Another Look at the (Ir)Relevance of Long-Run Risks for Equity Risk Premia

This paper derives a three-factor consumption-based asset pricing model that extends the baseline Consumption CAPM by adding two long-run risk factors – the innovation in expected future consumption growth (“consumption growth news”) and the innovation in the expected future variance of consumption growth (“consumption variance news”) – and then asks whether those factors are priced in a reasonably demanding cross-section of U.S. equity risk premia. Because the model is derived from recursive (Epstein-Zin) preferences, its three factor risk prices map directly onto the coefficient of relative risk aversion and the elasticity of intertemporal substitution, so the cross-sectional estimates can be read as estimates of the preference parameters the long-run risks literature calibrates. Using quarterly data from 1963:III to 2018:IV and decile portfolios sorted on seven prominent CAPM anomalies – book-to-market, asset growth, price momentum, accruals, net stock issues, operating profitability, and residual return variance – plus an augmented test that prices 43 excess returns simultaneously, the author finds the model is largely rejected on both statistical and economic grounds: in no single estimation does it deliver small pricing errors together with economically plausible and statistically significant risk prices, the cross-sectional explanatory ratio is negative in most cases, and the estimated elasticity of intertemporal substitution is near zero, insignificant, or negative rather than above one. The conclusion the author draws is that long-run consumption risks do not rescue the Consumption CAPM, which he presents as a major challenge for the voluminous long-run risks literature; the finding is stated as an empirical rejection within this model class, this VAR-based factor construction, and this test-asset set, not as a general claim about all consumption-based models.

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Another Look at the (Ir)Relevance of Long-Run Risks for Equity Risk Premia