Applications in Finance

  • Wolfgang Härdle
  • Léopold Simar


A portfolio is a linear combination of assets. Each asset contributes with a weight c j , to the portfolio. The performance of such a portfolio is a function of the various returns of the assets and of the weights c = (c 1,, c p )T. In this chapter we investigate the “optimal choice” of the portfolio weights c. The optimality criterion is the mean-variance efficiency of the portfolio. Usually investors are risk-averse, therefore, we can define a mean-variance efficient portfolio to be a portfolio that has a minimal variance for a given desired mean return. Equivalently, we could try to optimize the weights for the portfolios with maximal mean return for a given variance (risk structure). We develop this methodology in the situations of (non)existence of riskless assets and discuss relations with the Capital Assets Pricing Model (CAPM).


Risky Asset Capital Asset Price Model Portfolio Return Portfolio Choice Riskless Asset 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Wolfgang Härdle
    • 1
  • Léopold Simar
    • 2
  1. 1.CASE — Center for Applied Statistics and Economics, Institut für Statistik und ÖkonometrieHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Inst. StatistiqueUniversité Catholique LouvainLouvain-la-NeuveBelgium

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