John D. Lamb

Data envelopment analysis models of investment funds

This paper develops theory missing in the sizable literature that uses data envelopment analysis to construct return–risk ratios for investment funds. It explores the production possibility set of the investment funds to identify an appropriate form of returns to scale. It discusses what risk and return measures can justifiably be combined and how to deal with negative risks, and identifies suitable sets of measures. It identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it. It identifies relationships between diversification, coherent measures of risk and stochastic dominance. It shows how the iterative procedure makes a practical difference using monthly returns of 30 hedge funds over the same time period. It discusses possible shortcomings of the procedure and offers directions for future research.

Resampling DEA estimates of investment fund performance

Data envelopment analysis (DEA) is attractive for comparing investment funds because it handles different characteristics of fund distribution and gives a way to rank funds. There is substantial literature applying DEA to funds, based on the time series of funds’ returns. This article looks at the issue of uncertainty in the resulting DEA efficiency estimates, investigating consistency and bias. It uses the bootstrap to develop stochastic DEA models for funds, derive confidence intervals and develop techniques to compare and rank funds and represent the ranking. It investigates how to deal with autocorrelation in the time series and considers models that deal with correlation in the funds’ returns.

A note on the weighted matching with penalty problem

Abstract Given a weight on each edge and a penalty on each vertex of a bipartite graph, the bipartite weighted matching with penalty problem is to find a matching that minimises the sum of the weights of the matched edges and the penalties of the unmatched vertices. It is shown that this problem can be reduced easily to the standard bipartite weighted matching problem. The method easily generalises to graphs that are not necessarily bipartite.

Optimal allocation of runs in a simulation metamodel with several independent variables

Cheng and Kleijnen (Oper. Res. 47(5) (1999) 762) propose a very general regression metamodel for modelling the output of a queuing system. Its main limitations are that the regression function is based on a polynomial and that it can use only one independent variable. These limitations are removed here. We derive an explicit formula for the optimal way of assigning simulation runs to the different design points.

Interactive implementation of optimal simulation experiment designs

An attractive feature of many simulation packages is their availability on desktop computers and their potential for allowing the user to run a simulation model under different conditions in a highly interactive way. Such a way of studying a system is attractive because of its immediacy and the direct control it offers the user. However, partly as a consequence of this, good practice in the use of the methodology of the design of experiments is not always followed. As a result the efficiency and effectiveness of the overall simulation study may not be as good as it should be. In this paper we investigate how design of experiments methodology can be explicitly incorporated into interactive desktop studies. In particular we show how the optimal design of experiments methodology proposed by Cheng and Kleijnen (1998) for studying queues with highly heteroscedastic output can be used to provide a front-end advisory interface for controlling and conducting the study of an actual system. To illustrate our discussion, we show how the interface can be set up for the SIMUL8 simulation package and show its use in the actual analysis of a particular queueing model.

Variable neighbourhood structures for cycle location problems

Variable neighbourhood search is a metaheuristic used mainly to tackle combinatorial optimization problems. Its performance depends on having a good variable neighbourhood structure: that is, a sequence of neighbourhoods that are ideally pairwise disjoint and contain feasible solutions further and further from a given feasible solution. This article defines a variable neighbourhood structure with these properties that is new for cycle location problems. It find bounds for the neighbourhood sizes and shows how to iterate over then when the cycle is a circuit. It tests the structure and iteration method using variable neighbourhood search on a range of median cycle problems and finds a neighbourhood size beyond which there is, on average, no benefit in applying local search. This neighbourhood size is found not to depend on problem size or bound on circuit length.

Making efficient simulation experiments interactively with a desktop simulation package

It has been shown how a design of simulation experiments methodology can be used interactively with practical simulation models constructed in a desktop simulation package (SIMUL8). The methodology includes new ideas on how to improve the accuracy of a simulation response. It is implemented as a set of computer program modules that are not specific to a particular simulation model and provide an interface that lets the modeller construct an efficient simulation experiment with only an operational understanding of how the methodology works. The methodology and program modules are illustrated with a practical simulation model, and the results show how they can improve simulation response with negligible increase in computational effort.

Novel supervisor-searcher cooperation algorithms for minimization problems with strong noise

This work continues the investigation in Ref. [1]: designing minimization algorithms in the framework of supervisor and searcher cooperation (SSC). It explores a wider range of possible supervisors and search engines to be used in the construction of SSC algorithms. Global convergence is established for algorithms with general supervisors and search engines in the absence of noise, and the convergence rate is studied. Both theoretical analysis and numerical results illustrate the appealing attributes of the proposed algorithms.

Making Cornish–Fisher Distributions Fit

The truncated Cornish–Fisher inverse expansion is well known. It is used, for example, to approximate value-at-risk and conditional value-at-risk. It is known that this expansion gives a distribution for limited skewness and kurtosis and that the distribution may be a poor fit. drawing on Maillard (2012) we show how to find a unique corrected Cornish–Fisher distribution efficiently for a wide range of skewness and kurtosis. We show it has a unimodal density and a quantile function that is twice continuously differentiable as a function of mean, variance, skewness and kurtosis. We show how to obtain random variates efficiently and how to test goodness-of-fit. We apply the Cornish–Fisher distribution to fit hedge-fund returns and estimate conditional value-at risk. Finally, we investigate various generalisations of the Cornish–Fisher distributions and show they do not have the same desirable properties.

Resampling Data Envelopment Analysis (DEA) Estimates of Investment Fund Performance

Data envelopment analysis (DEA) is attractive for comparing investment funds because it handles different characteristics of fund distribution and gives a way to rank funds. There is substantial literature applying DEA to funds, based on the time series of funds’ returns. This article looks at the issue of uncertainty in the resulting DEA efficiency estimates, investigating consistency and bias. It uses the bootstrap to develop stochastic DEA models using sample Hedge funds, derive confidence intervals and develop techniques to compare and rank funds and represent the ranking. It investigates how to deal with autocorrelation in the time series and considers models that deal with correlation in the funds’ returns.