Optimal and equilibrium execution strategies with generalized price impact

This paper examines the execution problems of large traders with a generalized price impact. Constructing two related models in a discrete-time setting, we solve these problems by applying the backward induction method of dynamic programming. In the first problem, we formulate the expected utility maximization problem of a single large trader as a Markov decision process and derive an optimal execution strategy. Then, in the second model, we formulate the expected utility maximization problem of two large traders as a Markov game and derive an equilibrium execution strategy at a Markov perfect equilibrium. Both of these two models enable us to investigate how the execution strategies and trade performances of a large trader are affected by the existence of other traders. Moreover, we find that these optimal and equilibrium execution strategies become deterministic when the total execution volumes of non-large traders are deterministic. We also show, by some numerical examples, the comparative statics results with respect to several problem parameters.     

An empirical analysis of marginal conditional stochastic dominance

Stochastic dominance is a more general approach to expected utility maximization than the widely accepted mean–variance analysis. However, when applied to portfolios of assets, stochastic dominance rules become too complicated for meaningful empirical analysis, and, thus, its practical relevance has been difficult to establish. This paper develops a framework based on the concept of Marginal Conditional Stochastic Dominance (MCSD), introduced by Shalit and Yitzhaki (1994), to test for the first time the relationship between second order stochastic dominance (SSD) and stock returns. We find evidence that MCSD is a significant determinant of stock returns. Our results are robust with respect to the most popular pricing models.     

Volatility spillovers between oil prices and the stock market under structural breaks

This paper employs univariate and bivariate GARCH models to examine the volatility of oil prices and US stock market prices incorporating structural breaks using daily data from July 1, 1996 to June 30, 2013. We endogenously detect structural breaks using an iterated algorithm and incorporate this information in GARCH models to correctly estimate the volatility dynamics. We find no volatility spillover between oil prices and US stock market when structural breaks in variance are ignored in the model. However, after accounting for structural breaks in the model, we find strong volatility spillover between the two markets. We compute optimal portfolio weights and dynamic risk minimizing hedge ratios to highlight the significance of our empirical results which underscores the serious consequences of ignoring these structural breaks. Our findings are consistent with the notion of cross-market hedging and sharing of common information by financial market participants in these markets.     

Beliefs regarding fundamental value and optimal investing

Standard optimal portfolio selection models take no account of the special information that active investors believe they possess. For example, active investors who believe they can place bounds on the price of a security will want to use that information when assessing risk and expected return in order to construct an optimal portfolio. In this paper, we use two continuous-time models to analyze how placing boundaries on the price of a stock affects assessed risk, expected returns, and the optimal holdings of an active investor, and how those vary as a function of the relation between the stock price and the boundaries. In particular, the optimal strategy takes significant long/short positions as the price nears its lower/upper boundary.     

恒生指数和沪深300股指期货套期保值效果对比研究

本文利用OLS、ECM、ECM-GARCH模型对沪深300股指期货和恒生指数期货的最优套期保值率进行了估算,并在风险最小化框架下对它们的套期保值效果进行了对比研究。结果发现:无论是哪种股指期货,不考虑期现货间存在的协整关系会使估算的最优套期保值率偏高,影响套期保值效果;其次是虽然在样本内外,沪深300股指期货的套期保值效果比恒生指数期货的好,但是沪深300股指期货套期保值效果的稳定性比恒生指数差。此时,ECM-GARCH和OLS模型分别为样本内外投资者利用沪深300指数期货进行套期保值时的最佳选择;对于恒生指数股指期货,最优模型是ECM。     

The impact of the market portfolio on the valuation,incentives and optimality of executive stock options

This paper examines the effect on valuation and incentives of allowing executives receiving options to trade on the market portfolio. We propose a continuous time utility maximization model to value stock and option compensation from the executive's perspective. The executive may invest non-option wealth in the market and riskless asset but not in the company stock itself, leaving them subject to firm-specific risk for incentive?purposes. Since the executive is risk averse, this unhedgeable firm risk leads them to place less value on the options than their cost to the company.

By distinguishing between these two types of risks, we are able to examine the effect of stock volatility, firm-specific risk and market risk on the value to the executive. In particular, options do not give incentive to increase total risk, but rather to increase the proportion of market relative to firm-specific risk, so executives prefer high beta companies. The paper also examines the relationship between risk and incentives, and finds firm-specific risk decreases incentives whilst market risk may decrease incentives depending on other parameters. The model supports the use of stock rather than options if the company can adjust cash pay when granting stock-based compensation.     

Generalized DEA model of fundamental analysis and its application to portfolio optimization

Fundamental analysis is used in asset selection for equity portfolio management. In this paper, a generalized data envelopment analysis (DEA) model is developed to analyze a firm’s financial statements over time in order to determine a relative financial strength indicator (RFSI) that is predictive of firm’s stock price returns. RFSI is based on maximizing the correlation between the DEA-based score of financial strength and the stock market performance. This maximization involves a difficult binary nonlinear program that requires iterative re-configuration of parameters of financial statements as inputs and outputs. We utilize a two-step heuristic algorithm that combines random sampling and local search optimization. The proposed approach is tested with 230 firms from various US technology-industries to determine optimized RFSI indicators for stock selection. Then, those selected stocks are used within portfolio optimization models to demonstrate the usefulness of the scheme for portfolio risk management.     

Optimal investment strategies for general utilities under dynamic elasticity of variance models

This paper studies the optimal investment strategies under the dynamic elasticity of variance (DEV) model which maximize the expected utility of terminal wealth. The DEV model is an extension of the constant elasticity of variance model, in which the volatility term is a power function of stock prices with the power being a nonparametric time function. It is not possible to find the explicit solution to the utility maximization problem under the DEV model. In this paper, a dual-control Monte-Carlo method is developed to compute the optimal investment strategies for a variety of utility functions, including power, non-hyperbolic absolute risk aversion and symmetric asymptotic hyperbolic absolute risk aversion utilities. Numerical examples show that this dual-control Monte-Carlo method is quite efficient.     

Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model

We consider an optimal time-consistent reinsurance-investment strategy selection problem for an insurer whose surplus is governed by a compound Poisson risk model. In our model, the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a simplified financial market consisting of a risk-free asset and a risky stock. The dynamics of the risky stock is governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity as well as the feedback effect of an asset’s price on its volatility. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategies and the corresponding value functions are obtained in both the compound Poisson risk model and its diffusion approximation. Numerical examples are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary.     

Estimation and Evaluation of Conditional Asset Pricing Models

We find that several recently proposed consumption‐based models of stock returns, when evaluated using an optimal set of managed portfolios and the associated model‐implied conditional moment restrictions, fail to capture key features of risk premiums in equity markets. To arrive at these conclusions, we construct an optimal Generalized Method of Moments (GMM) estimator for models in which the stochastic discount factor (SDF) is a conditionally affine function of a set of priced risk factors, and we show that there is an optimal choice of managed portfolios to use in testing a null model against a proposed alternative generalized SDF.     

Timing and diversification: A state-dependent asset allocation approach

Abstract

The influence of changing economic environment leads the distribution of stock market returns to be time-varying. A conditionally optimal investment hence requires a dynamic adjustment of asset allocation. In this context, this paper examines the improvement in portfolio performance by simulating portfolio strategies that are conditioned on the Markov regime switching behaviour of stock market returns. Including a memory effect eliminates the empirical shortcoming of discrete state models, namely that they produce a standard and an extreme state in stock returns. So far, this has prevented the regimes from being used as a valuable conditioning variable. Based on a discrete state indicator variable, is presented evidence of considerable performance improvement relative to the static model due to optimal shifting between aggressive and well diversified portfolio structures.     

Mixed Integer Programming Revealed Preference Tests of Utility Maximization and Weak Separability of Consumption,Leisure, and Money

Swofford and Whitney (1987, 1988, 1994) investigated the validity of two key assumptions underlying representative agent models of macroeconomics. These assumptions are utility maximization and weak separability. Using mixed integer programming, we check revealed preference conditions for these assumptions. We find that M1, money defined by Friedman and Schwartz (1963), and a broad aggregate are weakly separable. We find that consumption goods and leisure and nondurables and services are weakly separable. We find that M2, M3, and MZM are not weakly separable. Finally, we find three categories of consumption, durables, nondurables and services, do not form an aggregate.     

Optimal execution with uncertain order fills in Almgren–Chriss framework

The classical price impact model of Almgren and Chriss is extended to incorporate the uncertainty of order fills. The extended model can be recast as alternatives to uncertain impact models and stochastic liquidity models. Optimal strategies are determined by maximizing the expected final profit and loss (P&L) and various P&L-risk tradeoffs including utility maximization. Closed form expressions for optimal strategies are obtained in linear cases. The results suggest a type of adaptive volume weighted average price, adaptive percentage of volume and adaptive Almgren–Chriss strategies. VWAP and classical Almgren–Chriss strategies are recovered as limiting cases with a different characteristic time scale of liquidation for the latter.     

Predicting bear and bull stock markets with dynamic binary time series models

Despite the voluminous empirical research on the potential predictability of stock returns, much less attention has been paid to the predictability of bear and bull stock markets. In this study, the aim is to predict U.S. bear and bull stock markets with dynamic binary time series models. Based on the analysis of the monthly U.S. data set, bear and bull markets are predictable in and out of sample. In particular, substantial additional predictive power can be obtained by allowing for a dynamic structure in the binary response model. Probability forecasts of the state of the stock market can also be utilized to obtain optimal asset allocation decisions between stocks and bonds. It turns out that the dynamic probit models yield much higher portfolio returns than the buy-and-hold trading strategy in a small-scale market timing experiment.     

Estimation of expected return: CAPM vs. Fama and French

Most practitioners favour a one-factor model (CAPM) when estimating expected return for an individual stock. For estimation of portfolio returns, academics recommend the Fama and French three-factor model. The main objective of this paper is to compare the performance of these two models for individual stocks. First, estimates for individual stock returns based on CAPM are obtained using different time frames, data frequencies, and indexes. It is found that 5 years of monthly data and an equal-weighted index, as opposed to the commonly recommended value-weighted index, provide the best estimate. However, performance of the model is very poor; it explains on average 3% of differences in returns. Then, estimates for individual stock returns are obtained based on the Fama and French model using 5 years of monthly data. This model, however, does not do much better; independent of the index used, it explains on average 5% of differences in returns. These results therefore bring into question the use of either model for estimation of individual expected stock returns.     

Wealth-path dependent utility maximization in incomplete markets

Motivated by an optimal investment problem under time horizon uncertainty and when default may occur, we study a general structure for an incomplete semimartingale model extending the classical terminal wealth utility maximization problem. This modelling leads to the formulation of a wealth-path dependent utility maximization problem. Our main result is an extension of the well-known dual formulation to this context. In contrast with the usual duality approach, we work directly on the primal problem. Sufficient conditions for characterizing the optimal solution are also provided in the case of complete markets, and are illustrated by examples.Received: December 2003, Mathematics Subject Classification (2000): 91B28, 91B16, 49N15, 49N30JEL Classification: G11The authors would like to thank the anonymous referees for their remarks and suggestions which greatly improved this paper. We also thank participants at the Oberwolfach workshop in 2003 for comments and discussions.     

中国个人投资者处置效应研究——一个非理性信念的视角

处置效应是指投资者过早卖出盈利股票而长期持有亏损股票的现象。大量文献表明金融市场投资者存在显著的处置效应,但其产生的原因和机理存在争议。本文在前景理论框架下,构建了包含投资者非理性预期的离散时间投资组合决策模型,发现处置效应随投资者情绪升高而减弱。本文使用我国某券商2007—2009年近177万个人投资者股票账户的交易数据进行了实证分析,得到与理论模型预测的一致结果,即投资者情绪与投资者处置效应之间呈现显著的负相关关系。而且,受情绪影响,投资者处置效应在估值难度较大的股票中更弱。本文结论对理解投资者处置效应、优化投资者卖出决策和加强资本市场基础制度建设具有一定理论和实践意义。     

A Model of Equity Based Compensation with Tax

In this paper, we develop a two‐stage continuous time model of employee stock option (ESO) valuation under different tax regimes. We show that tax rules can have significant effects on ESO exercise behavior. In addition, we find that incentive stock options (ISO) are the optimal form of compensation for all levels of employees in the UK. In the US, restricted stock plans are preferred, and tax breaks offered by incentive schemes are only beneficial to employees with high liquid wealth (or small option holdings relative to wealth) or low risk aversion. We also analyze 83b elections for restricted stock plans in the US and find that making an election is a sub‐optimal decision for both the employee and the firm.     

投资者情绪是导致我国投资者对市场信息出现反应偏差的原因吗：基于贝叶斯分位数回归模型的研究

本文使用贝叶斯分位数回归模型实证分析包含投资者情绪的投资者最优选择模型,结果表明：投资者情绪对于股票收益率存在非线性的正向影响,这是造成投资者对于市场信息出现反应偏差的一个重要原因.同时,市场信息和投资者情绪指标对于我国股票收益率都有着较大的影响作用;当股票出现不同涨跌幅时,市场信息对于股票收益率的影响有着较大的差异性.而考虑了投资者情绪指标之后,投资者对于市场信息的反应偏差明显减小,说明投资者情绪是造成我国投资者对于市场信息出现过度反应和反应不足的重要原因.我国投资者应该树立起良好的投资意识和心态,避免潜在的投资损失.