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.     

An Improved Two‐step Regularization Scheme for Spot Volatility Estimation

We are concerned with the problem of spot volatility estimation in the presence of microstructure noise. We introduce an estimator based on the technique of multi‐step regularization. A preliminary form for such an estimator was proposed in Ogawa (2008) and was shown to work in a real‐time manner. However, the main drawback of this scheme is that it needs a lot of observation data. The aim of the present paper is to introduce an improvement to this scheme, such that the modified estimator can work more efficiently and with a data set of smaller size. The technical aspects of implementation of the proposed scheme and its performance on simulated data are analysed. The scheme is tested against other spot volatility estimators, namely a realized volatility type estimator, the Fourier estimator and three kernel estimators.     

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.     

Non-addictive habits: optimal consumption-portfolio policies

We formulate a model of preferences with non-addictive habits, where consumption is required to be non-negative at all times, but can fall below a “standard of living” index that aggregates past consumption. We study the consumption-portfolio problem taking account of the non-negativity constraint on consumption, and provide a constructive proof for the existence of an optimal policy on a finite time-horizon [0,T]. We show that the consumption constraint binds up to an endogenous stopping time τ∗∈[0,T], after which it remains slack until T. A decomposition of constrained consumption involving an Asian average-strike capped call-option is demonstrated.     

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.     

Lifetime consumption and investment: Retirement and constrained borrowing

Retirement flexibility and inability to borrow against future labor income can significantly affect optimal consumption and investment. With voluntary retirement, there exists an optimal wealth-to-wage ratio threshold for retirement and human capital correlates negatively with the stock market even when wages have zero or slightly positive market risk exposure. Consequently, investors optimally invest more in the stock market than without retirement flexibility. Both consumption and portfolio choice jump at the endogenous retirement date. The inability to borrow limits hedging and reduces the value of labor income, the wealth-to-wage ratio threshold for retirement, and the stock investment.     

Financial liberalization,private investment and portfolio choice: Financialization of real sectors in emerging markets

Using firm level panel data, we analyze the impacts of rates of return gap between financial and fixed investments under uncertainty on real investment performance in three emerging markets, Argentina, Mexico and Turkey. Employing a portfolio choice model to explain the low fixed investment rates in developing countries during the 1990s, we suggest that rather than investing in irreversible long-term fixed investments, firms may choose to invest in reversible short-term financial investments depending on respective rates of returns and the overall uncertainty in the economy. The empirical results show that increasing rates of return gap and uncertainty have an economically and statistically significant fixed investment reducing effect while the opposite is true with respect to financial investments.     

Investment under Uncertainty, Debt and Taxes

It is common practice in financial derivative valuation to use a discount factor based on the riskless debt rate. But, to what extent is this discount factor appropriate for cash flows emerging in capital budgeting? To answer this question, we introduce a framework for real asset valuation that considers both personal and corporate taxation. We first discuss broad circumstances under which personal taxes do not affect valuation. We show that the appropriate discount rate for equity‐financed flows in a risk‐neutral setting is an equity rate that differs from the riskless debt rate by a tax wedge due to the presence of personal taxation. We extend this result to the valuation of the interest tax shield for exogenous debt policy with default risk. Interest tax shields, which accrue at a net rate corresponding to the difference between the corporate tax rate and a tax rate related to the personal tax rates, can have either positive or negative values. We also provide an illustrative real options application of our valuation approach to the case of an option to delay investment in a project, showing that the application of Black and Scholes formula may be incorrect in presence of personal taxes.     

Bond Price and Impulse Response Function for the Balduzzi, Das, Foresi and Sundaram (1996) Model

In this paper, we analyse the Affine Term Structure Model (ATSM) proposed by Balduzzi, Das, Foresi and Sundaram (BDFS, 1996) and provide the closed-form expression of the bond price. In addition, we extend the notion of Impulse Response Function to the class of ATSM. We show that it is closely related to the duration measure, and we compute it explicitly in the BDFS model.     

Optimal annuitization, uncertain survival probabilities, and maxmin preferences

We consider a life-cycle model with bequest motives, and assume that the individual does not know his/her survival probability and has maxmin utility preferences; we show that it is optimal not to annuitize but to purchase pure life insurance policies instead.     

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.     

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.     

Occupational choice, incentives and wealth distribution

We consider a model of occupational choice in large economies where individuals differ in their wealth endowment. Individuals can remain self-employed or engage in productive matches with another individual, i.e., form firms. Matches are subject to a moral hazard problem with limited liability. The division of the gains from such matches is determined by competitive forces. When the incentive problem is asymmetric, matches are typically wealth-heterogeneous, with richer individuals choosing the occupation for which incentives are more important. The utilities attained within a match depend on the wealth distribution and changes in the latter give rise to ‘trickle down’ effects.     

The dynamics of a complex system: The exchange rate crisis in Southeast Asia

We investigate the dynamics of the exchange rate market just after and prior to the 1997 crisis. The return of the exchange rate is well characterized by a power law, with the relaxation exponent to vary significantly across countries.     

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.     

Risk aversion and allocation to long-term bonds

As risk aversion approaches infinity, the portfolio of an investor with utility over consumption at time T is shown to converge to the portfolio consisting entirely of a bond maturing at time T. Previous work on bond allocation requires a specific model for equities, the term structure, and the investor's utility function. In contrast, the only substantive assumption required for the analysis in this paper is that markets are complete. The result, which holds regardless of the underlying investment opportunities and the utility function, formalizes the “preferred habitat” intuition of Modigliani and Sutch (Amer. Econom. Rev. 56 (1966) 178).     

Relative deprivation and migration preferences

In this letter, we overcome the existing shortages with respect to the assignment of individuals to reference groups and are the first to show that individual aversion to relative deprivation plays a decisive role in shaping migration preferences.     

Modeling non-monotone risk aversion using SAHARA utility functions

We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk averse for very low values of wealth. The class contains the well-known exponential and power utility functions as limiting cases. We investigate the optimal investment problem under SAHARA utility and derive the optimal strategies in an explicit form using dual optimization methods. We also show how SAHARA utility functions extend the class of contingent claims that can be valued using indifference pricing in incomplete markets.     

EARTHQUAKE RISKS AND LAND PRICES: EVIDENCE FROM THE TOKYO METROPOLITAN AREA*

The current paper empirically addresses risk aversion of households and firms toward earthquake risks using a hazard map compiled for the entire region by the Tokyo metropolitan government in 1998. It finds strong evidence for the impact of earthquake risks on land pricing; land prices have been substantially lower in risky areas than in safe areas. That impact became more evident in the 1990s than in the 1980s, indicating that households and firms were becoming more sensitive to earthquake risks. In addition, this paper carefully examines the consistency of the estimated magnitude of earthquake risk premiums within a framework of the expected utility hypothesis.     

On the Use of the Moving Average Trading Rule to Test for Weak Form Efficiency in Capital Markets

The examination for the possible existence of predictive power in the moving average trading rule has been used extensively to test the hypothesis of weak form market efficiency in capital markets. This work focuses mainly on the study of the variation of the moving average (MA) trading rule performance as a function of the length of the longer MA. Empirical analysis of daily data from NYSE and the Athens Stock Exchange reveal high variability of the performance of the MA trading rule as a function of the MA length and on some occasions the series of successive trading rule total returns is non‐stationary. These findings have direct implications in weak form market efficiency testing. Indeed, given this high variability of the performance of the MA trading rule, by just finding out that trading rules with some specific combinations of MA lengths can or cannot beat the market, as is the case in most of the published work thus far, is not enough evidence for or against the existence of weak form market efficiency. Results also show that on average in about three out of four cases trading rule signals are false, a fact that leaves a lot of space for improved trading rule performance if trading rule signals are combined with other information (e.g. filters, or volume of trade). Finally, some evidence of enhanced trading rule performance for the shorter MA lengths was found. This enhanced performance is partly attributed to the higher probability that a trading rule signal is not a whipsaw, as well as to the larger number of days out‐of‐the‐market which are associated with shorter MA lengths.