Topic
Efficient frontier
About: Efficient frontier is a research topic. Over the lifetime, 2634 publications have been published within this topic receiving 59935 citations. The topic is also known as: portfolio frontier.
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TL;DR: In this article, a test for the ex ante efficiency of a given portfolio of assets is analyzed, and the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean-variance efficient frontier is analyzed.
Abstract: A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean-variance efficient frontier. Several intuitive interpretations of the test are provided, including a simple mean-standard deviation geometric explanation. A univariate test, equivalent to our multivariate-based method, is derived, and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected. Empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics.
2,129 citations
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TL;DR: In this paper, the authors discuss the mathematical programming approach to frontier estimation known as Data Envelopment Analysis (DEA) and examine the effect of model orientation on the efficient frontier.
1,873 citations
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TL;DR: In this article, a portfolio optimization model using the L1 risk (mean absolute deviation risk) function can remove most of the difficulties associated with the classical Markowitz's model while maintaining its advantages over equilibrium models.
Abstract: The purpose of this paper is to demonstrate that a portfolio optimization model using the L1 risk (mean absolute deviation risk) function can remove most of the difficulties associated with the classical Markowitz's model while maintaining its advantages over equilibrium models In particular, the L1 risk model leads to a linear program instead of a quadratic program, so that a large-scale optimization problem consisting of more than 1,000 stocks may be solved on a real time basis Numerical experiments using the historical data of NIKKEI 225 stocks show that the L1 risk model generates a portfolio quite similar to that of the Markowitz's model within a fraction of time required to solve the latter
1,408 citations
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TL;DR: In this paper, the authors consider the execution of portfolio transactions with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact, and they explicitly construct the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty.
Abstract: We consider the execution of portfolio transactions with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. For a simple linear cost model, we explicitly construct the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty. We may then select optimal strategies either by minimizing a quadratic utility function, or by minimizing Value at Risk. The latter choice leads to the concept of Liquidity-adjusted VAR, or L-VaR, that explicitly considers the best tradeoff between volatility risk and liquidation costs. ∗We thank Andrew Alford, Alix Baudin, Mark Carhart, Ray Iwanowski, and Giorgio De Santis (Goldman Sachs Asset Management), Robert Ferstenberg (ITG), Michael Weber (Merrill Lynch), Andrew Lo (Sloan School, MIT), and George Constaninides (Graduate School of Business, University of Chicago) for helpful conversations. This paper was begun while the first author was at the University of Chicago, and the second author was first at Morgan Stanley Dean Witter and then at Goldman Sachs Asset Management. †University of Toronto, Departments of Mathematics and Computer Science; almgren@math.toronto.edu ‡ICor Brokerage and Courant Institute of Mathematical Sciences; Neil.Chriss@ICorBroker.com
1,258 citations
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TL;DR: In this paper, a nonparametric estimator based on the concept of expected minimum input function (or expected maximal output function) is proposed, which is related to the FDH estimator but will not envelop all the data.
1,023 citations