Information, Expected Utility, and Portfolio Choice

SSRN Electronic Journal, 2017

This paper constructs a recursive utility version of a canonical Merton (1971) model with uninsurable labor income and unknown income growth to study how the interaction between two types of uncertainty due to ignorance affects strategic consumption-portfolio rules and precautionary savings. Specifically, after solving the model explicitly, we theoretically and quantitatively explore (i) how these ignorance-induced uncertainties interact with intertemporal substitution, risk aversion, and the correlation between the equity return and labor income, and (ii) how they jointly affect strategic asset allocation, precautionary savings, and the equilibrium asset returns. Furthermore, we use data to test our model's predictions on the relationship between ignorance and asset allocation and quantitatively show that the interaction between the two types of uncertainty is the key to explain the data. Finally, we find that the welfare costs of ignorance can be very large.

2003

Abstract: We develop a model of portfolio selection with subjective uncertainty and learning in order to explain why some people hold stocks while others don't. We model heterogeneity in information directly, which is an alternative to the existing explanations that emphasized heterogeneity in transaction costs of investment. We plan to calibrate the model to survey data (when available) on people's perception about the distribution of stock market returns.

SSRN Electronic Journal, 2019

This paper presents an optimal allocation problem in a financial market with one risk-free and one risky asset, when the market is driven by a stochastic market price of risk. We solve the problem in continuous time, for an investor with a Constant Relative Risk Aversion (CRRA) utility, under two scenarios: when the market price of risk is observable (the full information case), and when it is not (the partial information case). The corresponding market models are complete in the partial information case and incomplete in the other case, hence the two scenarios exhibit rather different features. We study how the access to more accurate information on the market price of risk affects the optimal strategies and we determine the maximal price that the investor would be willing to pay to get such information. In particular, we examine two cases of additional information, when an exact observation of the market price of risk is available either at time 0 only (the initial information case), or during the whole investment period (the dynamic information case).

1985

The three sections of this paper support three related conclusions. First, asset demands with the familiar properties of wealth homogeneity and linearity in expected returns follow as close approximations from expected utility maximizing behavior under the assumptions of constant relative risk aversion and joint normally distributed asset returns. Second, although such asset demands exhibit a symmetric coefficient matrix with respect to the relevant vector of expected asset returns, symmetry is not a general property, and the available empirical evidence warrants rejecting it for both institutional and individual investors in the United States. Finally, in a manner analogous to the finite maximum exhibited by quadratic utility, a broad class of mean-variance utility functions also exhibits a form of wealth satiation which necessarily restricts it range of applicability.

Management Science, 2016

This paper provides a tractable continuous-time constant-absolute-risk averse (CARA)-Gaussian framework to explore how the interactions of fundamental uncertainty, model uncertainty due to a preference for robustness (RB), and state uncertainty due to information-processing constraints (rational inattention or RI) affect strategic consumption-portfolio rules and precautionary savings in the presence of uninsurable labor income. Specifically, after solving the model explicitly, I compute and compare the elasticities of strategic asset allocation and precautionary savings to risk aversion, robustness, and inattention. Furthermore, for plausibly estimated and calibrated model parameters, I quantitatively analyze how the interactions of model uncertainty and state uncertainty affect the optimal share invested in the risky asset, and show that they can provide a potential explanation for the observed stockholding behavior of households with different education and income levels.

manuscript, University of …, 2007

We study the portfolio decision of an agent with limited information-processing capacity in the sense of Shannon (1948).

Journal of Economic Theory

In this paper we examine implications of model uncertainty due to robustness (RB) for consumption and saving and the market price of uncertainty under limited information-processing capacity (rational inattention or RI). We first solve the robust permanent income models with inattentive consumers and show that RI by itself creates an additional demand for robustness that leads to higher "induced uncertainty" facing consumers. Second, we explore how the induced uncertainty composed of (i) model uncertainty due to RB and (ii) state uncertainty due to RI, affects consumption-saving decisions and the market price of uncertainty. We find that induced uncertainty can better explain the observed market price of uncertainty-low attention increases the effect of model misspecification. We also show the observational equivalence between RB and risk-sensitivity (RS) in environment. * This paper was previously circulated under tht title "Consumption, Market Price of Risk, and Wealth Accumulation under Induced Uncertainty". We are indebted to Tom Sargent for helpful guidance and suggestions. We also would like to thank

Journal of Banking & Finance, 1984

This paper examines the relationship between perceived information costs and expected returns, expected range of returns, ownership and sources of information for a group of affluent investors in a multi-market setting (across a variety of investments). Findings show that investors expect excess returns and greater risk in areas characterized by high information costs and that ownership is more limited (less diversified) in these investment areas. Additionally, the involvement of certain types of advisors (information sources) substantially increases information costs.

Journal of Banking & Finance, 1988

This study extends the theoretical analysis and empirical research of risk aversion in securities markets. The analysis of the determinants of the market price of risk, part of an equilibrium modei of asset pricing, involves relative risk aversion and is carried out for the continuous time case. Micro relationships which are equilibrium demand functions of individual investors are derived; on the macro level the determinants of the market price of risk are determined. The analysis is carried out first assuming that a!! assets are marketable; then this assumption is relaxed and non-marketable assets (human-capital) are considered. Finally, we consider explicitly the effects of uncertain inflation on risk aversion. The major empirical results are: the assumption of constant relative risk seems to be a reasonable approximation of the market; secondly, the coefficient of relative risk aversion seems to be greater than unity; thirdly, for the first time trends in risk aversion were estimated. where r. is the return on an asset uncorrelated with the market return (a zero-beta asset), and Yk is the ratio of the kth individual wealth (wk) to total wealth W A specific form of the assumption of an infinitesimal planning horizon and no finite changes in value in an infinitesimal period, would imply for a finite interval a log normal distribution of returns.* If we assume that all wealth is invested in risky assets, i.e. W= K we get here an identical expression to the discrete case, except that y. is substituted for rf. It should be noted that the measure of absolute risk aversioa in the discrete case is replaced here by the relative measure, i.e. wkak =ck. Parallel to Friend and Blume (1975) we apply the continuous time solution to the situation in which not all wealth is invested in risky assets, but rather as in the discrete case, part of the wealth is invested in risk-free asset with a certain rate of return. *See Merton (19?3), I! Landskroner, Risk aversion in securities markets 133 We assume in common to all studies cited above homogenous expectations for all individuals. In the literature we find models focusing on differences in expectations or on differences in attitudes towards risk. The reason that different models focus on one or the other is that to understand how each of them works they are best studied in isolation-in our study, to understand the effects of differences in attitudes towards risk on portfolio allocation we assume that individuals have the same expectations.* We can write the wealth dynamics for individual k in stochastic difference equation form and then, by taking limits, in stochastic differential equation form. Thus for individual k, f&t +dr) = Wkr[ 1 + (1-ak)rf dt + a&, dt], (4) where LI indicates a random variable; t a point in time; ak the proportion invested in risky assets (the existence of 'many risky assets does not pose a problem where the separation theorem holds). First assume that the market rate of return ?,,,, il generated by a continuous Gaussian (Wiener) process:3

Journal of Interdisciplinary Economics, 1994

In behavioural psychology the relationship between the information provided by a stimulus and an individual’s reaction thereto is widely accepted as parabolic and commonly referred to as a Wundt curve. The present paper invokes this relationship in order to examine the apparent failure of the efficient markets model as a paradigm for describing security price behaviour. Discrepancies between the prices and intrinsic values of securities are explained in terms of the amount of information entering the price determination process, with the amount required for an efficient market found to have an interior solution. The social invention of the stock market provides a convenient meeting ground in which to study the nexus between the psychology of investor behaviour and the economics of asset pricing.