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Robust Portfolio Rules and Asset Pricing

Review of Financial Studies 2004 17(4), 951-983
I present a new approach to the dynamic portfolio and consumption problem of an investor who worries about model uncertainty (in addition to market risk) and seeks robust decisions along the lines of Anderson, Hansen, and Sargent (2002). In accordance with max-min expected utility, a robust investor insures against some endogenous worst case. I first show that robustness dramatically decreases the demand for equities and is observationally equivalent to recursive preferences when removing wealth effects. Unlike standard recursive preferences, however, robustness leads to environment-specific “effective” risk aversion. As an extension, I present a closed-form solution for the portfolio problem of a robust Duffie-Epstein-Zin investor. Finally, robustness increases the equilibrium equity premium and lowers the risk-free rate. Reasonable parameters generate a 4% to 6% equity premium.

Robust Portfolio Rules and Asset Pricing

Review of Financial Studies 2004 17(4), 951-983
I present a new approach to the dynamic portfolio and consumption problem of an investor who worries about model uncertainty (in addition to market risk) and seeks robust decisions along the lines of Anderson, Hansen, and Sargent (2002). In accordance with max-min expected utility, a robust investor insures against some endogenous worst case. I first show that robustness dramatically decreases the demand for equities and is observationally equivalent to recursive preferences when removing wealth effects. Unlike standard recursive preferences, however, robustness leads to environment-specific "effective" risk aversion. As an extension, I present a closed-form solution for the portfolio problem of a robust Duffie-Epstein-Zin investor. Finally, robustness increases the equilibrium equity premium and lowers the risk-free rate. Reasonable parameters generate a 4% to 6% equity premium.

The Price of Correlation Risk: Evidence from Equity Options

Journal of Finance 2009 64(3), 1377-1406
We study whether exposure to marketwide correlation shocks affects expected option returns, using data on S&P100 index options, options on all components, and stock returns. We find evidence of priced correlation risk based on prices of index and individual variance risk. A trading strategy exploiting priced correlation risk generates a high alpha and is attractive for CRRA investors without frictions. Correlation risk exposure explains the cross-section of index and individual option returns well. The correlation risk premium cannot be exploited with realistic trading frictions, providing a limits-to-arbitrage interpretation of our finding of a high price of correlation risk.

Consumption and Portfolio Choice over the Life Cycle

Review of Financial Studies 2005 18(2), 491-533
This article solves a realistically calibrated life cycle model of consumption and portfolio choice with non-tradable labor income and borrowing constraints. Since labor income substitutes for riskless asset holdings, the optimal share invested in equities is roughly decreasing over life. We compute a measure of the importance of human capital for investment behavior. We find that ignoring labor income generates large utility costs, while the cost of ignoring only its risk is an order of magnitude smaller, except when we allow for a disastrous labor income shock. Moreover, we study the implications of introducing endogenous borrowing constraints in this incomplete-markets setting.

Robustness and dynamic sentiment

Journal of Financial Economics 2025 163, 103953
Errors in survey expectations display waves of pessimism and optimism. This paper develops a novel theoretical framework of time-varying beliefs capturing this fact. In our model, dynamic beliefs arise endogenously due to agents’ attitude towards alternative models. Decision-maker’s distorted beliefs generate countercyclical risk aversion, procyclical portfolio weights, and countercyclical equilibrium asset returns. A calibrated version of our model is shown to jointly match salient features in survey data and equity markets.

Consumption and Portfolio Choice over the Life Cycle

Review of Financial Studies 2005 18(2), 491-533
This article solves a realistically calibrated life cycle model of consumption and portfolio choice with non-tradable labor income and borrowing constraints. Since labor income substitutes for riskless asset holdings, the optimal share invested in equities is roughly decreasing over life. We compute a measure of the importance of human capital for investment behavior. We find that ignoring labor income generates large utility costs, while the cost of ignoring only its risk is an order of magnitude smaller, except when we allow for a disastrous labor income shock. Moreover, we study the implications of introducing endogenous borrowing constraints in this incomplete-markets setting.

The Price of Correlation Risk: Evidence from Equity Options

Journal of Finance 2009 64(3), 1377-1406 open access
ABSTRACT We study whether exposure to marketwide correlation shocks affects expected option returns, using data on S&P100 index options, options on all components, and stock returns. We find evidence of priced correlation risk based on prices of index and individual variance risk. A trading strategy exploiting priced correlation risk generates a high alpha and is attractive for CRRA investors without frictions. Correlation risk exposure explains the cross‐section of index and individual option returns well. The correlation risk premium cannot be exploited with realistic trading frictions, providing a limits‐to‐arbitrage interpretation of our finding of a high price of correlation risk.

Stock Market Mean Reversion and the Optimal Equity Allocation of a Long-Lived Investor

Review of Finance 2001 5(3), 269-292 open access
This paper solves numerically the intertemporal consumption and portfolio choice problem of an infinitely-lived investor who faces a time-varying equity premium. The solutions we obtain are very similar to the approximate analytical solutions of Campbell and Viceira (1999), except at the upper extreme of the state space where both the numerical consumption and portfolio rules flatten out. We also consider a constrained version of the problem in which the investor faces borrowing and short-sales restrictions. These constraints bind when the equity premium moves away from its mean in either direction, and are particularly severe for risk-tolerant investors. The constraints have substantial effects on optimal consumption, but much more modest effects on optimal portfolio choice in the region of the state space where they are not binding. JEL classification: G12.

Model Ambiguity versus Model Misspecification in Dynamic Portfolio Choice

Journal of Finance 2026 81(3), 1741-1795 open access
ABSTRACT We study aversion to model ambiguity and misspecification in dynamic portfolio choice. Risk‐averse investors (relative risk aversion ) fear return persistence, while risk‐tolerant investors () fear mean reversion, when confronting model misspecification concerns of identically and independently distributed (IID) returns. The intuition is that risk‐averse investors, who want to hedge intertemporally, endogenously fear return persistence, which precludes hedging. A log investor is myopic and unaffected by model misspecification, therefore only worrying about model ambiguity. Our model can generate belief scarring, nonparticipation in equity markets, and extrapolative return expectations. Extending beyond IID returns, we study model misspecification for a mean‐reverting Sharpe ratio.