Short-Horizon Duesenberry Equilibrium

Battle Count: 50

The paper provides a novel theoretical framework for asset pricing that decomposes equity premia into consumption risk and impatience risk components, offering a new perspective on the equity premium puzzle. The volatility decomposition (ϑt = σct - σ−∂ηt) and the identification of the market price of risk with aggregate wealth volatility have direct implications for understanding risk premia. However, the paper is primarily theoretical and does not provide actionable trading signals, specific portfolio construction algorithms, or backtested strategies. The calibration in Table 1 and the interest rate decomposition (Equation 50) could inform macro-level asset allocation decisions. The framework's emphasis on aggregate market behavior rather than individual stocks limits direct applicability to stock-level quantitative trading. The future work on borrowing premia and term structure could yield more directly applicable results.

The paper requires deep expertise in stochastic calculus (Itô processes, semimartingales, Brownian flows of diffeomorphisms), general equilibrium theory, and mathematical finance. The population-flow aggregation framework with cocycle properties, the short-horizon rolling optimization, and the equilibrium characterization/existence proofs involve advanced mathematical machinery. Implementing the full framework would require solving stochastic PDEs, constructing Brownian flows, performing population-weighted aggregation of semimartingales, and verifying smooth market conditions. Even the empirical calibration requires careful estimation of aggregate wealth volatility, consumption risk premia, and impatience risk components. The theoretical nature and mathematical sophistication make this extremely challenging to implement computationally.

The paper provides complete mathematical proofs, explicit formulas for equilibrium characterization (Theorem 3), and calibration using publicly available historical data (Mehra 2003, Jorda et al. 2019, Campbell 1999). However, the theoretical framework is highly abstract with complex stochastic calculus machinery (Brownian flows, semimartingale aggregation, cocycle properties). No code or computational implementation is provided. The empirical calibration in Table 1 uses standard published estimates, making the quantitative comparison reproducible, but the full equilibrium construction requires significant mathematical expertise.