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series approximations to expected utility and optimal portfolio choice, Working Paper
"... This paper revisits the subject of Taylor series approximations to expected utility and investigates the applicability of the technique to optimal portfolio choice problems. We first provide conditions under which the approximate expected utility of a given portfolio converges to its exact counterpa ..."
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This paper revisits the subject of Taylor series approximations to expected utility and investigates the applicability of the technique to optimal portfolio choice problems. We first provide conditions under which the approximate expected utility of a given portfolio converges to its exact counterpart. We then extend the analysis to the optimal portfolio choice setting and provide conditions on the distribution of asset returns under which the solution to the approximate portfolio choice problem converges to its exact counterpart. Finally, we show that, when asset returns are skewed, one can improve the precision and efficiency of the Taylor expansion by applying a simple nonlinear transformation to asset returns designed to symmetrize the transformed return distribution and shrink its support. ∗We wish to thank participants at the 2008 Latin American Meeting of the Econometric Society (LAMES),
Sequential learning, predictability, and optimal portfolio returns
, 2012
"... This paper finds statistically and economically significant outofsample portfolio benefits for an investor who uses models of return predictability when forming optimal portfolios. The key is that investors must incorporate an ensemble of important features into their optimal portfolio problem inc ..."
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This paper finds statistically and economically significant outofsample portfolio benefits for an investor who uses models of return predictability when forming optimal portfolios. The key is that investors must incorporate an ensemble of important features into their optimal portfolio problem including timevarying volatility and timevarying expected returns driven by improved predictors such as measures of yield that include shares repurchase and issuance in addition to cash payouts. In addition, investors need to account for estimation risk when forming optimal portfolios. Prior research document a lack of benefits to return predictability, and our results suggest this was largely due to omitting timevarying volatility and estimation risk. We also study the learning problem of investors, documenting the sequential process of learning about parameters, state variables, and models as new data arrives.
What is the Chance that the Equity Premium Varies over Time? Evidence from Predictive Regressions, Unpublished Manuscript
, 2007
"... are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. What is the Chance that the Equity Premium Varies over Time? Evi ..."
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are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. What is the Chance that the Equity Premium Varies over Time? Evidence from Predictive Regressions We examine the evidence on excess stock return predictability in a Bayesian setting in which the investor faces uncertainty about both the existence and strength of predictability. When we apply our methods to the dividendprice ratio, we find that even investors who are quite skeptical about the existence of predictability sharply modify their views in favor of predictability when confronted by the historical time series of returns and predictor variables. Correctly taking into account the stochastic properties of the regressor has a dramatic impact on inference, particularly over the 20002005 period. 2 1
Human capital investment and portfolio choice over the lifecycle ∗
, 2003
"... 1 Human capital investment and portfolio choice over the lifecycle I study a theoretical model of lifecycle portfolio choice for an investor who has an option to invest in human capital but is liquidity constrained. I find that, since the young are more likely to exercise the option than the old, ..."
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1 Human capital investment and portfolio choice over the lifecycle I study a theoretical model of lifecycle portfolio choice for an investor who has an option to invest in human capital but is liquidity constrained. I find that, since the young are more likely to exercise the option than the old, they are more concerned about liquidity risk (i.e. the risk that the liquidity constraint binds when it is optimal to invest). This, in turn, implies a humpshaped pattern of lifetime risky asset holdings: portfolio share invested in equities is increasing for the young and decreasing for the older agents. Optimal investment rule and the precautionary demand for the riskless asset vary with the business cycle, which suggests potential implications for asset pricing.
Pricing kernels with coskewness and volatility risk. Charles A. Dice Center Working Paper No. 2008–25 and Fisher College of Business Working Paper No. 200803023, 2008b. Available online at SSRN: http://ssrn.com/abstract
"... I investigate a pricing kernel in which coskewness and the market volatility risk factors are endogenously determined. I show that the price of coskewness and market volatility risk are restricted by investor risk aversion and skewness preference. Consistent with theory, I find that the pricing kern ..."
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I investigate a pricing kernel in which coskewness and the market volatility risk factors are endogenously determined. I show that the price of coskewness and market volatility risk are restricted by investor risk aversion and skewness preference. Consistent with theory, I find that the pricing kernel is decreasing in the aggregate wealth and increasing in the market volatility. When I project my estimated pricing kernel on a polynomial function of the market return, doing so produces the puzzling behaviors observed in pricing kernel. Using pricing kernels, I examine the sources of the idiosyncratic volatility premium. I find that nonzero risk aversion and firms nonsystematic coskewness determines the premium on idiosyncratic volatility risk. When I control for the nonsystematic coskewness factor, I find no significant relation between idiosyncratic volatility and stock expected return. My results are robust across different sample periods, different measures of market volatility and firms characteristics.
Asset Allocation
 Annual Reviews of Financial Economics
, 2010
"... This review article describes recent literature on asset allocation, covering both static and dynamic models. The article focuses on the bond–stock decision and on the implications of return predictability. In the static setting, investors are assumed to be Bayesian, and the role of various prior be ..."
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This review article describes recent literature on asset allocation, covering both static and dynamic models. The article focuses on the bond–stock decision and on the implications of return predictability. In the static setting, investors are assumed to be Bayesian, and the role of various prior beliefs and specifications of the likelihood are explored. In the dynamic setting, recursive utility is assumed, and attention is paid to obtaining analytical results when possible. Results under both full and limitedinformation assumptions are discussed.
Duality theory and simulation in financial engineering
 In Proceedings of the Winter Simulation Conference
, 2003
"... This paper presents a brief introduction to the use of duality theory and simulation in financial engineering. It focuses on American option pricing and portfolio optimization problems when the underlying state space is highdimensional. In general, it is not possible to solve these problems exactl ..."
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This paper presents a brief introduction to the use of duality theory and simulation in financial engineering. It focuses on American option pricing and portfolio optimization problems when the underlying state space is highdimensional. In general, it is not possible to solve these problems exactly due to the socalled “curse of dimensionality ” and as a result, approximate solution techniques are required. Approximate dynamic programming (ADP) and dual based methods have recently been proposed for constructing and evaluating good approximate solutions to these problems. In this paper we describe these ADP and dualbased methods, and the role simulation plays in each of them. Some directions for future research are also outlined.
Do Investors dislike Kurtosis
 Economics Bulletin
, 2007
"... We show that decreasing absolute prudence implies kurtosis aversion. The ``proof' ' of this relation is usually based on the identification of kurtosis with the fourth centered moment of the return distribution and a Taylor approximation of the utility function. A more sound analysis is re ..."
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We show that decreasing absolute prudence implies kurtosis aversion. The ``proof' ' of this relation is usually based on the identification of kurtosis with the fourth centered moment of the return distribution and a Taylor approximation of the utility function. A more sound analysis is required, however, as such heuristic arguments have been shown to be logically flawed.
Control of Diffusions via Linear Programming
"... In this chapter we present an approach that leverages linear programming to approximate optimal policies for controlled diffusion processes, possibly with highdimensional state and action spaces. The approach fits a linear combination of basis functions to the dynamic programming value function; th ..."
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In this chapter we present an approach that leverages linear programming to approximate optimal policies for controlled diffusion processes, possibly with highdimensional state and action spaces. The approach fits a linear combination of basis functions to the dynamic programming value function; the resulting approximation guides control decisions. Linear programming is used here to compute basis function weights. What we present extends the linear programming approach to approximate dynamic programming, previously developed in the context of discretetime stochastic control [19, 20, 7, 8, 9]. One might question the practical merits of such an extension relative to descretizing continuoustime models and treating them using previously developed methods. As will be made clear in this chapter, there are indeed important advantages in the simplicity and efficiency of computational methods made possible by working directly with a diffusion model. We begin in Section 1.1 by presenting a problem formulation and a linear programming characterization of optimal solutions. The numbers of variables and constraints defining this linear program are both infinite. In Section 1.2, we describe algorithms that apply finitedimensional linear programming to approximately solve this infinitedimensional problem. To illustrate practical qualities, we discuss in Section 1.3 computational results from case studies in dynamic portfolio optimization. A closing section summarizes merits of the new approach.