Theoretical Foundations of Asset Allocation and Pricing Models with Higher‐order Moments

Jurczenko, Emmanuel; Maillet, Bertrand

doi:10.1002/9781119201830.ch1

Cited by 15 publications

(8 citation statements)

References 78 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…7. This is also the reason why the stronger conditions given by Theorem 5 in Jurczenko and Maillet (2006), which specify quartic polynomial utility functions that exhibit decreasing absolute risk aversion, decreasing absolute prudence and constant or increasing relative risk aversion, are not met by the given set: nonzero preferences over all four moments are necessary for this. 8.…”

Section: Resultsmentioning

confidence: 87%

“…Whether the results obtained are reasonable can best be checked by verifying that they are compatible with those for the MVK problem, which we know to be correct. Given the greater freedom afforded by considering utility functions with four nonzero coefficients, the eight new functions introduced, given in Table 5.5, meet the stronger conditions of Theorem 5 in Jurczenko and Maillet (2006) over the two subintervals [0; 0.5%] and [0; 0.25%] comprised within the range of observed data returns. The theorem then implies that they verify the standard properties of decreasing absolute risk aversion (DARA), constant or increasing relative risk aversion (CRRA) and decreasing absolute prudence for the intervals concerned, which as in the MVK case allows us to specify functions that model strong preferences with respect to the third and fourth moments while matching standard desirable characteristics over at least part of the applicable domain.…”

Section: Mean-variance-skewness-kurtosis (Mvsk) Optimizationmentioning

confidence: 90%

“…8 The only exceptions to this are utility function #6, which penalizes both second and fourth moments as much as was feasible given the conditions from Jurczenko and Maillet (2006), and function #7, which models the largest aversion to the fourth moment in the set used. It seems plausible to suggest these again represent limit cases, for which the risk minimization component of the optimization tradeoff becomes predominant, such that there remains little scope for maneuver.…”

Section: Mean-variance-kurtosis (Mvk) Optimizationmentioning

confidence: 97%

See 2 more Smart Citations

Understanding Investment Funds

Terraza¹,

Razafitombo²

2013

View full text Add to dashboard Cite

Section: Resultsmentioning

confidence: 87%

Section: Mean-variance-skewness-kurtosis (Mvsk) Optimizationmentioning

confidence: 90%

Section: Mean-variance-kurtosis (Mvk) Optimizationmentioning

confidence: 97%

See 1 more Smart Citation

Understanding Investment Funds

Terraza¹,

Razafitombo²

2013

View full text Add to dashboard Cite

“…Let us note that there is a reasonable amount of the literature available (see, e.g. [ 30 , 33 ]) discussing portfolio selection based on higher moments of asset returns, but not much has been done from the perspective of the distribution of portfolio weights. This article is a step further in this direction.…”

Section: Introductionmentioning

confidence: 99%

Higher order moments of the estimated tangency portfolio weights

Javed

Mazur

Ngailo

2020

Journal of Applied Statistics

View full text Add to dashboard Cite

In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order noncentral and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and t-distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments.

show abstract

“…Furthermore, numerous theoretical articles and empirical studies show that it is unlikely that investors do not care about higher-order moments (e.g. Scott and Horwath, 1980;Golec and Tamarkin, 1998;Harvey and Siddique, 2000;Jondeau and Rockinger, 2006;Jurczenko and Maillet, 2006, and references herein).…”

Section: Introductionmentioning

confidence: 99%

“On the (Ab)use of Omega ?”

Caporin

Costola

Jannin

et al. 2018

Journal of Empirical Finance

Self Cite

View full text Add to dashboard Cite

Several recent finance articles use the Omega measure (Keating and Shadwick, 2002), defined as a ratio of potential gains out of possible losses, for gauging the performance of funds or active strategies, in substitution of the traditional Sharpe ratio, with the arguments that return distributions are not Gaussian and volatility is not always the relevant risk metric. Other authors also use Omega for optimizing (non-linear) portfolios with important downside risk. However, we question in this article the relevance of such approaches. First, we show through a basic illustration that the Omega ratio is inconsistent with the Second-order Stochastic Dominance criterion. Furthermore, we observe that the trade-off between return and risk corresponding to the Omega measure, may be essentially influenced by the mean return. Next, we illustrate in static and dynamic frameworks that Omega-based optimal portfolios can be closely associated with classical optimization paradigms depending on the chosen threshold used in Omega. Finally, we present robustness checks on long-only asset and hedge fund databases, that confirm our results.

show abstract

Theoretical Foundations of Asset Allocation and Pricing Models with Higher‐order Moments

Cited by 15 publications

References 78 publications

Understanding Investment Funds

Understanding Investment Funds

Higher order moments of the estimated tangency portfolio weights

“On the (Ab)use of Omega ?”

Contact Info

Product

Resources

About