Optimal hedging with higher moments

This study proposes a utility-based framework for the determination of optimal hedge ratios (OHRs) that can allow for the impact of higher moments on hedging decisions. We examine the entire hyperbolic absolute risk aversion family of utilities which include quadratic, logarithmic, power, and exponential utility functions. We find that for both moderate and large spot (commodity) exposures, the performance of out-of-sample hedges constructed allowing for nonzero higher moments is better than the performance of the simpler OLS hedge ratio. The picture is, however, not uniform throughout our seven spot commodities as there is one instance (cotton) for which the modeling of higher moments decreases welfare out-of-sample relative to the simpler OLS. We support our empirical findings by a theoretical analysis of optimal hedging decisions and we uncover a novel link between OHRs and the minimax hedge ratio, that is the ratio which minimizes the largest loss of the hedged position. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark

Determination of the density of the multiple access interference of a CDMA system from its moments

A standard CDMA system is considered and an extension of Pearson's results is used to determine the density function of the interference. The method is shown to work well in some cases, but not so in others. However this approach can be useful in further determining the probability of error of the system with minimal computational requirements.

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

Thick viewing : empirical examples of condensed moments of narrative impact in fiction film developing theoretical concepts for intensified engagements

Abstract  In a case study about viewing habits in a Swedish audience I sampled 309 questionnaires; interviews with five focus group were conducted together with ten in-depth individual interviews discussing altogether fifteen favorite films exploring specific scenes of idiosyncratic relevance.  The outcome supports claims about viewers as active and playful (cf. Höijer 1998, Frampton 2006, Hoover 2006, Plantinga 2009). In line with mediatization theory I also argue that spiritual meaning making takes place through mediated experiences and I support theories about fiction films as important sources for moral and spiritual reflection (Partridge 2004, Zillman 2005, Lynch 2007, Plantinga 2009). What Hjarvard calls the soft side of mediatization processes (2008) is illustrated showing adults experiencing enchantment through favorite films (Jerslev 2006, Partridge 2008, Klinger 2008, Oliver & Hartmann 2010).  Vernacular meaning making embedded in everyday life and spectators dealing with fiction narratives such as Gladiator, Amelie from Montmartre or Avatar highlights the need for a more nuanced understanding of elevated cinematic experiences. The reported impact of specific movies is analyzed through theories where cognition and affect are central aspects of spectators’ engagements with a film (Tan 1996, Caroll 1999, Grodal 2009). Crucially important are theories of meaning-making where viewers’ detailed interpretation of specific scenes are embedded in high-level meaning-making where world view issues and spectators’ moral frameworks are activated (Zillman 2005, Andersson & Andersson 2005, Frampton 2006, Lynch 2007, Avila 2007, Axelson 2008, Plantinga 2009).  Also results from a growing body of empirical oriented research in film studies are relevant with an interest in what happens with the flesh and blood spectator exposed to filmic narratives (Jerslev 2006, Klinger 2008, Barker 2009, Suckfüll 2010, Oliver & Hartmann 2010). Analyzing the qualitative results of my case study, I want to challenge the claim that the viewer has to suspend higher order reflective cognitive structures in order to experience suture (Butler & Palesh 2004). What I find in my empirical examples is responses related to spectators’ highest levels of mental activity, all anchored in the sensual-emotional apparatus (Grodal 2009). My outcome is in line with a growing number of empirical case studies which support conclusions that both thinking and behavior are affected by film watching (Marsh 2007, Sückfull 2010, Oliver & Hartmann 2010, Axelson forthcoming). The presentation contributes to a development of concepts which combines aesthetic, affective and cognitive components in an investigation of spectator’s moves from emotional evaluation of intra-text narration to extra-textual assessments, testing the narrative for larger significance in idiosyncratic ways (Bordwell & Thompson 1997, Marsh 2007, Johnston 2007, Bruun Vaage 2009, Axelson 2011). There are a several profitable concepts suggested to embrace the complex interplay between affects, cognition and emotions when individuals respond to fictional narratives. Robert K. Johnston label it “deepening gaze” (2007: 307) and “transformative viewing” (2007: 305). Philosopher Mitch Avila proposes “high cognition” (2007: 228) and Casper Thybjerg ”higher meaning” (2008: 60). Torben Grodal talks about “feelings of deep meaning” (Grodal 2009: 149). With a nod to Clifford Geertz, Craig Detweiler adopts “thick description” (2007: 47) as do Kutter Callaway altering it to ”thick interpretations” (Callaway 2013: 203).  Frampton states it in a paradox; ”affective intelligence” (Frampton 2006: 166). As a result of the empirical investigation, inspired by Geertz, Detweiler & Callaway, I advocate thick viewing for capturing the viewing process of these specific moments of film experience when profound and intensified emotional interpretations take place. The author As a sociologist of religion, Tomas Axelsons research deals with people’s use of mediated narratives to make sense of reality in a society characterized by individualization, mediatization and pluralized world views.  He explores uses of fiction film as a resource in every day life and he is currently finishing his three year project funded by the Swedish Research Council: Spectator engagement in film and utopian self-reflexivity. Moving Images and Moved Minds. http://www.du.se/sv/AVM/Personal/Tomas-Axelson Bibliography Axelson, T. (Forthcoming 2014). Den rörliga bildens förmåga att beröra.[1] Stockholm: Liber Axelson, T. (In peer review). Vernacular Meaning Making. Examples of narrative impact in fiction film questioning the ’banal’ notion in mediatization theory. Nordicom Review. Nordicom Göteborg. Axelson, T. (2011). Människans behov av fiktion. Den rörliga bildens förmåga att beröra människan på djupet.[2]Kulturella perspektiv. Volume 2. Article retrieved from www.kultmed.umu.se/digitalAssets/74/74304_axelson-22011.pdf Axelson, Tomas (2010) “Narration, Visualization and Mind. Movies in everyday life as a resource for utopian self-reflection.” Paper presentation at CMRC, 7th Conference of Media, Religion & Culture in Toronto, Canada 9 – 13th August 2010. Axelson, Tomas (2008) Movies and Meaning. Studying Audience, Favourite Films and Existential Matters. Particip@tions : Journal of Audience and Reception Studies. Volume 5, (1). Doctoral dissertation summary. ACTA UNIVERSITATIS UPSALIENSIS. Article retrieved from http://www.participations.org/Volume%205/Issue%201%20-%20special/5_01_axelson.htm  [1] English translation: Moving Images and Moved Minds. [2] English translation: Our need for fiction. Deeply Moved by Moving Images. Cultural Perspectives.

Do higher moments really matter in portfolio choice?

We present explicit formulas for evaluating the difference between Markowitz weights and those from optimal portfolios, with the same given return, considering either asymmetry or kurtosis. We prove that, whenever the higher moment constraint is not binding, the weights are never the same. If, due to special features of the first and second moments, the difference might be negligible, in quite many cases it will be very significant. An appealing illustration, when the designer wants to incorporate an asset with quite heavy tails, but wants to moderate this effect, further supports the argument.

A few more moments to finance theory: introducing higher moments in investment theory and econometrics

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Introducing higher moments in the CAPM: some basic ideas

We show how to include in the CAPM moments of any order, extending the mean-variance or mean-variance-skewness versions available until now. Then, we present a simple way to modify the formulae, in order to avoid the appearance of utility parameters. The results can be easily applied to practical portfolio design, with econometric inference and testing based on generalised method of moments procedures. An empirical application to the Brazilian stock market is discussed.

A CAPM with higher moments: theory and econometrics

We develop portfolio choice theory taking into consideration the first p~ moments of the underIying assets distribution. A rigorous characterization of the opportunity set and of the efficient portfolios frontier is given, as well as of the solutions to the problem with a general utility function and short sales allowed. The extension of c1assical meanvariance properties, like two-fund separation, is also investigated. A general CAPM is derived, based on the theoretical foundations built, and its empirical consequences and testing are discussed

On certain geometric aspects of portfolio optimisation with higher moments

We discuss geometric properties related to the minimisation of a portfolio kurtosis given its first two odd moments, considering a risk-less asset and allowing for short sales. The findings are generalised for the minimisation of any given even portfolio moment with fixed excess return and skewness, and then for the case in which only excess return is constrained. An example with two risky assets provides a better insight on the problems related to the solutions. The importance of the geometric properties and their use in the higher moments portfolio choice context is highlighted.