Classic portfolio optimization according to Markowitz uses only variance as a measure of portfolio risk (PF). However, risk-averse investors are in principle happy to accept a positive deviation of their PF return (relative to a given benchmark), while negative deviations are seen as the "real" risk. This fact leads to the so-called "downside" risk measures such as lower partial moments.

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a) Potential questions

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• How can alternative risk measures, e.g., lower partial moments (LPM) or special subsets (e.g., semivariances) be used to measure risk in portfolios?
• Under what aspects are utility-theoretic LPM risk measures optimal with respect to a risk-averse investor?
• LPM portfolios are to be empirically compared with Markowitz's conventional theory using performance and risk measures in an out-of-sample study, and the relation to theoretical properties is to be illustrated.

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b) Data

• A data set is to be selected independently on the basis of the literature
• For example, stock, commodity, currency and index returns are conceivable for this purpose

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c) Additional information

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It is necessary to use a true out-of-sample methodology for evaluating portfolios with R: Here, the "Rolling Window" or "Expanding Window" methods are to be used. These have to be programmed with the help of the statistical software R.

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Literature

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Books

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• Introductory Statistics with R von Daalgard (in der Bibliothek verfügbar)
• Time Series Models for Business and Economic Forecasting von Franses, van Dijk und Opschoor, Cambridge 威尼斯赌博游戏_威尼斯赌博app-【官网】 Press (kann per Fernleihe bezogen werden)
• Probability and Statistics with R von Ugarte, Militino und Arnholt (in der Bibliothek verfügbar)
• Angewandte Statistik: Methodensammlung mit R vonSachs/Hedderich (in der Bibliothek verfügbar)
• Introductory Econometrics von Wooldridge (in der Bibliothek verfügbar)
• The R Book von Crawley (in der Bibliothek verfügbar)
• Albrecht A., Maurer R. (2005), 2. Auflage Sch?ffler Poeschel, Investment- und Risikomanagement

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Papers

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• Grootveld, H., Hallerbach, W., 1999, Variance vsdownside risk: Is there really that much difference? European Journal of Operational Research, Vol. 114, p. 304-319.
• Cumova, D., Nawrocki, D., 2011, A symmetric LPM model for heuristic mean-semivarianceanalysis, Journal of Economics and Business, vol. 63(3), p. 217-236.

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