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A Note on the Kinks at the Mean Variance Frontier
TL;DR: In this paper the standard portfolio case with short sales restrictions is analyzed and the sufficient condition is given here and a new procedure is used to derive the efficient frontier, i.e. the characteristics of the mean variance frontier.
Abstract: In this paper the standard portfolio case with short sales restrictions is analyzed.Dybvig pointed out that if there is a kink at a risky portfolio on the efficient frontier, then the securities in this portfolio have equal expected return and the converse of this statement is false.For the existence of kinks at the efficient frontier the sufficient condition is given here and a new procedure is used to derive the efficient frontier, i.e. the characteristics of the mean variance frontier.
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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.
Abstract: Portfolio selection is recognised as the birth-place of modern finance; portfolio optimisation has become a developed tool. However, efficient frontiers are piece-wisely made up by connected parabo...
10 citations
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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.
Abstract: Emerging countries’ and particularly China's savings in the U.S. money market financed the U.S. overconsumption in the 2000s, which eventually led to the global financial crisis. The real estate mortgage market was the starting point. Non-equilibrium processes have been launched in the U.S. financial markets, which contradicted all previous theories concerning the economic equilibrium. The economic sciences do not have a model or empirically applied theories to this new situation. So the crisis could not be prevented nor predicted. The question is to what extent the existing market theories, the computational methods and the latest financial products may be responsible for the non-equilibrium. The paper examines these questions, namely the influence of the efficient market and modern portfolio theories also the Li copula function on the U.S. investment market. The problematic of moral hazard, greed, credit rating, corporate governance, limited liability and market regulation cannot be ignored neither. In conclusion, the author outlines a possible alternative measure against the outbreak of a new crise, indicates new trends in the research and draws lessons from the Hungarian economic policy.
7 citations
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.
Abstract: Portfolio selection is widely recognized as the birth-place of modern finance; portfolio optimization has become a developed tool for portfolio selection by the endeavor of generations of scholars. Multiple optima are an important aspect of optimization. Unfortunately, there is little research for multiple optima of portfolio optimization. We present examples for the multiple optima, emphasize the risk of overlooking the multiple optima by (ordinary) quadratic programming, and report the software failure by parametric quadratic programming. Moreover, we study multiple optima of multiple-objective portfolio selection and prove the nonexistence of the multiple optima of an extension of the model of Merton. This paper can be a step-stone of studying the multiple optima.
4 citations
Cites background from "A Note on the Kinks at the Mean Var..."
...[27] comment the work of [7] and study the sufficient conditions for kinks....
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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.
Abstract: One-fund theorem states that an efficient portfolio in a Mean-Variance (M-V) portfolio selection problem for a set of some risky assets and a riskless asset can be represented by a combination of a unique risky fund (tangency portfolio) and the riskless asset In this paper, we introduce a method for which the tangency portfolio can be produced as a corner portfolio So, the tangency portfolio can be computed easily and fast by any algorithm designed for tracing out the M-V efficient frontier via computing the corner portfolios Moreover, we show 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
2 citations
Additional excerpts
..., the points of nondifferentiability (see [2, 4, 18])....
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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.
Abstract: With a short sales restriction, there may be switching points along the mean variance frontier corresponding to changes in the set of assets held. Traditional wisdom holds that each switching point corresponds to a kink, while Ross has claimed that kinks never occur. This paper shows that the truth lies between the two views, since the efficient frontier may or may not be kinked at a switching point. There is some indication that kinks are rare, since a kink corresponds to a portfolio in which all assets have the same expected return.
46 citations
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).
14 citations
"A Note on the Kinks at the Mean Var..." refers background in this paper
...Thus (6) is a convex parabola in r and its discriminant is 4(d2 - ef) which is always negative except when ai = j for every i,j ∈M and in this case its value is zero (see Vörös (1987))....
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...Citation for published version (APA): Vörös, J., Kriens, J., & Strijbosch, L. W. G. (1997). A Note on the Kinks at the Mean Variance Frontier....
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...Thus (6) is a convex parabola in r and its discriminant is 4(d 2 - ef) which is always negative except when a i = j for every i,j ∈M and in this case its value is zero (see Vörös (1987))....
[...]
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.
Abstract: Portfolio selection is recognised as the birth-place of modern finance; portfolio optimisation has become a developed tool. However, efficient frontiers are piece-wisely made up by connected parabo...
10 citations
Posted Content•
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.
Abstract: Emerging countries’ and particularly China's savings in the U.S. money market financed the U.S. overconsumption in the 2000s, which eventually led to the global financial crisis. The real estate mortgage market was the starting point. Non-equilibrium processes have been launched in the U.S. financial markets, which contradicted all previous theories concerning the economic equilibrium. The economic sciences do not have a model or empirically applied theories to this new situation. So the crisis could not be prevented nor predicted. The question is to what extent the existing market theories, the computational methods and the latest financial products may be responsible for the non-equilibrium. The paper examines these questions, namely the influence of the efficient market and modern portfolio theories also the Li copula function on the U.S. investment market. The problematic of moral hazard, greed, credit rating, corporate governance, limited liability and market regulation cannot be ignored neither. In conclusion, the author outlines a possible alternative measure against the outbreak of a new crise, indicates new trends in the research and draws lessons from the Hungarian economic policy.
7 citations
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.
Abstract: Portfolio selection is widely recognized as the birth-place of modern finance; portfolio optimization has become a developed tool for portfolio selection by the endeavor of generations of scholars. Multiple optima are an important aspect of optimization. Unfortunately, there is little research for multiple optima of portfolio optimization. We present examples for the multiple optima, emphasize the risk of overlooking the multiple optima by (ordinary) quadratic programming, and report the software failure by parametric quadratic programming. Moreover, we study multiple optima of multiple-objective portfolio selection and prove the nonexistence of the multiple optima of an extension of the model of Merton. This paper can be a step-stone of studying the multiple optima.
4 citations