Why stockholders bear disproportionate long-run consumption risk: mechanisms, slow dynamics, and equilibrium reconciliation

Malloy, Moskowitz, and Vissing-Jorgensen (2009) documented that the long-horizon covariance of stockholder consumption growth with asset returns is larger and more dispersed across assets than the corresponding covariances of aggregate or nonstockholder consumption, and that this dispersion rises with stockholder wealth: using the consumption of the wealthiest stockholders, a consumption-based pricing model matches the cross-section of average returns with a relative risk aversion near 10. The paper documents this pattern but does not explain it, explicitly identifying the underlying mechanisms, the slow multi-year consumption response to asset-price news, the historical variation of the covariances, the integration with general-equilibrium models, and the measurement of wealthy households' consumption as open problems. This problem asks for that explanation: which economic mechanisms quantitatively generate, in equilibrium, the documented facts (i)–(iii) stated in the Problem Statement. The paper's other open questions (which macroeconomic shocks drive the slow multi-quarter responses of consumption and returns, why the return-covariance pattern varies historically, how the estimates should be integrated with general-equilibrium models that jointly match the risk-free rate and long-run risks, and whether the facts survive the measurement limitations of household survey data) are relevant context for assessing any proposed mechanism rather than additional required deliverables. No established mechanism is known in the literature; the problem remains open.

Background

In the consumption capital asset pricing model (CCAPM), an asset's expected excess return is determined by the covariance of its payoff with the marginal utility of consumption: assets that pay badly when consumption is low must offer compensation, and the coefficient of relative risk aversion $\gamma$ scales that compensation. With standard power utility, empirical tests using aggregate per-capita consumption imply implausibly large $\gamma$ (often above 100) because aggregate consumption growth is smooth and its covariances with returns are small and nearly identical across assets — this is the equity premium puzzle.

Two broad responses shaped the literature. The first changes preferences: recursive preferences of the Epstein–Zin type separate $\gamma$ from the elasticity of intertemporal substitution (EIS), the sensitivity of consumption growth to expected returns; with such preferences and a preference for early resolution of uncertainty, Bansal and Yaron (2004) showed that persistent movements in expected consumption growth and in its volatility ("long-run risks") command sizeable premia. The second changes whose consumption prices assets: only a minority of US households hold stocks, so equity is priced by stockholders' marginal utility. Mankiw and Zeldes (1991) showed stockholder consumption growth covaries more with equity returns than nonstockholder consumption; Vissing-Jorgensen (2002) and Brav, Constantinides, and Geczy (2002) found that using stockholder consumption improves consumption-based pricing; Constantinides and Duffie (1996) provided the theoretical foundation showing that incomplete markets and countercyclical idiosyncratic risk can rationalize high premia with moderate risk aversion. Parker and Julliard (2005) showed that measuring risk by covariance with consumption growth accumulated over long future horizons ("ultimate consumption risk") improves the pricing of the Fama–French size and value portfolios — portfolios of US stocks sorted by firm market capitalization and book-to-market equity.

Malloy, Moskowitz, and Vissing-Jorgensen (2009) combined these strands. Using the Consumer Expenditure Survey (CEX), the US quarterly household survey that is the main source of micro-level consumption data, they grouped households into stockholders (holders of stocks or mutual funds), nonstockholders, and top stockholders (the wealthiest stockholder group), constructed group-level consumption growth accumulated over horizons $S = 1, 2, 4, 8, 12, 16, 20, 24$ quarters (the baseline long-run measure being 16-quarter consumption growth discounted at a 5% annual rate), and estimated long-horizon covariances with returns and Euler-equation pricing models by generalized method of moments (GMM), a standard econometric estimator for moment conditions. Their findings: long-run stockholder consumption risk captures cross-sectional variation in average returns far better than aggregate or nonstockholder consumption; covariance dispersion across assets (assessed by F-tests on the joint equality of the first-stage covariances across the 25 Fama–French portfolios) is much larger for stockholders, permitting a risk aversion around 10 (rather than implausibly larger values) to match premia for the wealthiest stockholders across the 25 Fama–French portfolios, the market, bond portfolios, and the whole cross-section of stocks; and the choice of EIS has little effect on the cross-sectional $\gamma$ estimates. Because the CEX sample (January 1982–November 2004) is short and noisy for long-horizon covariance estimation, they also built consumption-growth factor (CGF) mimicking portfolios — traded portfolios whose returns mimic group-level stockholder consumption growth — to extend the sample (the resulting CGF series run from July 1926 to November 2004) and sharpen inference.

The paper concludes by stating that the pattern is documented but not explained, and identifies the following open questions and caveats: (1) the economic mechanism explaining why stockholders, especially the wealthiest, bear disproportionately more long-run aggregate consumption risk — candidate explanations discussed in the source and the surrounding literature being preference heterogeneity and selection into stockholding (the source's conclusion highlights preference heterogeneity combined with fixed costs of stock-market participation as one step toward an equilibrium explanation), differences in labor or entrepreneurial income exposure, tax and transfer systems that reallocate risk, and equilibrium asset-market mechanisms that shift bond risk onto stockholders; (2) why consumption responds slowly, over multi-year horizons, to asset-price news, and which macroeconomic shocks (for example, persistent technology shocks, after which consumption and production peak at 3-to-4-year horizons) generate the multi-quarter peak responses observed in both consumption and returns; (3) why covariances between returns and macro variables appear larger in the earlier historical sample (1926–1951) than in the later sample; (4) how the long-run patterns emerge as an equilibrium outcome, including how the cross-sectional estimates should be integrated with general-equilibrium models that jointly match riskless-rate behavior and long-run risks; and (5) as a caveat on its own evidence, whether the facts survive measurement limitations of the CEX, including possible underreporting of indirect equity holdings in pension plans and limited representation of the very wealthy.

Problem Statement

Explain, rather than merely document, the stockholder long-run consumption-risk evidence of Malloy, Moskowitz, and Vissing-Jorgensen (2009). Identify and quantitatively establish which economic mechanism or combination of mechanisms generates, in equilibrium, the documented facts that (i) the long-horizon covariances of stockholder consumption growth with asset returns — consumption growth accumulated over horizons $S = 1, 2, 4, 8, 12, 16, 20, 24$ quarters (baseline: 16-quarter discounted consumption growth at a 5% annual discount rate), estimated from the CEX over January 1982–November 2004 against returns on the 25 Fama–French size/book-to-market portfolios, the market portfolio, bond portfolios, and the individual-stock cross-section, with cross-asset dispersion assessed by F-tests on the joint equality of the covariances across the 25 portfolios — are larger and more dispersed than the corresponding covariances of aggregate or nonstockholder consumption, with the dispersion rising in stockholder wealth so that top-stockholder consumption matches observed premia at a relative risk aversion around 10; (ii) stockholder consumption responds slowly, over multi-year horizons, to news in asset returns, with the full response arriving at roughly 3-to-4-year horizons, about the same horizon over which consumption and production peak after technology shocks; and (iii) covariances of returns with the constructed consumption-growth-factor (CGF) mimicking portfolios, which extend the group-level series to July 1926–November 2004, are larger and more dispersed across the 25 Fama–French portfolios in the earlier, pre-war (1926–1951) sample than in the later sample.

The source's conclusion frames the open target as determining why stockholders, in equilibrium, end up taking on more of this aggregate long-run risk, and understanding how these long-run patterns emerge as an equilibrium outcome. As one step in that direction it points to preference heterogeneity combined with fixed costs of stock-market participation; the surrounding literature suggests further candidate channels, including differences in labor-income and entrepreneurial-income exposure, tax-and-transfer systems that reallocate risk across households, and equilibrium asset-market mechanisms that shift bond risk onto stockholders. No candidate list is exclusive: the question is which mechanism or combination of mechanisms quantitatively reproduces facts (i)–(iii).

The paper states its remaining directions as independent suggestions for further work, not as conditions a proposed explanation must satisfy, beyond reproducing facts (i)–(iii): why consumption growth responds slowly to asset-price news and which macroeconomic shocks drive the multi-quarter responses of consumption and returns; why return–macro covariances appear larger in the earlier pre-war sample; and the integration of the long-run patterns with general-equilibrium models that jointly match riskless-rate behavior and long-run risks. The paper also notes, as a caveat on its own evidence, that the facts may be affected by measurement limitations of the CEX, including possible underreporting of indirect equity holdings in pension plans and limited representation of the very wealthy; the authors were unable to address this issue and suggest their results may be conservative under a cleaner separation of stockholders and nonstockholders. These directions and caveats are relevant context for assessing any proposed mechanism, while the open target is the equilibrium mechanism explanation of facts (i)–(iii) itself.

References

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