Nonconvex Transaction Costs Research Articles

Nonconvex Transaction Costs and Land Rental Market Participation in Malawi

Nonconvex Transaction Costs and Land Rental Market Participation in Malawi

Cutting plane algorithms for mean-CVaR portfolio optimization with nonconvex transaction costs

This paper studies the mean-risk portfolio optimization problem with nonconvex transaction costs. We employ the conditional value-at-risk (CVaR) as a risk measure. There are a number of studies that aim at efficiently solving large-scale CVaR minimization problems. None of these studies, however, take into account nonconvex transaction costs, which are present in practical situations. To make a piecewise linear approximation of the transaction cost function, we utilized special ordered set type two constraints. Moreover, we devised a subgradient-based cutting plane algorithm to handle a large number of scenarios. This cutting plane algorithm needs to solve a mixed integer linear programming problem in each iteration, and this requires a substantial computation time. Thus, we also devised a two-phase cutting plane algorithm that is even more efficient. Numerical experiments demonstrated that our algorithms can attain near-optimal solutions to large-scale problems in a reasonable amount of time. Especially when rebalancing a current portfolio that is close to an optimal one, our algorithms considerably outperform other solution methods.

REBALANCE SCHEDULE OPTIMIZATION OF A LARGE SCALE PORTFOLIO UNDER TRANSACTION COST

This paper is concerned with an optimization problem associated with a rebalancing schedule of a large scale fund subject to nonconvex transaction cost. We will formulate this problem as a 0-1 mixed integer programming problem under linear constraints using absolute deviation as the measure of risk. This problem can be solved by an integer programming software if the size of the universe is small. However, it is still beyond the reach of the state-of-the-art technology to solve a large scale rebalancing problem. We will show that we can now solve these problems almost exactly within a practical amount of time by using an elaborate heuristic approach.

Impact of Land Certification on Land Rental Market Participation in Tigray Region, Northern Ethiopia

There is a renewed interest in whether land reforms can contribute to market development in Africa and whether land reforms can be pro-poor. This paper uses unique household panel data from Tigray region in Ethiopia to assess the impact of the 1998 low-cost land registration and certification reform on land rental market participation over a period of eight years after the reform, using random effects probit and tobit panel data models for land leased out and leased in, while correcting for unobservable heterogeneity and endogeneity of having certificate. The analysis revealed that the land reform contributed to increased land rental market participation. Female-headed households became more willing to rent out land and making land available for more efficient producers. Average areas leased out and leased in increased after certification. The land rental market remained characterised with significant and non-convex transaction costs also after the reform as evidenced by significant state dependence, a low response to own holding size and a high share of non-participation in the land market, leaving room for further improvement.

Integer programming approaches in mean-risk models

This paper is concerned with porfolio optimization problems with integer constraints. Such problems include, among others mean-risk problems with nonconvex transaction cost, minimal transaction unit constraints and cardinality constraints on the number of assets in a portfolio. These problems, though practically very important have been considered intractable because we have to solve nonlinear integer programming problems for which there exists no efficient algorithms. We will show that these problems can now be solved by the state- of-the-art integer programming methodologies if we use absolute deviation as the measure of risk.

Optimization of a Long-Short Portfolio under Nonconvex Transaction Cost

The purpose of this paper is to propose a practical branch and bound algorithm for solving a class of long-short portfolio optimization problem with concave and d.c. transaction cost and complementarity conditions on the variables. We will show that this algorithm can solve a problem of practical size and that the long-short strategy leads to a portfolio with significantly better risk-return structure compared with standard purchase only portfolio both in terms of ex-ante and ex-post performance.

Global Optimization Versus Integer Programming in Portfolio Optimization under Nonconvex Transaction Costs

This paper is concerned with a portfolio optimization problem under concave and piecewise constant transaction cost. We formulate the problem as nonconcave maximization problem under linear constraints using absolute deviation as a measure of risk and solve it by a branch and bound algorithm developed in the field of global optimization. Also, we compare it with a more standard 0---1 integer programming approach. We will show that a branch and bound method elaborating the special structure of the problem can solve the problem much faster than the state-of-the integer programming code.

Portfolio optimization under D.C. transaction costs and minimal transaction unit constraints

This paper addresses itself to a portfolio optimization problem under nonconvex transaction costs and minimal transaction unit constraints. Associated with portfolio construction is a fee for purchasing assets. Unit transaction fee is larger when the amount of transaction is smaller. Hence the transaction cost is usually a concave function up to certain point. When the amount of transaction increases, the unit price of assets increases due to illiquidity/market impact effects. Hence the transaction cost becomes convex beyond certain bound. Therefore, the net expected return becomes a general d.c. function (difference of two convex functions). We will propose a branch-and-bound algorithm for the resulting d.c. maximization problem subject to a constraint on the level of risk measured in terms of the absolute deviation of the rate of return of a portfolio. Also, we will show that the minimal transaction unit constraints can be incorporated without excessively increasing the amount of computation.

Consumer Durables and Inertial Behaviour: Estimation and Aggregation of (S, s) Rules for Automobile Purchases

The (S, s) model, originally introduced in the study of inventories (see Arrow et al. (1951), Scarf (1959)), has recently received renewed attention both in the durable consumption and in the investment and labour demand literatures. Caballero (1993), for instance, appeals to these type of models to explain the time series properties of durable expenditure and, in particular, the persistence or slow adjustment of such a variable. In this paper, I model the purchase behaviour of automobiles by U.S. households as an (S, s) rule. I estimate a flexible specification of such a rule using a large microeconomic data set and study some of the aggregate implications of this type of inertial behaviour. The paper is one of the first attempts at estimating directly the parameters of an (S, s) rule using micro data.' Because of this, some of the methodological issues concerning the specification and the estimation of (S, s) rules are relevant for many potential applications. Furthermore, the paper is one of the first to discuss and quantify the aggregate implications of an (S, s) rule estimated on micro data. In the presence of non-convex transaction costs, a full and consistent characterization of individual behaviour is very hard and typically requires strong restrictions. Grossman and Laroque (1991) prove that an (S, s) rule is optimal for a consumption and investment problem under very special circumstances. Some of their results were extended by Eberly (1991) and Beaulieu (1993a, b). Eberly (1991), in particular, has derived some closed-form solutions for durable consumption in the presence of transaction costs while Caballero and Engel (1994) construct a model of investment where an (S, s) rule is optimal. The main problem with these theoretical results is that it is only possible to show optimality of (S, s) rules under very stringent conditions. In particular, a necessary condition to derive them is that the optimization problem faced by an individual consumer can be reduced to a problem with a single state variable. Unfortunately, as pointed out by Bar-Ilan and Blinder (1992), even simple generalizations are extremely difficult to analyse

Mean-absolute deviation portfolio optimization model under transaction costs

We will propose a branch and bound algorithm for solving a portfolio optimization model under nonconvex transaction costs. It is well known that the unit transaction cost is larger when the amount of transaction is small while it remains stable up to a certain point and then increases due to illiquidity effects. Therefore, the transaction cost function is typically nonconvex. The existence of nonconvex transaction costs very much affects the optimal portfolio particularly when the amount of fund is small. However, the portfolio optimization problem under nonconvex transaction cost are largely set aside due to its computational difficulty. In fact, there are only a few studies which treated nonconvex costs in a rigorous manner. In this paper, we will propose a branch and bound algorithm for solving a mean-absolute deviation portfolio optimization model assuming that the cost function is concave. We will use a linear underestimating function for a concave cost function to calculate a good bound, and demonstrate that a fairly large scale problem can be solved in an efficient manner using the real stock data and transaction cost table in the Tokyo Stock Exchange. Finally, extension of our algorithm to rebalancing will be briefly touched upon.

MEAN-ABSOLUTE DEVIATION PORTFOLIO OPTIMIZATION MODEL UNDER TRANSACTION COSTS

We will propose a branch and bound algorithm for solving, a portfolio optimization model under nonconvex transaction costs. It is well known that the unit transaction cost is larger when the amount of transaction is small while it remains stable up to a certain point and then increases due to illiquidity effects. Therefore, the transaction cost function is typically nonconvex. The existence of nonconvex transaction costs very much affects the optimal portfolio particularly when the amount of fund is small. However, the portfolio optimization problem under nonconvex transaction cost are largely set aside due to its computational difficulty. In fact, there are only a few studies which treated nonconvex costs in a rigorous manner. In this paper, we will propose a branch and bound algorithm for solving a mean-absolute deviation portfolio optimization model assuming that the cost function is concave. We will use a linear underestimating function for a concave cost function to calculate a good bound, and demonstrate that a fairly large scale problem can be solved in an efficient manner using the real stock data and transaction cost table in the Tokyo Stock Exchange. Finally, extension of our algorithm to rebalancing will be briefly touched upon.

Malleable Property Rights and Smooth‐Pasting Conditions

In their classic paper on the evolution of property rights in the American West, Anderson and Hill take a historical view of the changing costs of defining and enforcing property rights, and show that ...by expressing the amount of property rights definition and enforcement activity as a function of marginal benefits and marginal costs, and by specifying the shift parameters for each function, it is possible to explain the existing structure of property rights in a society and provide a vehicle with which we can analyze changes in property rights over time. The authors show convincing historical evidence for their marginal adjustment hypothesis applied to land and livestock on the Great Plains from 1850 to 1900. In this paper the same viewpoint of endogenous institutional evolution is taken, but it is specified as malleable, changing in discrete jumps due to nonconvex transaction costs and uncertainty in water supplies and property rights rather than through a smooth marginal evolution. Despite a gradual increase in the expected value marginal product of water in the West, this study shows that institutional change is influenced by nonconvexities in costs and the inherent stochasticity in water supply. Because of these conditions, the economically optimal development of water property rights will continue to follow the historical precedence of discrete switches rather than smooth changes in property rights. Discussion of the changes facing water allocation and development in the West has moved from the topic of whether water markets can aid in the reallocation of water to questioning why there are so few examples (Young, Colby, McCormick). Implicit in this question is the assumption that, given the gains from trade based marginal value differences between regions or uses of water and a physical connection between the two locations, trade should occur. Commentators on this subject all recognize that the existence of gains from trade is a necessary but not sufficient condition for trade. The costs

Consumer Durables: Evidence on the Optimality of Usually Doing Nothing

The authors argue that lumpy, nonconvex transaction costs are the norm for a wide range of economic decisions, which are thus characterized by inertial behavior. Application of this idea to the consumption of durable goods yields an (S,s) decision rule, which, when aggregated, highlights the different expected behavior of average expenditure per purchase versus the number of purchases. The empirical implications of this rule are presented and compared to other theories. A battery of empirical tests generally supports the predictions of the model; in particular, it does a good job of explaining the time pattern of response of spending on durables to a change in income. Copyright 1992 by Ohio State University Press.