Aggregation, Liquidity, and Asset Prices with Incomplete Markets

This manuscript builds a tractable theory of asset pricing and household consumption behavior starting from the two-account incomplete-markets model of Kaplan and Violante (2014, 2022) – designed to match realistic, heterogeneous household-level consumption and asset-holding patterns, including large fractions of “wealthy hand-to-mouth” households – and extends it with aggregate shocks in a way that still permits a closed-form solution. The key move is to assume idiosyncratic risk speeds up whenever the representative-agent valuation ratio for aggregate output is low (a stylized version of the empirically documented countercyclical skewness of labor-income shocks); under this assumption, the aggregate value of each asset type equals its value in the corresponding frictionless representative-agent economy multiplied by a constant, asset-specific “liquidity factor” that is invariant to the process and history of aggregate shocks and can be recovered from the model’s steady state alone. Liquid assets carry a larger liquidity factor than illiquid ones because they additionally insure households against running out of funds before their next trading opportunity – a mechanism the authors show reproduces the “wealthy hand-to-mouth” pattern even for households with substantial wealth. Translated into expected returns, this produces liquidity premia that move inversely with valuation ratios, while risk premia and other second-moment properties of asset prices are unchanged from the representative-agent benchmark. Calibrating the model’s few sufficient-statistic moments to U.S. data, the authors argue the evidence points to small average risk premia and large, volatile liquidity premia: the model can quantitatively account for the gap between the high risk-free rate implied by low-EIS representative-agent models and the low return on Treasury bills, for why aggregate consumption Euler equations fit well for a zero-beta stock portfolio but poorly for Treasury bills, and for most of the predictability of excess stock returns.

The Zero-Beta Interest Rate

This paper proposes and measures the zero-beta rate — the expected return on a portfolio of stocks with zero market beta, constructed to be orthogonal to the SDF innovations spanned by standard factors — as the correct intertemporal price of consumption, and argues that safe interest rates (Treasury bill yields) are not. Using 130 stock portfolios (81 sorted on combinations of beta, size, value, investment, and profitability; 49 industry portfolios) and GMM estimation with five macro instruments (T-bill yield, inflation, term spread, excess bond premium, and the U6 unemployment rate) over January 1973 to December 2020, the paper estimates the zero-beta rate to average 8.3% per year in real terms with a standard deviation of 9.3%, producing a spread of roughly 7.6% per year over the expected real Treasury bill yield. The paper then shows that this zero-beta rate fits the aggregate consumption Euler equation remarkably well: the macro instruments that best predict the real return of the zero-beta portfolio are nearly proportional to those that predict real consumption growth, a non-mechanical result that survives when the sample is restricted to exclude COVID. Statistical Euler equation tests (Stock-Wright [2000] weak-instrument-robust GMM) reject the Euler equation for all IES values when applied to the Treasury bill, fail to reject it for any IES value when applied to the volatile market return (weak identification), but fail to reject it only for IES below 0.5 (risk aversion above 2) when applied to the zero-beta rate — providing identification from the intermediate predictability of the zero-beta portfolio. Monetary policy shock regressions using Romer-Romer and Nakamura-Steinsson shocks further show that an unexpected monetary tightening raises the real Treasury bill yield but lowers the real zero-beta rate, consistent with the Euler equation’s prediction that the intertemporal price should fall when expected consumption growth falls. Finally, the high level and volatility of the zero-beta rate implies that the entire variation of the price-dividend ratio of a consumption claim can be attributed to variation in the zero-beta rate without requiring time-varying equity risk premia — resolving the equity premium puzzle and Campbell’s [1991] excess volatility puzzle simultaneously, at the cost of an unexplained convenience spread on safe assets.

Pablo Kurlat | Macro Paper Warehouse

Aggregation, Liquidity, and Asset Prices with Incomplete Markets

The Zero-Beta Interest Rate