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A note on the kinks at the mean variance frontier

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TLDR
In this article, the standard portfolio case with short sales restrictions is analyzed and a new procedure is used to derive the efficient frontier, i.e. the characteristics of the mean variance frontier.
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This article is published in European Journal of Operational Research.The article was published on 1999-01-01 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Efficient frontier & Portfolio optimization.

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Citations
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Parametrically computing efficient frontiers of portfolio selection and reporting and utilizing the piecewise-segment structure

TL;DR: The software of parametric quadratic programming is utilised, the structure of efficient frontiers is analysed, two models to minimise rebalancing cost are proposed, and three models to transform them into linear programming or integer programming are proposed and solved.
Posted Content

Anatomy and Lessons of the Global Financial Crisis

TL;DR: In this article, the authors examined the influence of the efficient market and modern portfolio theories also the Li copula function on the U.S. financial markets, which contradicted all previous theories concerning the economic equilibrium.
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On analyzing and detecting multiple optima of portfolio optimization

TL;DR: It is proved the nonexistence of the multiple optima of an extension of the model of Merton and the risk of overlooking themultiple optima by (ordinary) quadratic programming is emphasized, and the software failure by parametric quadratics programming is reported.
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Producing the tangency portfolio as a corner portfolio

TL;DR: This paper introduces a method for which the tangency portfolio can be produced as a corner portfolio and shows that how this method can be used for tracing out the M-V efficient frontier when problem contains a riskless asset in which the borrowing is not allowed.
References
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Journal ArticleDOI

Short Sales Restrictions and Kinks on the Mean Variance Frontier

TL;DR: The authors showed that the truth lies between the two views, since the efficient frontier may or may not be kinked at a switching point, since a kink corresponds to a portfolio in which all assets have the same expected return.
Journal ArticleDOI

The explicit derivation of the efficient portfolio frontier in the case of degeneracy and general singularity

TL;DR: In this article, the efficient portfolio frontier is derived explicitly for cases in which short sales are not allowed and more than one variable vanishes in a point of investment returns (degenerate case).
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Frequently Asked Questions (4)
Q1. What are the contributions in "A note on the kinks at the mean variance frontier" ?

In this paper the standard portfolio case with short sales restrictions is analyzed. 

Since multiplying (5a) by r and using (3c), from (5) the authors have: u2 (fr 2 - 2dr + e) = p-r , from which the authors gain that u2 = (p-r)/( fr 2 - 2dr + e) (7a) and u1 = r(r-p)/( fr 2 - 2dr + e). (7b) As in (4) the value of variables x depends on only the Lagrange variables u1 and u2, (7) gives the solution. 

To analyze (2), let us suppose that for a given p, with y=0, the authors know the optimal status of the variables satisfying the Kuhn-Tucker conditions, and p is in an open interval where the value of every variable belonging to a set, let us call this set M, is positive, while the value of the variables not in M is zero at this interval. 

Taking the crucial second iteration when M2 = {2, 3} (M1 = {3}), the problem can be structured in the following way: N2 = {1}, a2 =[1], and 1+ε 2 V11 = , a1 = [3, 4], V21 = [0, 0].