Multiperiod Portfolio Efficiency Analysis Via the Geometric Mean

Gressis, Nicolas; Hayya, Jack C.; Philippatos, George C.

doi:10.1111/j.1540-6288.1974.tb01451.x

Cited by 9 publications

(5 citation statements)

References 14 publications

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“…:

{\overset{R}{true}}_{I} = \prod_{i = 1}^{N} {\overset{false~}{R}}_{i} = {ln}^{- 1} [\sum_{t = 1}^{N} ln ({\overset{R}{true}}_{i})]

Assuming that the distribution of

{\overset{R}{true}}_{i}

is stationary (i.e. that the parameters of the distribution remain constant over time) with finite mean and variance 3 , it can be shown that

{\overset{R}{true}}_{I}

is asymptotically lognormal [1], [12]. This would indicate that the leptokurtosis observed in the distribution of daily returns will become less severe as the distribution of monthly, quarterly, and annual returns become successively closer to lognormality.…”

Section: Asymptotic Implication Of Sp and Sspmentioning

confidence: 99%

The Stable Paretian Distribution, Subordinated Stochastic Processes, and Asymptotic Lognormality: An Empirical Investigation

Upton¹,

Shannon²

1979

The Journal of Finance

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“…:

{\overset{R}{true}}_{I} = \prod_{i = 1}^{N} {\overset{false~}{R}}_{i} = {ln}^{- 1} [\sum_{t = 1}^{N} ln ({\overset{R}{true}}_{i})]

Assuming that the distribution of

{\overset{R}{true}}_{i}

is stationary (i.e. that the parameters of the distribution remain constant over time) with finite mean and variance 3 , it can be shown that

{\overset{R}{true}}_{I}

Section: Asymptotic Implication Of Sp and Sspmentioning

confidence: 99%

The Stable Paretian Distribution, Subordinated Stochastic Processes, and Asymptotic Lognormality: An Empirical Investigation

Upton¹,

Shannon²

1979

The Journal of Finance

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“…Assuming that the distribution of Rj is stationary (i.e. that the parameters of the distribution remain constant over time) with finite mean and variance3, it can be shown that R, is asymptotically lognormal [1,12]. This would indicate that the leptokurtosis observed in the distribution of daily returns will become less severe as the distribution of monthly, quarterly, and annual returns become successively closer to lognormality.…”

mentioning

confidence: 99%

The Stable Paretian Distribution, Subordinated Stochastic Processes, and Asymptotic Lognormality: An Empirical Investigation

Upton¹,

Shannon²

1979

The Journal of Finance

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I. IntroductionLOGNORMALITY OF ASSET RETURNS is a popular assumption in investigations of investor behavior. Empirical observation, however, has disclosed that daily returns are consistently more leptokurtic (are more peaked and have fatter tails) than lognormality indicates. Two responses to these empirical findings have evolved. The first was that the stable paretian' (SP) class of distribution, with a-characteristic <2, is better suited to the description of asset returns [7,9,18,20,23]. More recently the description of asset returns as a subordinated stochastic process (SSP) has developed [4, 6, 19, 21, 22, 24].The use of a daily period in investigations of the nature of the return distribution contrasts sharply with the use of monthly [3], quarterly [5], and annual [4, 15] returns in investigations of investor behavior. Several authors [2, 12, 13, 16] have noted that the nature of the return distribution may change as the period length changes. Section II and the appendix discuss this disparity and point out that the asymptotic tendency under the SSP approach is lognormality. Alternatively, the SP distribution reproduces itself asymptotically. Thus, the observed distributions of asset returns over longer period lengths have relevance for the SP/SSP controversy.The present paper, then has two purposes. The first is a direct empirical investigation of the suitability of the lognormal assumptions for returns to common stocks over monthly, quarterly, and annual periods. The second is to comment on the SP and SSP approaches by comparing the empirical observations to the asymptotic implications. The tests and comparisons are reported in Section III. Our results support the use of the lognormal assumption for the period lengths studied. We also conclude that the asymptotic tendencies of the return distribution are in agreement with the implications of the SSP approach. II. Asymptotic Implication of SP and SSPThe traditional justification of lognormality is based on a multiplicative version * The authors would like to thank Peter K. Clark for his insightful comments. ' While the description "stable" is often used in the literature, the distribution referred to is actually ln-stable, since the variable investigated is usually the ln of returns (price changes). Unfortunately, the literature often fails to discriminate between the two variables. See, for instance, Officer [20] p. 811, note 13. 1031

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“…Some papers that include studies of the wealth distribution when applying the GOP includes Hakansson (1971a), Gressis, Hayya, and Philippatos (1974), Michaud (1981) and Thorp (1998). Somewhat related to this is the study by Jean (1980), which relates the GOP to n-th order stochastic dominance.…”

Section: Notesmentioning

confidence: 99%

On the History of the Growth-Optimal Portfolio

Christensen

2012

Advances in Computer Science and Engineering: Texts

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The growth optimal portfolio (GOP) is a portfolio which has a maximal expected growth rate over any time horizon. As a consequence, this portfolio is sure to outperform any other significantly different strategy as the time horizon increases. This property in particular has fascinated many researchers in finance and mathematics created a huge and exciting literature on growth optimal investment. This paper attempts to provide a comprehensive survey of the literature and applications of the GOP. In particular, the heated debate of whether the GOP has a special place among portfolios in the asset allocation decision is reviewed as this still seem to be an area where some misconceptions exists. The survey also provides an extensive review of the recent use of the GOP as a pricing tool, in for instance the so-called "benchmark approach". This approach builds on the numéraire property of the GOP, that is, the fact that any other asset denominated in units of the GOP become a supermartingale

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Multiperiod Portfolio Efficiency Analysis Via the Geometric Mean

Cited by 9 publications

References 14 publications

The Stable Paretian Distribution, Subordinated Stochastic Processes, and Asymptotic Lognormality: An Empirical Investigation

The Stable Paretian Distribution, Subordinated Stochastic Processes, and Asymptotic Lognormality: An Empirical Investigation

The Stable Paretian Distribution, Subordinated Stochastic Processes, and Asymptotic Lognormality: An Empirical Investigation

On the History of the Growth-Optimal Portfolio

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