Diversification Return and Leveraged Portfolios

Qian, Edward E.

doi:10.3905/jpm.2012.38.4.014

Cited by 24 publications

(19 citation statements)

References 3 publications

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“…Sharpe (1972)'s measure is based on portfolio idiosyncratic risk. Fernholz and Shay (1982) introduce the excess growth rate, also known as diversification return (see Booth and Fama, 1992;Bouchey et al, 2012;Chambers and Zdanowicz, 2014;Qian, 2012;Willenbrock, 2011), while Woerheide and Persson (1993) appeals to the Gini-Simpson (GS) index of the portfolio. More recently, Statman and Scheid (2005) base their proposed measure on the return gaps (RG), Rudin and Morgan (2006) develop portfolio diversification indices (PDI) derived from principal component analysis (PCA), Choueifaty and Coignard (2008) recommend their diversification ratio (DR), Goetzmann et al (2005) and Goetzmann and Kumar (2008) put forward their portfolio variance normalized while Meucci (2009) and Meucci et al (2014) analyze measures based on the effective number of bets (ENB) using a PCA, a minimum torsion bets and Shannon entropy.…”

Section: Portfolio Diversification Measuresmentioning

confidence: 99%

Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy

2015

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Abstract:This paper extends the use of Rao(1982b)'s Quadratic Entropy (RQE) to modern portfolio theory. It argues that the RQE of a portfolio is a valid, flexible and unifying approach to measuring portfolio diversification. The paper demonstrates that portfolio's RQE can encompass most existing measures, such as the portfolio variance, the diversification ratio, the normalized portfolio variance, the diversification return or excess growth rates, the Gini-Simpson indices, the return gaps, Markowitz's utility function and Bouchaud's general free utility. The paper also shows that assets selected under RQE can protect portfolios from mass destruction (systemic risk) and an empirical illustration suggests that this protection is substantial.

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Section: Portfolio Diversification Measuresmentioning

confidence: 99%

Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy

2015

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“…Similarly, Willenbrock (2011) argues that "the underlying source of the diversification return is the rebalancing", and Qian (2012) states that a "diversified portfolio, if left alone and not rebalanced, does not provide diversification return". These statements are misleading.…”

Section: These Authors Claim That These Effects Boost Returns Even Ifmentioning

confidence: 99%

“…For simplicity we follow Dempster et al (2007) and Qian (2012) in also normalising these returns to zero 8 . Under these assumptions these authors find that the expected geometric mean return of a portfolio which is 50% risky asset and 50% risk-free is σ a 2 /8.…”

Section: Portfolios Of One Risky Asset and One Risk-free Assetmentioning

confidence: 99%

“…Another strand of the literature considers weights that are often not "optimal" but constitute an arbitrary fixed weight portfolio which is compared with a B&H strategy (e.g. Fernholz and Shay 1982, Luenberger 1997, Booth & Fama 1992, Mulvey et al 2007, Qian 2012, Willenbrock, 2012. A theoretical result from this approach is that a portfolio of independently and identically distributed (IID) assets sees more rapid portfolio growth than the corresponding B&H strategy, and this "excess growth" increases with the volatility of the underlying portfolio assets.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we examine the claims originally made in Fernholz and Shay (1982) and endorsed by an increasing number of subsequent papers (e.g. Luenberger 1997, Mulvey et al 2007, Stein et al, 2009, Qian 2012, Willenbrock, 2012, Bouchey et al 2012) that the process of rebalancing directly boosts long-term growth rates and terminal wealth even when returns have no predictable time structure (for example when asset prices evolve following geometric Brownian motion), and that rebalanced portfolios must be expected to outperform because they generate these "rebalancing returns"…”

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confidence: 99%

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Diversification Returns, Rebalancing Returns and Volatility Pumping

Hayley

2013

SSRN Journal

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There is now a substantial literature on the effects of rebalancing on portfolio performance. It is widely argued in the theoretical literature that rebalanced strategies are inherently likely to generate greater terminal wealth than unrebalanced strategies, although empirical studies do not generally support this claim. We show that this claim is based on a misattribution between 'rebalancing returns' which are specific to the act of rebalancing, and 'diversification returns' which can be earned by both rebalanced and unrebalanced strategies. Confusion appears to have increased because in some situations these two distinct effects have the same magnitude. This issue has important implications for return attribution in diversified portfolios. Misleading claims about the benefits of rebalancing are likely to lead investors into strategies which involve insufficient diversification and excessive transactions costs.

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