Macro economic innovations and asset alphas show significant mutual causation.

Olivia London

2023-12-03 11:33:00 Sun ET

Macro innovations and asset alphas show significant mutual causation.

April 2023

 

This brief article draws from the recent research publication:

Hung, M.W. and Yeh, A.J.Y. (2023). Dynamic stock market alphas help predict macroeconomic innovations. Macroeconomic Dynamics, April 2023.

 

Abstract

We extract dynamic conditional factor premiums from the Fama-French factor model and find that most anomalies disappear after one accounts for time variation in these premiums. Vector autoregression evidence shows that mutual causation between dynamic conditional alphas and macroeconomic surprises serves as a core qualifying condition for fundamental factor selection. This economic insight is an incremental step toward drawing a distinction between rational risk and behavioral mispricing models. To the extent that dynamic conditional alphas can reveal the marginal investor’s fundamental news and expectations about the cross-section of average asset returns, our economic insight helps enrich macroeconomic asset return prediction.

 

Summary

Fama and French’s seminal contributions shed skeptical light on the empirical performance of the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965). The subsequent search for a better asset return model has been a hot pursuit for many financial economists (Fama and French, 1993, 1995, 1996, 1998, 2006b, 2008, 2015; Hou, Xue, and Zhang, 2014). Financial economists engage in the relentless debate over whether dramatic movements in market valuation such as the Global Financial Crisis reflect a “rational” fair-value price correction or a lack of compensation for risk. The debate has left many financial economists at a time-worn impasse (Fama and French, 2004). Empiricists continue to discover new asset anomalies (e.g. Titman, Wei, and Xie (2004); Fama and French (2006b, 2008); Cooper, Gulen, and Schill (2008); Li, Livdan, and Zhang (2009); Novy-Marx (2013)).

 

Kozak, Nagel, and Santosh’s (2017; 2018) recent studies show that many recent empirical horse races cannot draw a distinction between both rational and behavioral theories of average return evolution. Kozak et al (2018) report that a factor model with a small number of statistical principal-components (PCs) performs as well as the prior factor models (e.g. Fama and French (1993); Hou, Xue, and Zhang (2014); Fama and French (2015); Novy-Marx and Velikov (2016); Barillas and Shanken (2018)). For typical portfolios, these few factors dominate the covariance matrix of returns. In the absence of near-arbitrage investment opportunities, these factor models include only a few dominant factors, which can be fundamental characteristics such as size and book-to-market or purely statistical PCs. Because these models exhibit few conceptual links to investor beliefs and preferences, the q-theoretic factor models are as much “behavioral models” as the models are “rational models” (cf. Berk, Green, and Naik (1999); Johnson (2002); Gomes, Kogan, and Zhang (2003); Liu, Whited, and Zhang (2011); Liu and Zhang (2008); Lin, and Zhang (2013); Liu and Zhang (2014)). In a similar vein, the prior tests of characteristics-versus- covariances inform us little of whether and how behavioral barriers such as investor sentiment and overconfidence affect asset returns (e.g. Daniel and Titman (1997); Brennan, Chordia, and Subramanyam (1998); Davis, Fama, and, French (2000); Stambaugh and Yuan (2017)). Overall, it seems futile to implement these horseraces to assess the complex convolution of both investor sentiment and rationality in most asset return tests.

 

In the current study, we carry out an alternative approach to tackling this important issue in finance. We first extract all dynamic conditional factor premiums from the Fama-French (2015) model and then find that most anomalies disappear after one accounts for time variation in these premiums. Granger-causality tests suggest new mutual causation between dynamic conditional alpha spreads and macroeconomic innovations. This mutual causation therefore serves as a core qualifying condition for factor selection with sound economic motivation. In the current study, our economic insight is an incremental step toward drawing a distinction between both rational risk and behavioral models in response to Kozak, Nagel, and Santosh (2017; 2018). To the extent that macroeconomic surprises manifest in the form of dynamic conditional alphas, this causation can reveal the marginal investor’s fundamental news and expectations about the cross-section of average returns. Hence, our evidence contributes to macroeconomic asset return prediction.

 

Kozak, Nagel, and Santosh (2018) point out that the presence of arbitrageurs will connect the covariance structure to the cross-section of average returns. Insofar as this cross-section at least partially reflects investor sentiments such as overconfidence, salience of recent experience, and other cognitive biases, behavioral mispricing factors can help price assets with reasonable bounds on the Sharpe ratios. In this context, these behavioral factors load reasonable premiums to correctly price assets. However, these behavioral factors and premiums “will not necessarily covary with aggregate macroeconomic risks, as the [fundamental factors] would…” (cf. Kozak, Nagel, and Santosh (2017, 2018); Daniel et al (2017); Daniel, Hirshleifer, and Sun (2017)). In fact, Kozak, Nagel, and Santosh (2018) suggest several alternative routes to design asset return tests that are more informative about investor beliefs, behaviors, and preferences:

 

“To devise tests that are more informative about investor beliefs, researchers must exploit additional predictions of a factor model that relate returns to other data such as macroeconomic variables, information on portfolio holdings, or data on investor beliefs” (cf. Kozak, Nagel, and Santosh (2018): Section III.C first paragraph with our own bold italic emphasis).

 

In the current study, we pick the low-hanging fruit through an empirical analysis of mutual causation between macroeconomic innovations and dynamic conditional factor premiums. To the extent that macroeconomic innovations manifest in the form of dynamic conditional alphas and betas, the conditional moments of returns and factors convey information about the cross-section of average returns. This causation can thus serve as a core qualifying condition for valid and sound factor selection in macroeconomic asset return prediction. In particular, our evidence lends credence to the ubiquitous use of Fama-French (2015) factors that can reveal the marginal investor’s response to fundamental expectations about the cross-section of average returns. At the same time, however, our econometric tests support Fama and French’s (1996, 2008, 2015, 2016) perennial reluctance to consider the Carhart (1997) momentum factor in their factor model. We connect our dynamic conditional factor model results to recent advances in the intertemporal CAPM context (Merton, 1973; Campbell, 1993; Campbell and Vuolteenaho, 2004; Campbell et al, 2017). On balance, our current study represents an incremental step toward better deciphering a distinction between the rational risk paradigm and the behavioral mispricing conjecture.

 

We acknowledge the fact that some recent studies replicate a broader basket of anomalies (cf. Fama and French (2016); Harvey et al (2016); Harvey (2017); Hou, Xue, and Zhang (2017); Chordia, Goyal, and Saretto (2017)). Our primary and ultimate goal is not to compete with these prominent authors with more empirical replication. Instead, we establish new Granger causation between dynamic conditional alpha spreads and macroeconomic innovations as a core qualifying condition for fundamental factor selection in macro asset return prediction. This condition adds sound economic rigor and intuition to macroeconomic asset return prediction. So this condition contributes to our fresh insight that bilateral causation between macroeconomic surprises and dynamic conditional alpha spreads reflects the marginal investor’s fundamental news and macro expectations about the cross-section of average returns. This fresh insight can help demystify the empirical puzzle that Kozak, Nagel, and Santosh (2018) suggest in their recent research.

 

Macroeconomic innovations move in tandem with dynamic conditional factor premiums that provide unique economic insights into the implicit nexus between state-dependent alphas and betas across fundamental factors. This nexus reveals rich information about the conditional factor covariance matrix in contrast to the unconditional counterpart, the latter of which omits informative restrictions across the conditional moments of both asset returns and factors from the empirical assessment of goodness-of-fit (Nagel and Singleton, 2011). Not only do dynamic conditional alpha spreads change over time, but these alpha spreads also exhibit a robust causal relation with macroeconomic surprises in a standard vector autoregressive system (Sims, 1980). Macroeconomic innovations Granger-cause most dynamic conditional alpha spreads except for momentum and partial value. Granger causation runs in a bilateral direction such that dynamic conditional alpha spreads both lead and convey material information about macro innovations (cf. our subsequent explanatory text on Section 4 and Tables 6 to 9).

 

This evidence enriches our key interpretation of the intertemporal CAPM that macroeconomic gyrations both lead and vary with the conditional expectations of terminal payoffs in the marginal investor’s intertemporal selection (Merton, 1973; Campbell, 1993; Fama, 1996; Campbell and Vuolteenaho, 2004; Campbell et al, 2017). Macro innovations manifest in the form of dynamic conditional alpha spreads that persist as abnormal returns. Therefore, mutual Granger causation between macro surprises and dynamic conditional alpha spreads becomes an informative piece of evidence that we can apply to help resolve some long prevalent asset anomalies.

 

With this theoretical justification of the intertemporal CAPM, we contribute to the empirical design of a workhorse asset return model by qualifying specific fundamental factors as useful and reasonable state variables. Our core qualifying condition is equivalent to mutual causation between macro surprises and alpha spreads that reflect changes in the conditional expectations of structural shifts in terminal wealth for the marginal investor. To the extent that many residual macroeconomic fluctuations lead dynamic conditional alpha spreads and vice versa, this causal relation becomes a necessary condition for valid and effective factor selection in empirical asset return research. For this pivotal purpose, sound theoretical justification of fundamental factors with respect to causal macroeconomic innovations should precede pure empirical motivation in macroeconomic asset return prediction (Harvey, 2017; Harvey, Liu, and Zhu, 2016).

 

Our current study also contributes to the conditional multifactor model literature. It is well-known that a dynamic conditional mean-variance efficient return need not unconditionally price the static portfolios with constant weights (cf. Cochrane (2005: 140)). Specifically, if a portfolio return is on the conditional mean-variance efficient frontier, this return may or may not land on the unconditional mean-variance efficient frontier. Cochrane (2005: 168) describes this issue in a succinct statement: “Whether the [multifactor model] can be rescued by more careful treatment of conditioning information remains an empirical question”. In the current study, we attempt to fill this theoretical void by conditioning the main prediction of average returns on Fama-French (2015) factors up to each time increment. Subsequent work substantiates our economic insight that reconciles a reasonable array of anomalies within the dynamic conditional factor model.

 

Our unique use of fresh econometric tools serves as another empirical contribution to the asset return literature. Both the conditional specification test and recursive multivariate filter help extract dynamic conditional factor premiums that covary with macro surprises substantially over time. Conditional on the expectation of zero prior prediction error, the recursive multivariate filter updates all of the dynamic alpha-beta factor premiums up to each time increment in real-time. This important econometric innovation extends and generalizes the Fama-French multiple-regression approach and therefore can become part of the standard toolkit for subsequent asset pricing analysis. This application reconciles a baseline array of anomalies with the central theme of “dynamic” multifactor mean-variance efficiency (cf. dynamic MMVE in Fama (1996) and Merton (1973)). Further, the concomitant tests provide evidence in support of this notion. As a result, dynamic MMVE can serve as an informative benchmark for the empirical assessment of pervasive anomalies or portfolio strategies that generate persistent abnormal returns in a static context. Overall, our dynamic conditional factor model thus has key implications for equity cost estimation, risk management, fund performance evaluation, and corporate event assessment.

 

Applying the recursive multivariate filter adds value to the notion of dynamic multifactor mean variance efficiency (MMVE) in the intertemporal asset pricing context (cf. Merton (1973); Campbell (1993); Fama (1996); Campbell and Vuolteenaho (2004); Campbell et al (2017)). In this context, investors care about not only their terminal wealth but also state variables such as human capital, labor income, consumption, and hedging investment opportunities that covary with their terminal wealth (Fama and French, 2004). For instance, several studies suggest that inter-industry heterogeneity in both human capital and labor mobility can help explain the cross-section of average returns (Eiling, 2013; Donangelo, 2014). An international factor model with Epstein-Zin (1989) recursive investor preferences explains the high correlation of stock market indices despite the low correlation of fundamental factors (Colacito and Croce, 2011). A twin-country model can demystify both the carry trade puzzle and low correlation between exchange rate movements and cross-country differences in total consumption in the intertemporal context (Colacito and Croce, 2013). Hence, the Fama-French (2015) factors serve as valid and relevant empirical hedging instruments for the marginal investor’s intertemporal selection between his or her current and future investment opportunities. Our current work suggests that the exclusion of Fama-French factors leads the econometrician to reject the null hypothesis of a correct factor model specification (Fama and French, 2016). Specifically, we find mutual Granger causation between macroeconomic surprises and dynamic conditional alphas for the Fama-French (2015) fundamental factors, except for momentum and partial value. This latter falsification provides empirical justification of Fama and French’s (1993, 1996, 2015, 2016) perennial reluctance to encompass Carhart (1997) momentum as a new fundamental factor in the rational risk paradigm. All of this evidence thus bolsters our intertemporal CAPM interpretation of fundamental factors for the dynamic conditional factor model.

 

To the extent that macroeconomic surprises manifest in the form of dynamic conditional alphas, this causation reveals the marginal investor’s fundamental news and expectations about the cross-section of average returns. Our evidence enriches and contributes to the intertemporal CAPM interpretation of dynamic conditional factor models. In this context, macro innovations serve as fundamental news and expectations that induce cash-flow and future-risk betas as “bad betas” or negative discount-rate betas as “good betas”. In accordance with this intertemporal CAPM thesis, we expect assets with positive cash-flow shocks, future-risk spillovers, or subpar discount-rate news to yield low average returns. Conversely, we would expect other assets with negative cash-flow shocks, volatility declines, or optimistic discount-rate news to generate high average returns. Therefore, mutual causation between macroeconomic innovations and dynamic conditional alpha spreads serves as a core qualifying condition for fundamental factor selection with sound economic rigor and intuition. This economic insight is one of our main contributions to macroeconomic asset return prediction.

 

In addition to the use of a recursive multivariate filter for dynamic conditional alpha and beta estimation, the conditional specification test helps draw a crucial distinction between both the static and dynamic conditional factor models. This conditional specification test examines whether the core distance between the static and dynamic conditional estimators turns out to be significant so that there is sufficient evidence for one to reject the null hypothesis of a consistent and efficient static specification. Under the alternative hypothesis, only the dynamic conditional estimator is consistent although this more generic alternative specification may or may not be efficient in the econometric sense. In our empirical analysis of 100 decile returns on the major anomalies plus their respective 10 long-short stock portfolio strategies that focus on the extreme deciles, about 95% of the stock portfolio tilts point to the statistically reliable rejection of the null hypothesis that the static factor model is a correct specification. The key preponderance of empirical results thus supports our chosen dynamic conditional factor model in contrast to the static baseline factor model.

 

For complete details, the reader can delve into the full pre-print research article available on our AYA fintech network platform:

https://ayafintech.network/library/stock-market-alphas-help-predict-macroeconomic-innovations/

 

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