Lower Partial Moments in econometric risk measurement

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.


a) Potential questions


  • 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.


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


c) Additional information


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.








  • 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 University 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 Schäffler Poeschel, Investment- und Risikomanagement




  • 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.



Academic Council
Faculty of Business and Economics
  • Room 2319 (Building J)