical and prone to clustering. It tends to be greater on the downside of mean returns. Far from following a random walk, volatility is serially autocorrelated. Periods of high volatility tend to cluster together, as do periods of relative calm. Different approaches to the measurement of volatility, from time-series analysis to options-based implied measures and the Yilmaz-Diebold model of volatility transmission, reveal feedback and spillover effects.

Abstract

A direct relationship between risk and return—in the sense that return should vary positively and proportionately to volatility—is so essential that this should be designated as the first law of finance. Investors otherwise would never be induced to commit capital to risky assets. In reality, low-volatility stocks offer abnormally high returns relative to their riskier counterparts. By undermining conventional assumptions about the relationship between risk and return, the low-volatility anomaly arguably represents the most significant challenge to mathematical finance. The value premium in the Fama and French’s three-factor model is arguably a special case of the low-volatility premium, attributable to the costly reversibility of physical investments and human capital during recessions and economic downturns. The literature of strategic management has identified a similar effect, called Bowman’s paradox. That discipline identifies managerial culture, especially corporate and social responsibility, as a possible explanation for abnormal returns on low-volatility stocks.

Abstract

Financial theory and practice place great emphasis on volatility, in its absolute sense and in relative terms as the ratio between asset-specific and market-wide volatility. But correlation appears to be the true driver of the risk-return relationship. “In falling markets, the only thing that rises is correlation,” Correlation tightening poses a unique threat to risk-return relationships and to portfolios built upon them. Meta-analysis of emerging market data reveals that the risk associated with this asset class subsists almost entirely in its vulnerability to the tightening of its correlation with developed markets during times of crisis. Although some sources dispute this characterization, correlation risk is priced into risky securities and quite likely explains the low-volatility anomaly. Correlation risk also appears to be closely related to liquidity risk and to theories of contagion.

Abstract

Conventional asset pricing models assume, rather unrealistically, that investors live for exactly a single time span, during which they will confront no potential changes in consumption preferences, liquidity needs, or tolerance for risk. Robert Merton’s intertemporal capital asset pricing model fills this theoretical gap. Among other applications, the intertemporal CAPM accommodates consumption smoothing across different life stages. The desire to preserve future investment or consumption opportunities may justify holding assets that counterbalance potential decline in more rewarding but riskier components of a portfolio.

Abstract

On average, equities historically deliver returns that exceed those on safe assets by several percentages every year. Over time and in nearly all developed economies, the equity risk premium is considerable. Yet puzzles persist. Despite that premium, why do so many potential investors avoid holding stocks? Stock market nonparticipation is a major contributory to social insecurity, particularly in the USA, where many aging households are financially unprepared for retirement. The equity premium puzzle consists of two parts. First, why are risk-free rates so low? Second, why do equities command a premium beyond the level that any realistic model of risk aversion would predict? The answer lies in habit formation over the course of the economic life-cycle. Unlike other components of aggregate wealth, human capital cannot be readily traded. Returns on human capital in the form of wages are peculiarly vulnerable to job loss during recessions and economic downturns. Maintaining an ever more comfortable lifestyle—catching up with the Joneses, so to speak—exposes households to macroeconomic risks that conventional asset pricing models do not fully reflect.

Abstract

Beta as the basic unit of systematic risk may be further bifurcated into distinct components reflecting firm-specific changes in cash flow and changes in the economy-wide discount rate. By analogy to cholesterol, these components may be regarded as “bad” and “good.” Whereas “good” beta resulting from unexpectedly negative discount-rate news may be mitigated by later macroeconomic developments, “bad” beta resulting from shocks to cash flow dictates an enduring reduction in the valuation of a firm. The disproportionately high contribution of cash-flow effects to value firms’ betas (relative to growth stock betas) explains the premium on value stocks and provides a related solution to the low-volatility anomaly.

Abstract

Although beta’s cash-flow and discount-rate components are conceptually distinct, the empirical boundary between cash-flow beta and discount-rate beta is far from clear-cut. To facilitate the interpretation of these components of systematic risk, this chapter introduces the distinction between epistemic risk and aleatory uncertainty. This conceptual dichotomy originates in economic work by Frank Knight and John Maynard Keynes and reflects principles of uncertainty in physics. It prominently in evaluations of cash-flow and discount-rate information. A special case of uncertainty, information uncertainty, is readily adapted for the interpretation of economic data that has ambiguous implications for individual firms, capital markets, and the broader economy. Although information uncertainty is compatible with behavioral interpretations of investor reactions to ambiguity, it is equally consistent with theories of rational learning.

Abstract

Relative to discount-rate effects, the cash-flow component of beta should dominate risk-based models of asset pricing. In principle, even weakly efficient markets should assimilate all publicly available information affecting a firm’s cash flow. But two forms of short-term price continuation persist: post-earnings announcement drift (PEAD) and momentum. Although both forms of drift have invited explanations rooted in behavioral finance, PEAD in particular is consistent with rational learning as a slow but thoroughly reasoned response to the ambiguous interpretation of corporate earnings and accruals. The durability of price continuation anomalies indicates the presence of liquidity constraints and other limits to arbitrage. Moreover, the possibility that earnings information may shed light on economy-wide discount rates as well as firm-specific cash-flow effects adds to the uncertainty surrounding this sort of information, which in turn reveals itself through the drift of prices from the levels that strict efficiency would otherwise predict.

Abstract

The stock market fares poorly as an economic indicator. The reverse relationship—the impact of macroeconomic events on stock returns—often proves no less ambiguous. Closer examination of discount-rate effects, however, reveals the circumstances under which bonds decouple from stocks in a reversal of their usual positive correlation. Bad news for the broader economy often lifts stock prices, but not invariably. Negative macroeconomic news, in addition to signaling potential monetary intervention to lower interest rates, also conveys bad times ahead for corporate cash-flow and broader uncertainty about economic conditions. The potential impact of macroeconomic information on asset prices is often so contested that bonds and stocks move more upon the release of scheduled macroeconomic news than they respond to the substantive content of those announcements. Ultimately, uncertainty over a potential investor’s ability to maintain the ratio of consumption to aggregate wealth, especially labor income drawn from vulnerable and irreplaceable human capital, elevates investment risk in ways that can be understood only in light of macroeconomic risk over the course of the individual life-cycle as well as the broader economy’s business cycle.

Abstract

This book has invoked physics as a guide to constructing models of economic behavior that obey basic rules at different scales. Even cursory examination of stock–bond correlations and the impact of macroeconomic news on capital markets suggests that econophysics hinges on perhaps no more than two sets of rules. First, the binary state of the economy matters. Whether a capital market is on the positive or negative side of mean returns matters. So do investor sentiment and the current phase of the business cycle. Second, comovement is the other great force in finance. Correlation indicates comovement between an asset and the broader market. For its part, the discount-rate component of beta addresses the vulnerability of stock values to macroeconomic forces far beyond strictly idiosyncratic cash-flow effects. The structural unity of economic dynamics at the individual, household, firm-specific, market-wide, and macroeconomic levels is reminiscent of scientific efforts to reconcile the Standard Model of particle physics with levels general relativity, through string theory or some other explanatory framework that can harmonize chromodynamics with cosmology.