The Optimal Log-Utility Asset Management under Incomplete Information

In this paper, we propose a theory for deriving the optimal portfolio that assures the log-utility investors of maximizing their expected utility. Restricting investors' information at defined levels, we propose the sample path-wise optimal portfolio (SPOP), which is consistent with the back-test framework used in actualinvestment. It is proven that, at any finite terminal time, this SPOP is asymptotically optimal among all the portfolios which are predictable under investors' incompleteinformation. The optimality is guaranteed by the continuous Bayesian updating formula. Finally, we discuss an algorithm for searching the SPOP, based on asset prices at discrete time intervals.     

Optimal Portfolio Choice Under Incomplete Information

Models of asset pricing generally assume that the variables which characterize the state of the economy are observable. However, the distributional properties of asset prices that are relevant for portfolio decisions are in general not observable, and therefore must be estimated. The estimation of expected returns is a particularly difficult problem and estimation errors are likely to be substantial. In this light, it is reasonable to examine whether the assumption of observability of expected returns and other relevant state variables causes significant mis-specification in equilibrium models of asset prices. This paper has three main objectives: first, to derive optimal estimators for the unobservable expected instantaneous returns using observations of past realized returns; second, to establish that estimation and portfolio choice can be solved in two separate steps; third, to analyze the impact of estimation error on investment choices. The estimators of expected returns are in general not consistent, i.e., the estimation error does not tend to disappear asymptotically. The effects of the estimation error, therefore, cannot be ignored even if realized returns are observed continuously over an infinite time period.     

Information Uncertainty and Expected Returns

This study examines the role of information uncertainty (IU) in predicting cross-sectional stock returns. We define IU in terms of “value ambiguity,” or the precision with which firm value can be estimated by knowledgeable investors at reasonable cost. Using several different proxies for IU, we show that (1) on average, high-IU firms earn lower future returns (the “mean” effect), and (2) price and earnings momentum effects are much stronger among high-IU firms (the “interaction” effect). These findings are consistent with analytical models in which high IU exacerbates investor overconfidence and limits rational arbitrage.This revised version was published online in August 2005 with a corrected cover date.     

Asset Pricing in a Production Economy with Incomplete Information

This paper analyzes an economy in which investors operate under partial information about technology-relevant state variables. It is shown that for Gaussian information structures under incomplete observations, the consumer's problem can be transformed into an equivalent program with a completely observed state: the conditional expectation of the underlying unobservable state variables. A consequence of this transformation is that classic results in finance remain valid under an appropriate reinterpretation of the state variables.     

Discussion of “Information Uncertainty and Expected Returns”

Jiang, Lee, and Zhang (Review of Accounting Studies, 2005, this issue) show that stock returns are smaller for young firms, volatile stocks, high volume stocks, and stocks with long equity durations. In addition to having lower returns, momentum effects are particularly strong in these stocks. The focus of this discussion is on the informal behavioral model that is used to explain these results and how well the variables used in the study proxy for information uncertainty, the model’s focus.This revised version was published online in August 2005 with a corrected cover date.     

Incomplete Information, Heterogeneity, and Asset Pricing

We consider a pure exchange economy where the drift of aggregateconsumption is unobservable. Agents with heterogeneous beliefsand preferences act competitively on financial and goods markets.We discuss how equilibrium market prices of risk differ acrossagents, and in particular we discuss the properties of the marketprice of risk under the physical (objective) probability measure.We propose a number of specifications of risk aversions andbeliefs where the market price of risk is much higher, and theriskless rate of return lower, than in the equivalent full informationeconomy (homogeneous and heterogeneous preferences) and thuscan provide an(other) answer to the equity premium and risk-freerate puzzles. We also derive a representation of the equilibriumvolatility and numerically assess the role of heterogeneityin beliefs. We show that a high level of stock volatility canbe obtained with a low level of aggregate consumption volatilitywhen beliefs are heterogeneous. Finally, we discuss how incompleteinformation may explain the apparent predictability in stockreturns and show that in-sample predictability cannot be exploitedby the agents, as it is in fact a result of their learning processes.     

Using Multiple Imputation in the Analysis of Incomplete Observations in Finance

Incomplete observations are a common feature of financial applicationsthat use survey response, annual report, and proprietary bankingand security issue and pricing data. Finance researchers usea variety of procedures, including deleting offending observationsand imputing ad hoc values, that potentially fail to deliverefficient and unbiased parameter estimates. This article examinesthe application of a statistical framework, multiple imputationmethods, that minimizes incomplete data problems if the missingnesssatisfies certain criteria. When applied to two financial datasetsinvolving severe data incompleteness, the imputation methodsoutperform the ad hoc approaches commonly used in the financeliterature.     

Strategic Auditing: An Incomplete Information Model

This paper presents a stylized model of the strategy game between the auditor and the client. The client is assumed to have either good or bad inherent risk in her reporting system. She chooses a reporting effort level to maintain the accounting records and data management depending on her type of inherent risk. The auditor chooses a high or low level of audit procedures. A high level of auditing procedures will reveal the client's type and effort from which the auditor can decide either to qualify the financial statements or to issue a clean report. The client and the auditor are assumed to move simultaneously. Pure strategy equilibria are derived for all the undominated strategies between the auditor and the client in the region of the model that is more similar to the Fellingham and Newman (1985) model. Unlike their model in which a high auditing level is never a pure strategy in equilibrium, we obtain pure strategy equilibria for high auditing levels.     

不完全信息下的供应链风险评估方法研究

本文使用多属性决策方法进行供应链风险评估,在风险属性权重信息不完全的情况下,建立非线性规划模型求得各风险属性的权重值,并通过求与理想解之间的加权欧氏距离来评估风险值的大小,解决了评估专家由于知识、经验和偏好不完全相同而意见难以统一的困难,最后用一个例子说明了该方法的有效性和实用性。     

Portfolio Optimization in Discontinuous Markets under Incomplete Information

We consider the problem of maximization of expected utility from terminal wealth for log and power utility functions in a market model that leads to purely discontinuous processes. We study this problem as a stochastic control problem both under complete as well as incomplete information. Our contribution consists in showing that the optimal strategy can be obtained by solving a system of equations that in some cases is linear and that a certainty equivalence property holds not only for log-utility but also for a power utility function. For the case of a power utility under incomplete information we also present an independent direct approach based on a Zakai-type equation.      

Expected Idiosyncratic Volatility Measures and Expected Returns

We find that idiosyncratic volatility forecasts using information available to traders at the time of the forecast are not related to expected returns. The positive relation documented in a number of other papers only exists when forward‐looking information is incorporated into the volatility estimate. That positive relation is driven by the realized idiosyncratic volatility component that cannot be forecasted by investors. Our findings are robust to several different empirical tests, volatility forecasting models and time periods.     

不完全信息下基于风险偏好的生态系统服务付费契约设计

基于信息经济学理论,考量生态系统服务付费投资方与供给方在不同风险偏好下的契约设计问题,结果显示:在完全信息条件下,投资方的可变补偿成本与治污成本参数和市场环境不确定性的变化呈负相关;在不完全信息条件下,投资方提供分离契约更利于实现自身期望收益最大化,而高技术类型的供给方则偏向于单一契约;生态系统服务付费双方期望收益与供给方的不同技术水平均呈正相关;在不同风险组合偏好下,高技术类型的供给方在面临分离契约时的努力水平总高于单一契约,低技术的供给方则相反;当双方均为风险中性时,投资方收益最高;而当双方均为风险规避时,投资方收益最低.     

信息不完全、动态博弈与金融衍生品监管

本文拟建立不完全信息动态监督博弈,分析各种博弈均衡的约束条件,针对性地调整相关变量大小,从而提高金融监管机构的可置信的监管威胁,有效降低银行违规操作概率,扩大以银行为主的金融机构合法参与衍生品投资的范围,实现改革的预期目标,达到帕累托最优状态.     

Relationship Lending and Liquidation Under Imperfect Information

Journal of Financial Services Research - Using a model of a competitive credit market, we study a firm’s choice between financing a production project using a transaction loan and a...     

Information Quality and the Expected Rate of Return: A Structural Equation Modelling Approach

Asia-Pacific Financial Markets - We use structural equation modelling for a robust test of the role information quality plays in explaining the cost of equity capital (CoE). SEM allows us to...     

Effective Use of Survey Information in Estimating the Evolution of Expected Inflation

The evolution of the term structure of expected U.S. inflation is modeled using survey data to provide timely information on structural change not contained in lagged inflation data. To capture shifts in subjective perceptions, the model is adaptive to long‐horizon survey expectations. However, even short‐horizon survey expectations inform shifting‐endpoint estimates that capture the lag between inflation and the perceived inflation target, which anchors inflation expectations. Results show movements of the perceived target are an important source of inflation persistence and suggest historical U.S. monetary policy was not fully credible for much of the postwar sample.     

Incomplete Intertemporal Consumption Smoothing and Incomplete Risk Sharing

This paper develops a method to estimate jointly the degree of intertemporal consumption smoothing and the degree of “inter‐regional” risk sharing. The empirical results for the U.S. states and OECD and EU countries suggest that: (i) regardless of the assumption on the degree of intertemporal consumption smoothing, the degree of risk sharing within a country is larger than across countries; (ii) the degree of intertemporal consumption smoothing within a country is also larger than across countries; and (iii) the difference between the degree of intertemporal consumption smoothing within U.S. states and across OECD and EU countries is as large as the difference between the degree of risk sharing, contrary to the findings of some past studies.     

Earnings and Expected Returns

The aggregate dividend payout ratio forecasts excess returns on both stocks and corporate bonds in postwar U.S. data. High dividends forecast high returns. High earnings forecast low returns. The correlation of earnings with business conditions gives them predictive power for returns; they contain information about future returns that is not captured by other variables. Dividends and earnings contribute substantial explanatory power at short horizons. For forecasting long-horizon returns, however, only (scaled) stock prices matter. Forecasts of low long-horizon stock returns in the mid-1990s are caused not by earnings or dividends, but by high stock prices.     

A Note on Utility Maximization with Unbounded Random Endowment

This paper addresses the applicability of the convex duality method for utility maximization, in the presence of random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true, for a wide class of utility functions and unbounded random endowments. We show this duality by exploiting Rockafellar’s theorem on integral functionals, to a random utility function.