Evidence on the “Growth‐optimum” Model

Roll, Richard

doi:10.1111/j.1540-6261.1973.tb01378.x

Cited by 41 publications

(5 citation statements)

References 21 publications

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“… 16. Our log CAPM is in ‘payoffs form’ and is consistent with the ‘returns form’ of this same log CAPM in Roll (1973) and Pennacci (2008: 116). …”

supporting

confidence: 83%

“…For a summary of some of the applications and extensions of Kelly’s invention in both gambling and financial markets, see MacLean et al (2011a). In professional gambling, the theoretical works on log-optimal capital growth produced by Thorp et al, including curiously mainstream finance authorities Markowitz (1959, 1976, 2006b), Roll (1973), Elton and Gruber (1974) and Rubinstein (1976), have a mythical status that goes beyond even the zealous affection for mean-variance analysis in corporate finance. 13…”

Section: Three Schools Of Rational Decision-makingmentioning

confidence: 99%

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Capital budgeting and Kelly betting

Johnstone

2022

Australian Journal of Management

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Capital investments are easily interpreted as bets and vice versa. The mathematical theory of betting, often known as ‘Kelly betting’, has implications for all financial decision-making under uncertainty. There have been attempts to exploit Kelly betting methods in financial portfolio optimization, but there has been little analysis of conventional capital budgeting methods against a Kelly framework. A simple comparison between methods reveals that capital budgeting decisions made using conventional finance methods can embed the error that Kelly theorists call ‘overbetting’. The outcome of overbetting is that the firm reduces its expected compound capital growth rate while simultaneously adding to the volatility of its anticipated growth path. That unfortunate pairing is mathematically precluded under Kelly betting rules but is implicitly, albeit unknowingly, sanctioned by accepted capital budgeting practices in finance. JEL Classification: G11, G12, G31

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“… 16. Our log CAPM is in ‘payoffs form’ and is consistent with the ‘returns form’ of this same log CAPM in Roll (1973) and Pennacci (2008: 116). …”

supporting

confidence: 83%

Section: Three Schools Of Rational Decision-makingmentioning

confidence: 99%

Capital budgeting and Kelly betting

Johnstone

2022

Australian Journal of Management

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“…Both Roll (1973) and Fama and Macbeth (1974) suggests that the market portfolio should approximate the GOP and both use an index as a GOP candidate 31 and both are unable to reject the conclusion that the GOP is well approximated by, the market portfolio. Using the first order condition as a test of growth optimality is also done by Long (1990), Hentschel and Long (2004).…”

Section: Notesmentioning

confidence: 99%

“…Possibly the first study to contain an extensive empirical study of the GOP was Roll (1973). Both Roll (1973) and Fama and Macbeth (1974) suggests that the market portfolio should approximate the GOP and both use an index as a GOP candidate 31 and both are unable to reject the conclusion that the GOP is well approximated by, the market portfolio.…”

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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“…Our result shows that in a dynamic general equilibrium, relative market values of assets are determined by the relative dividends of those assets. Valuation formulas for economies with CRRA utility are established in the finance literature (see, e.g., Roll (1973), Kraus andLitzenberger (1975), andRubinstein (1976)). Note, however, that in contrast to the standard partial equilibrium point of view, our valuation formulas take all feedback effects into account and are expressed solely in terms of such exogenous characteristics of the economy as the dividend process, the degree of risk aversion, and the time preference.…”

Section: Introductionmentioning

confidence: 99%

Dynamic General Equilibrium andT-Period Fund Separation

Gerber¹,

Hens

Woehrmann³

2010

J. Financ. Quant. Anal.

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In a dynamic general equilibrium model, we derive conditions for a mutual fund separation property by which the savings decision is separated from the asset allocation decision. With logarithmic utility functions, this separation holds for any heterogeneity in discount factors, while the generalization to constant relative risk aversion holds only for homogeneous discount factors but allows for any heterogeneity in endowments. The logarithmic case provides a general equilibrium foundation for the growth-optimal portfolio literature. Both cases yield equilibrium asset pricing formulas that allow for investor heterogeneity, in which the return process is endogenous and asset prices are determined by expected discounted relative dividends. Our results have simple asset pricing implications for the time series as well as the cross section of relative asset prices. It is found that on data from the Dow Jones Industrial Average, a risk aversion smaller than in the logarithmic case fits best.

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Evidence on the “Growth‐optimum” Model

Cited by 41 publications

References 21 publications

Capital budgeting and Kelly betting

Capital budgeting and Kelly betting

On the History of the Growth-Optimal Portfolio

Dynamic General Equilibrium andT-Period Fund Separation

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