Relative Effectiveness of Efficiency Criteria for Portfolio Selection
01 Mar 1970-Journal of Financial and Quantitative Analysis (Cambridge University Press)-Vol. 5, Iss: 01, pp 63-76
TL;DR: In this article, individual decisions about investment may be regarded as choices among alternative probability distributions of net returns, assuming that these distributions are completely known and independent of initial wealth positions, and that individuals determine the preferred portfolio of investment in accordance with a given, consistent set of preferences.
Abstract: Individual decisions about investment may be regarded as choices among alternative probability distributions of net returns. It is assumed that these distributions are completely known and independent of initial wealth positions, and that individuals determine the preferred portfolio of investment in accordance with a given, consistent set of preferences.
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TL;DR: In this paper, the first-, second-and third-order stochastic dominance rules are discussed with an emphasis on the development in the area since the 1980s, focusing on the early 1970s.
Abstract: While Stochastic Dominance has been employed in various forms as early as 1932, it has only been since 1969-1970 that the notion has been developed and extensively employed in the area of economics, finance, agriculture, statistics, marketing and operations research.
In this survey, the first-, second-and third-order stochastic dominance rules are discussed with an emphasis on the development in the area since the 1980s.
879 citations
TL;DR: In this article, the Third Order Stochastic Dominance (TSD) rule is shown to be the optimal rule when comparing uncertain prospects with equal means, and in the general case of unequal means, no known selection rule uses both necessary and sufficient conditions for dominance.
831 citations
Cites background or methods or result from "Relative Effectiveness of Efficienc..."
...Algorithms to obtain the admissible sets are outlined in Levy and Hanoch (1970) and Levy and Samat (1970) and an algorithm which is efficient even for large numbers of alternatives is provided in Porter, Wart and Ferguson (1973)....
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...…rules for ordering uncertain prospccrs 97 rather than variance, has been proposed [Mao (1970) Markowitz (1970)] as a measure of risk on the grounds that semivariance concentrates on reducing losses as opposed to variance which considers extreme gains, as well as extreme losses, as undesirable....
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...Hence, as is to be theoretically expected, and has been empirically verified by Levy and Hanoch (1970) Levy and Sarnat (1970) and Porter and Gaumnitz (1972) a large proportion of the given set of alternatives will still be members of the FSD admissible set; this restricts the practical…...
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...…Porter, Wart and Ferguson (1973) have developed an algorithm to obtain the admissible set for the TSD rule,’ which is ‘This algorithm also obtains FSD and SSD admissible sets; Levy and Hanoch (1970) and Levy and Sarnat (1970) have also provided algorithms to obtain FSD and SSD admissible sets....
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...[This is empirically varified in Levy and Hanoch (1970), Levy and Samat (1970). and Porter and Gaumnitz (1972).]...
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338 citations
TL;DR: This paper develops the first operational tests of portfolio efficiency based on the general stochastic dominance criteria that account for an infinite set of diversification strategies by reexpressing the SD criteria in T-dimensional Euclidean space, with elements representing rates of return in different states of nature.
Abstract: This paper develops the first operational tests of portfolio efficiency based on the general stochastic dominance (SD) criteria that account for an infinite set of diversification strategies. The main insight is to preserve the cross-sectional dependence of asset returns when forming portfolios by reexpressing the SD criteria inT-dimensional Euclidean space, with elements representing rates of return inT different states of nature. We characterize subsets of this state-space that dominate a given evaluated return vector by first- and second-order SD. This allows us to derive simple SD efficiency measures and test statistics, computable by standard mathematical programming algorithms. The SD tests and efficiency measures are illustrated by an empirical application that analyzes industrial diversification of the market portfolio.
237 citations
TL;DR: This article defined the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble and characterized this index by axioms, chief among them a "duality" axiom that, roughly speaking, asserts that less risk-averse individuals accept riskier gambles.
Abstract: Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a “duality” axiom that, roughly speaking, asserts that less risk‐averse individuals accept riskier gambles. The index is positively homogeneous, continuous, and subadditive; respects first‐ and second‐order stochastic dominance; and for normally distributed gambles is half of variance/mean. Examples are calculated, additional properties are derived, and the index is compared with others.
233 citations
References
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Book•
01 Jan 1944
TL;DR: Theory of games and economic behavior as mentioned in this paper is the classic work upon which modern-day game theory is based, and it has been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations.
Abstract: This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published "Theory of Games and Economic Behavior." In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.
19,337 citations
TL;DR: In this article, the authors derived the liquidity preference schedule from some assumptions regarding the behavior of the decision-making units of the economy, and those assumptions are the concern of this paper.
Abstract: One of basic functional relationships in the Keynesian model of the economy is the liquidity preference schedule, an inverse relationship between the demand for cash balances and the rate of interest. This aggregative function must be derived from some assumptions regarding the behavior of the decision-making units of the economy, and those assumptions are the concern of this paper.
3,727 citations
"Relative Effectiveness of Efficienc..." refers methods in this paper
...This is the most widely used efficiency criterion for portfolio selection, as developed by Markowitz [15] and as elaborated by Tobin [19]....
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TL;DR: In this paper, the authors suggest that an important class of reactions of individuals to risk can be rationalized by a rather simple extension of orthodox utility analysis, i.e., individuals frequently must, or can, choose among alternatives that differ, among other things, in the degree of risk to which the individual will be subject.
Abstract: T vHE purpose of this paper is to suggest that an important class of reactions of individuals to risk can be rationalized by a rather simple extension of orthodox utility analysis. Individuals frequently must, or can, choose among alternatives that differ, among other things, in the degree of risk to which the individual will be subject. The clearest examples are provided by insurance and gambling. An individual who buys fire insurance on a house he owns is accepting the certain loss of a small sum (the insurance premium) in preference to the combination of a small chance of a much larger loss (the value of the house) and a large chance of no loss. That is, he is choosing certainty in preference to uncertainty. An individual who buys a lottery ticket is subjecting himself to a large chance of losing a small amount (the price of the lottery ticket) plus a small chance of winning a large amount (a prize) in preference to avoiding both risks. He is choosing uncertainty in preference to certainty.
2,865 citations
"Relative Effectiveness of Efficienc..." refers methods in this paper
...16This is somewhat similar to the funetion described by Friedman and Savage [7], which serves to explain simultaneous insuranee and gambling strategies....
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1,748 citations
"Relative Effectiveness of Efficienc..." refers background or methods in this paper
...This studyfs purpose is to empirically compare the relative effectiveness of various efficiency criteria for portfolio selection proposed in the literature [8], [9], [10], [11] and to demonstrate the (inverse) relationship between the strength of assumptions about utility and the size of the efficient subset....
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...n-1 8See Hanoeh and Levy [11] and Hadar and Russel [8]....
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...This criterion was developed by Hanoch and Levy [11], by Hammond [9], and also (for a less general case) by Hadar and Russel [8]....
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TL;DR: In this paper, an analysis of the first step of the decision-making process of an individual decision maker among alternative risky ventures is presented, in terms of a single dimension such as money, both for the utility functions and for the probability distributions.
Abstract: Publisher Summary The choice of an individual decision maker among alternative risky ventures may be regarded as a two-step procedure. The decision maker chooses an efficient set among all available portfolios, independently of his tastes or preferences. Then, the decision maker applies individual preferences to this set to choose the desired portfolio. The subject of this chapter is the analysis of the first step. It deals with optimal selection rules that minimize the efficient set by discarding any portfolio that is inefficient in the sense that it is inferior to a member of the efficient set, from point of view of each and every individual, when all individuals' utility functions are assumed to be of a given general class of admissible functions. The analysis presented in the chapter is carried out in terms of a single dimension such as money, both for the utility functions and for the probability distributions. However, the results may easily be extended, with minor changes in the theorems and the proofs, to the multivariate case. The chapter explains a necessary and sufficient condition for efficiency, when no further restrictions are imposed on the utility functions. It presents proofs of the optimal efficiency criterion in the presence of general risk aversion, that is, for concave utility functions.
1,160 citations