Correlations between international equity market returns tend to increase in highly volatile bear markets, which has led some to doubt the benefits of international diversification. This article solves the dynamic portfolio choice problem of a U.S. investor faced with a time-varying investment opportunity set modeled using a regime-switching process which may be characterized by correlations and volatilities that increase in bad times. International diversification is still valuable with regime changes and currency hedging imparts further benefit. The costs of ignoring the regimes are small for all-equity portfolios but increase when a conditionally risk-free asset can be held. In standard international portfolio choice models such as Sercu (1980) and Solnik (1974a), agents optimally hold the world market portfolio and a series of hedge portfolios to hedge against real exchange rate risk. From the perspective of these models, investors across the world display strongly homebiased asset choices. One popular argument often heard to rationalize the “home bias puzzle” relies on the asymmetric correlation behavior of international equity returns. A number of empirical studies document that correlations between international equity returns are higher during bear markets than during bull markets. 1 If the diversification benefits from international investing are not forthcoming at the time that investors need them the most (when their home market experiences a downturn), the strong case for international investing may have to be reconsidered. Our goal is to formally evaluate this claim. To quantify the effect of these asymmetric correlations on optimal portfolio choice, we need a dynamic asset allocation model that accommodates time-varying correlations and volatilities. In the standard portfolio choice models and their empirical applications [French and Poterba (1991), Tesar and Werner (1995)], correlations

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International Asset Allocation With Regime Shifts

The authors undertake a comprehensive investigation of price and volume co-movement using daily New York Stock Exchange data from 1928 to 1987. They adjust the data to take into account well-known calendar effects and long-run trends. To describe the process, they use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: (1) positive correlation between conditional volatility and volume; (2) large price movements are followed by high volume; (3) conditioning on lagged volume substantially attenuates the "leverage" effect, and (4) after conditioning on lagged volume, there is a positive risk-return relation. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Stock Prices and Volume

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. Copyright 2005, Oxford University Press.

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Consumption and Portfolio Choice over the Life Cycle

https://www0.gsb.columbia.edu/faculty/aang/papers/corr.pdf

Asymmetric correlations of equity portfolios

We investigate the small-sample properties of three alternative generalized method of moments (GMM) estimators of asset-pricing models. The estimators that we consider include ones in which the weighting matrix is iterated to convergence and ones in which the weighting matrix is changed with each choice of the parameters. Particular attention is devoted to assessing the performance of the asymptotic theory for making inferences based directly on the deterioration of GMM criterion functions.

Finite sample properties of some alternative GMM estimators

The paper develops a discrete state space solution method for a class of nonlinear rational expectations models. The method works by using numerical quadrature rules to approximate the integral operators that arise in stochastic intertemporal models. The method is particularly useful for approximating asset pricing models and has potential applications in other problems as well. An empirical application uses the method to study the relationship between the risk premium and the conditional variability of the equity return under an ARCH endowment process. NONLINEAR DYNAMIC RATIONAL EXPECTATIONS MODELS rarely admit explicit solutions. Techniques like the method of undetermined coefficients or forward- looking expansions, which often work well for linear models, rarely provide explicit solutions for nonlinear models. The lack of explicit solutions compli- cates the tasks of analyzing the dynamic properties of such models and generat- ing simulated realizations for applied policy work and other purposes. This paper develops a discrete state-space approximation method for a specific class of nonlinear rational expectations models. The class of models is distinguished by two features: First, the solution functions for the endogenous variables are functions of at most a finite number of lags of an exogenous stationary state vector. Second, the expectational equations of the model take the form of integral equations, or more precisely, Fredholm equations of the second type. The key component of the method is a technique, based on numerical quadrature, for forming a discrete approximation to a general time series conditional density. More specifically, the technique provides a means for calibrating a Markov chain, with a discrete state space, whose probability distribution closely approximates the distribution of a given time series. The quality of the approximation can be expected to get better as the discrete state space is made sufficiently finer. The term "discrete" is used here in reference to the range space of the random variables and not to the time index; time is always discrete in our analysis. The discretization technique is primarily useful for taking a discrete approxi- mation to the conditional density of the strictly exogenous variables of a model. The specification of this conditional density could be based on a variety of 1Financial support under NSF Grants SES-8520244 and SES-8810357 is acknowledged. We thank the co-editor and referees of earlier drafts for many, many helpful comments that substantially improved the manuscript.

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Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models

Nonparametric estimation of structural models for high-frequency currency market data

Nonparametric evidence on asymmetry in business cycles using aggregate employment time series

This paper develops a nonparametric estimator for structural equilibrium models that combines numerical solution techniques for nonlinear rational expectations models with nonparametric statistical techniques for characterizing the dynamic properties of time series data. The estimator uses the the score function from a nonparametric estimate of the law of motion of the observed data to define a GMM criterion function. In effect, it forces the economic model to generate simulated data so as to match a nonparametric estimate of the conditional density of the observed data. It differs from other simulated method of moments estimators in using the nonparametric density estimate, thereby allowing the data to dictate what features of the data are important for the structural model to match. The components of the scoring function characterize important kinds of nonlinearity in the data, including properties such as nonnormality and stochastic volatility.

Computational Aspects of Nonparametric Simulation Estimation

This paper develops and solves a general equilibrium business cycle model with on-the-job search and wage rigidity arising from long-term labor contracts. Labor search models without these features have been criticized for failing to generate procyclical movements in job vacancies and insufficient volatility in the ratio of vacancies to unemployment. When calibrated to the match the magnitude and rates of labor turnover, the model successfully generates these patterns and matches other properties of labor turnover data

Robert Hussey

Papers

Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models

Nonparametric estimation of structural models for high-frequency currency market data

Nonparametric evidence on asymmetry in business cycles using aggregate employment time series

Computational Aspects of Nonparametric Simulation Estimation

On-the-Job Search and Wage Rigidity in a General Equilibrium Model