Geometric Mean Approximations of Individual Security and Portfolio Performance

Young, William E.; Trent, Robert H.

doi:10.2307/2329839

Cited by 94 publications

(39 citation statements)

References 15 publications

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“…6) examines this www.annualreviews.org Portfolio Theory: As I Still See Itapproximation using the annual returns on the nine securities used in the illustrative portfolio analysis discussed in chapter 2. Young & Trent (1969) investigate approximations to E½Ln(1 þ R) or, equivalently, the geometric mean (GM) and find the mean-variance approximation to be quite robust. Levy & Markowitz (1979) do similar experiments for a variety of utility functions and historical returns on mutual fund portfolios.…”

Section: Mean-variance Approximations To Eumentioning

confidence: 99%

Portfolio Theory: As I Still See It

Markowitz

2010

Annu. Rev. Financ. Econ.

121

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This essay summarizes my views on (a) the foundations of portfolio theory and its applications to current issues, such as the choice of criteria for practical risk-return analysis, and whether some form of risk-return analysis should be used in fact; (b) hypotheses about actual financial behavior, as opposed to idealized rational behavior, including two proofs of the fact that expected-utility maximizers would never prefer a multiple-prize lottery to all single-prize lotteries, as asserted in one of my 1952 papers; and (c) a simple proof of the theorem (which was initially greeted with some skepticism, especially by referees) that investors in capital asset pricing models do not get paid for bearing risk.

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Section: Mean-variance Approximations To Eumentioning

confidence: 99%

Portfolio Theory: As I Still See It

Markowitz

2010

Annu. Rev. Financ. Econ.

121

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“…See Chamberlain (1983). More important, various authors (Markowitz, 1959;Young and Trent, 1969;Levy and Markowitz, 1979;Dexter, Yu, and Ziemba, 1980;Pulley, 1981Pulley, , 1983Kroll, Levy, and Markowitz, 1984;Simaan, 1993) report that properly chosen mean-variance efficient portfolios give almost maximum expected utility for a wide variety of utility functions and return distributions like those of diversified investment portfolios. This includes portfolios of puts and calls, though not for portfolios consisting of a single put or call (Hlawitschka, 1994).…”

Section: Acknowledgmentsmentioning

confidence: 99%

The likelihood of various stock market return distributions, part 1: Principles of inference

Markowitz

Usmen²

1996

J Risk Uncertainty

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This is the first of two articles which apply certain principles of inference to a practical, financial question. The present article argues and cites arguments which contend that decision making should be Bayesian, that classical (R. A. Fisher, Neyman-Pearson) inference can be highly misleading for Bayesians as can the use of diffuse priors, and that Bayesian statisticians should show remote clients with a variety of priors how a sample implies shifts in their beliefs. We also consider practical implications of the fact that human decision makers and their statisticians cannot fully emulate Savage's rational decision maker.A companion article (Markowitz and Usmen, 1996) which follows in this issue describes how remote Bayesian clients should shift beliefs among various hypotheses concerning the probability distribution of daily changes in the Standard and Poor (S&P) 500 Index of stock prices, given a particular sample. The original motivation for the study was methodological. We wanted to see if useful data analysis could be performed on practical financial problems within constraints imposed by certain philosophical principles, namely, that financial research is primarily to improve financial decisions; rational decision making is Bayesian; the commonly used, commonly published classical (R.A. Fisher, Neyman-Pearson) inference methods are highly unreliable guides to Bayesians; the conjugate or diffuse priors frequently assumed in Bayesian studies are either restrictive (few hypotheses admit nontrivial conjugates) or are possibly highly misleading; and the Bayesian statistician should show remote clients, with a wide variety of priors, the extent to which they should shift beliefs, from prior to posterior, given the sample at hand (as opposed to assuming a single set of priors and showing the posterior beliefs implied by the sample mad these priors).

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“…and Ohlson ( 1975) present conditions under which mean and variance are asymptotically sufficient as the length of holding periods -that is, the intervals between portfolio revisions -approaches zero. For 'long' holding periods, for example for time between revisions as long as a year, , Young and Trent (1969), Levy and Markowitz (1979), Pulley (1981) and Kroll, Levy and Markowitz ( 1984) have each found mean-variance approximations to be quite accurate for a variety of utility functions and historical distributions of portfolio return.…”

Section: Mean-variance Analysis Harry M Markowitzmentioning

confidence: 99%

Finance

1989

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Geometric Mean Approximations of Individual Security and Portfolio Performance

Cited by 94 publications

References 15 publications

Portfolio Theory: As I Still See It

Portfolio Theory: As I Still See It

The likelihood of various stock market return distributions, part 1: Principles of inference

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