[We develop a new solution method for a broad class of discrete-time dynamic portfolio choice problems. The method efficiently approximates conditional expectations of the value function by using (i) a decomposition of the state variables into a component observable by the investor and a stochastic deviation; and (ii) a Taylor expansion of the value function. We illustrate the accuracy of the method in handling several realistic features of portfolio choice problems such as intermediate consumption, multiple assets, multiple state variables, portfolio constraints, non-time-separable preferences, and nonredundant endogenous state variables. We finally use the method to solve a realistic large-scale life-cycle portfolio choice and consumption problem with predictable expected returns and recursive preferences.]

[We evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the sample-based mean-variance strategy and its extensions to outperform the 1/N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets. This suggests that there are still many "miles to go" before the gains promised by optimal portfolio choice can actually be realized out of sample.]

[This paper examines the relationship between default probability and stock returns. Using the Expected Default Frequency (EDF) of Moody' s KMV, we document that higher default probabilities are not associated with higher expected stock returns. Within a model of bargaining between equity holders and debt holders in default, we show that the relationship between default probability and equity return is (i) upward sloping for firms where shareholders can extract little benefit from renegotiation (low "shareholder advantage") and (ii) humped and downward sloping for firms with high shareholder advantage. This dichotomy implies that distressed firms with stronger shareholder advantage should exhibit lower expected returns in the cross section. Our empirical evidence, based on several proxies for shareholder advantage, is consistent with the model's predictions.]

[We develop a model for an investor with multiple priors and aversion to ambiguity. We characterize the multiple priors by a "confidence interval" around the estimated expected returns and we model ambiguity aversion via a minimization over the priors. Our model has several attractive features: (1) it has a solid axiomatic foundation; (2) it is flexible enough to allow for different degrees of uncertainty about expected returns for various subsets of assets and also about the return-generating model; and (3) it delivers closed-form expressions for the optimal portfolio. Our empirical analysis suggests that, compared with portfolios from classical and Bayesian models, ambiguity-averse portfolios are more stable over time and deliver a higher out-of sample Sharpe ratio.]

We study a standard real-option problem in which sequential decisions are made through voting by a group of members with heterogeneous beliefs. We show that, when facing both investment and abandonment timing decisions, the group behavior cannot be replicated by that of a representative “median” member. As a result, members’ disagreement generates inertia—the group delays investment relative to a single-agent case—and underinvestment—the group rejects projects that are supported by a majority of members, acting in autarky. These coordination frictions hold in groups of any size, for general voting protocols, and are exacerbated by belief polarization.

We develop a new solution method for a broad class of discrete-time dynamic portfolio choice problems. The method efficiently approximates conditional expectations of the value function by using (i) a decomposition of the state variables into a component observable by the investor and a stochastic deviation; and (ii) a Taylor expansion of the value function. We illustrate the accuracy of the method in handling several realistic features of portfolio choice problems such as intermediate consumption, multiple assets, multiple state variables, portfolio constraints, non-time-separable preferences, and nonredundant endogenous state variables. We finally use the method to solve a realistic large-scale life-cycle portfolio choice and consumption problem with predictable expected returns and recursive preferences.

This paper studies whether house prices reflect belief differences about climate change. We show that in an equilibrium model of housing choice in which agents derive utility from ownership in a neighborhood of similar agents, prices exhibit different elasticities to climate risk. We use comprehensive transaction data to relate prices to inundation projections of individual homes and measures of beliefs about climate change. We find that houses projected to be underwater in believer neighborhoods sell at a discount compared to houses in denier neighborhoods. Our results suggest that house prices reflect heterogeneity in beliefs about long-run climate change risks.

We evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1-N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1-N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the sample-based mean-variance strategy and its extensions to outperform the 1-N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets. This suggests that there are still many "miles to go" before the gains promised by optimal portfolio choice can actually be realized out of sample. The Author 2007. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: [email protected], Oxford University Press.

This paper examines the relationship between default probability and stock returns. Using the Expected Default Frequency (EDF) of Moody's KMV, we document that higher default probabilities are not associated with higher expected stock returns. Within a model of bargaining between equity holders and debt holders in default, we show that the relationship between default probability and equity return is (i) upward sloping for firms where shareholders can extract little benefit from renegotiation (low “shareholder advantage”) and (ii) humped and downward sloping for firms with high shareholder advantage. This dichotomy implies that distressed firms with stronger shareholder advantage should exhibit lower expected returns in the cross section. Our empirical evidence, based on several proxies for shareholder advantage, is consistent with the model's predictions.

We develop a model for an investor with multiple priors and aversion to ambiguity. We characterize the multiple priors by a "confidence interval" around the estimated expected returns and we model ambiguity aversion via a minimization over the priors. Our model has several attractive features: (1) it has a solid axiomatic foundation; (2) it is flexible enough to allow for different degrees of uncertainty about expected returns for various subsets of assets and also about the return-generating model; and (3) it delivers closed-form expressions for the optimal portfolio. Our empirical analysis suggests that, compared with portfolios from classical and Bayesian models, ambiguity-averse portfolios are more stable over time and deliver a higher out-of sample Sharpe ratio.