Impossible Frontiers

(Im)Possible Frontiers: A Comment

The existence of mean-variance efficient positive portfolios – portfolios with no negative weights – is a key requirement for equilibrium in the Capital Asset Pricing Model (CAPM). Brennan and Lo (2010) define an “impossible frontier” as a frontier on which all portfolios have at least one negative weight. They prove that for randomly drawn covariance matrices the probability of obtaining an im...

Reply to “(Im)Possible Frontiers: A Comment”

In Brennan and Lo (2010), a mean-variance efficient frontier is defined as “impossible” if every portfolio on that frontier has negative weights, which is incompatible with the Capital Asset Pricing Model (CAPM) requirement that the market portfolio is mean-variance efficient. We prove that as the number of assets n grows, the probability that a randomly chosen frontier is impossible tends to o...

Stretching EU Frontiers Toward East: The Consequences For Agricultural Trade Integration

Estimating Most Productive Scale Size with Double Frontiers in Data Envelopment Analysis using Negative Data

In this paper, it is assumed that the “Decision Making Units“( ) are consist of positive and negative input and output. Firstly, the optimistic and pessimistic models have been suggested by using negative data and then units with most productive scale size are measured in optimistic and pessimistic models. These productive values are compared with double frontiers and Hurwicz’s Criterion to obt...

Differential Characteristics of Efficient Frontiers in DEA with Weight Restrictions

The non-differentiability and implicit definition of boundary of production possibility set (PPS) in data envelopment analysis (DEA) are two important difficulties for obtaining directional characteristics, including different elasticity measures and marginal rates of substitution. Also, imposing weight restrictions in DEA models have some shortcomings and misunderstandings. In this paper we ut...