Illiquidity, position limits, and optimal investment for mutual funds

We study the optimal trading strategy of mutual funds that face both position limits and differential illiquidity. We provide explicit characterization of the optimal trading strategy and conduct an extensive analytical and numerical analysis of the optimal trading strategy. We show that the optimal trading boundaries are increasing in both the lower and the upper position limits. We find that position limits can affect current trading strategy even when they are not currently binding and other seemingly intuitive trading strategies can be costly. We also examine the optimal choice of position limits.     

The existence, uniqueness, and optimality of the terminal wealth depletion time in life-cycle models of saving under uncertain lifetime and borrowing constraint

In life-cycle models of saving under uncertain lifetime and borrowing constraint, the consumer's wealth must be depleted before the maximum lifetime. This paper investigates the existence, uniqueness, and optimality of the terminal wealth depletion time. It is proved that the optimal terminal wealth depletion time, if such exists, must be unique. If the equation that determines the optimal terminal wealth depletion has multiple solutions, then the location of the optimal solution will depend on the configuration of the solutions. An optimality test is developed to verify whether a candidate solution for the terminal wealth depletion time is indeed optimal. The paper introduces a method new to economics, the Dubovitskii-Milyutin adjoint equation, to analyze the properties of the optimal control problem.     

Measuring and Optimizing Portfolio Credit Risk: A Copula‐based Approach*

In this work, we present a methodology for measuring and optimizing the credit risk of a loan portfolio taking into account the non‐normality of the credit loss distribution. In particular, we aim at modelling accurately joint default events for credit assets. In order to achieve this goal, we build the loss distribution of the loan portfolio by Monte Carlo simulation. The times until default of each obligor in portfolio are simulated following a copula‐based approach. In particular, we study four different types of dependence structure for the credit assets in portfolio: the Gaussian copula, the Student's t‐copula, the grouped t‐copula and the Clayton n‐copula (or Cook–Johnson copula). Our aim is to assess the impact of each type of copula on the value of different portfolio risk measures, such as expected loss, maximum loss, credit value at risk and expected shortfall. In addition, we want to verify whether and how the optimal portfolio composition may change utilizing various types of copula for describing the default dependence structure. In order to optimize portfolio credit risk, we minimize the conditional value at risk, a risk measure both relevant and tractable, by solving a simple linear programming problem subject to the traditional constraints of balance, portfolio expected return and trading. The outcomes, in terms of optimal portfolio compositions, obtained assuming different default dependence structures are compared with each other. The solution of the risk minimization problem may suggest us how to restructure the inefficient loan portfolios in order to obtain their best risk/return profile. In the absence of a developed secondary market for loans, we may follow the investment strategies indicated by the solution vector by utilizing credit default swaps.     

Discount functions and self-control problems

In this paper we propose a new strategy for comparing the behavior of a hyperbolic discounter who possesses self-control problems to an exponential discounter who does not. Our strategy controls for inherent differences in overall levels of impatience across discount functions, which thereby allows us to isolate the pure effect of self-control problems. We argue that self-control problems, in their pure form as we identify them, can have a very surprising effect on intertemporal choices. Our method reveals that differences in decision making that could be attributed to self-control problems are at least partly (and perhaps entirely) just an artifact of an uncontrolled comparison.     

A waste management model for optimal recycling-landfilling policies under macroeconomic conditions

This research provides a waste management model in the presence of macroeconomic conditions. An optimal control problem which integrates the recycling-landfilling decision with industry supply-demand dynamics is designed to achieve the value-maximizing objective. The model simultaneously considers idiosyncratic technical and aggregate demand shocks, while the stoppage time for landfill use is assumed to follow a Cox process with the intensity function of a firm's total waste collection. The closed-form solution of the optimal recycling ratio is also derived. The results suggest that when macroeconomic effects are neglected, optimal recycling ratios tend to be underestimated.     

Multi-objective private wealth allocation without subportfolios

As opposed to institutional investors, individual investors typically have several investment objectives in mind. The traditional utility maximization approach is not only oversimplified but also may not be suitable for real world application. Behavioral asset allocation divides a portfolio into subportfolios, which can cause potential problems. This paper follows the Modern Portfolio Theory and introduces the practical idea of treating some goals as constraints. How this works in practice is illustrated by an example of an individual having three different objectives. This article follows the idea of Chen et al. (2006) and includes life insurance. Consumption is modeled into three parts and accommodates a reasonable basis for calculating life insurance requirements and generally integrates consumption into the investment decision. As a whole, the model provides a customized solution for the environment and complex investment goals of an individual.     

The disposition effect and loss aversion: Do gender differences matter?

This paper analyzes gender differences in the disposition effect in an experiment based on Weber and Camerer (1998). The results emphasize that female investors realize less capital losses, have significantly higher disposition effects and are more loss averse than men.     

Equilibrium portfolios in the neoclassical growth model

This paper studies equilibrium portfolios in the standard neoclassical growth model under uncertainty with heterogeneous agents and dynamically complete markets. Preferences are purposely restricted to be quasi-homothetic. The main source of heterogeneity across agents is due to different endowments of shares of the representative firm at date 0. Fixing portfolios is the optimal equilibrium strategy in stationary endowment economies with dynamically complete markets. However, when the environment displays changing degrees of heterogeneity across agents, the trading strategy of fixed portfolios cannot be optimal in equilibrium. Very importantly, our framework can generate changing heterogeneity if and only if either minimum consumption requirements are not zero or labor income is not zero and the value of human and non-human wealth are linearly independent.     

Portfolio choice and pricing in illiquid markets

This paper studies portfolio choice and pricing in markets in which immediate trading may be impossible. It departs from the literature by removing restrictions on asset holdings, and finds that optimal positions depend significantly and naturally on liquidity: When expected future liquidity is high, agents take more extreme positions, given that they do not have to hold those positions for long when they become undesirable. Consequently, larger trades should be observed in markets with more frequent trading. Liquidity need not affect the price significantly, however, because liquidity has offsetting impacts on different agents' demands. This result highlights the importance of unrestricted portfolio choice. The paper draws parallels with the transaction-cost literature and clarifies the relationship between the price level and the realized trading frequency in this literature.     

On the impact of leverage constraints on asset prices and trading volume

Abstract. Researchers have used stylized facts on asset prices and trading volume in stock markets (in particular, the mean reversion of asset returns and the correlations between trading volume, price changes and price levels) to support theories where agents are not rational expected utility maximizers. This paper shows that this empirical evidence is in fact consistent with a standard infinite horizon – perfect information – expected utility economy where some agents face leverage constraints similar to those found in todays financial markets. In addition, and in sharp contrast to the theories above, we explain some qualitative differences that are observed in the price-volume relation on stock and on futures markets. We consider a continuous-time economy where agents maximize the integral of their discounted utility from consumption under both budget and leverage constraints. Building on the work by Vila and Zariphopoulou (1997), we find a closed form solution, up to a negative constant, for the equilibrium prices and demands in the region of the state space where the constraint is non-binding. We show that, at the equilibrium, stock holdings volatility as well as its ratio to stock price volatility are increasing functions of the stock price and interpret this finding in terms of the price-volume relation. We would like to thank the editor and two anonimous referees for valuable substantive comments. Our gratitude also to Franklin Allen, Kerry Back, Domenico Cuoco, Xavier Freixas, Sanford Grossman, Michel Habib, Lutz Hendricks, Richard Kihlstrom, Fernando Restoy, Mary Thomson, Jean-Luc Vila, participants to seminars at Birkbeck College, Carnegie-Mellon, Columbia, ESSEC, HEC, IAE, INSEAD, London Business School, London School of Economics, McGill, Michigan, National University of Singapore, Pompeu Fabra, North Carolina, Washington-St-Louis, Wharton, the Jornadas de Economía Financiera BBV, and the Meetings of the Society for Economic Dynamics and Control and the American Finance Association. Special thanks are due to Süleyman Basak for his enthusiastic support and many helpful suggestions. The usual disclaimer applies. We gratefully acknowledge the support of the BBV and Caja de Madrid Foundations and CREF (both authors) and of the Spanish Ministry of Education under DGICYT grant no. PB93-0388 (first author).     

Controlling portfolio skewness and kurtosis without directly optimizing third and fourth moments

In spite of their importance, third or higher moments of portfolio returns are often neglected in portfolio construction problems due to the computational difficulties associated with them. In this paper, we propose a new robust mean–variance approach that can control portfolio skewness and kurtosis without imposing higher moment terms. The key idea is that, if the uncertainty sets are properly constructed, robust portfolios based on the worst-case approach within the mean–variance setting favor skewness and penalize kurtosis.     

Time inconsistency and retirement planning

We quantify the welfare gains from better retirement planning using a model in which retirement planning is time inconsistent. A modest increase in a household’s planning horizon by just a few years generates large aggregate and individual welfare gains.     

Moving costs, nondurable consumption and portfolio choice

The substantial adjustment cost for housing affects nondurable consumption and portfolio allocations, as well as the frequency of housing transactions. A simple theoretical model, roughly calibrated, is used to assess the quantitative impact of adjustment costs on those decisions. The impact on portfolios is found to be significant, suggesting that housing wealth should be useful in empirical studies of portfolio choice. The welfare loss from the transaction cost is also substantial. The effect on nondurable consumption is small, however, so adjustment costs can explain only a small part of the equity premium puzzle.     

A nonsmooth, nonconvex model of optimal growth

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to 1, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches 1, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.     

Saving rates and portfolio choice with subsistence consumption

We analytically show that a common across rich/poor individuals Stone-Geary utility function with subsistence consumption in the context of a simple two-asset portfolio-choice model is capable of qualitatively and quantitatively explaining: (i) the higher saving rates of the rich, (ii) the higher fraction of personal wealth held in risky assets by the rich, and (iii) the higher volatility of consumption of the wealthier. On the contrary, time-variant “keeping-up-with-the-Joneses” weighted average consumption which plays the role of moving benchmark subsistence consumption gives the same portfolio composition and saving rates across the rich and the poor, failing to reconcile the model with what micro data say.