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Applications in Finance

In: Applied Multivariate Statistical Analysis

Author

Listed:
  • Wolfgang Karl Härdle

    (Humboldt-Universität zu Berlin, Ladislaus von Bortkiewicz Chair of Statistics)

  • Léopold Simar

    (Université Catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences)

  • Matthias R. Fengler

    (University of St. Gallen, School of Economics and Political Science)

Abstract

A portfolio is a linear combination of assets. Each asset contributes with a weight c j $$c_j$$ 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 ) ⊤ $$c = (c_1,\ldots ,c_p)^{\top }$$ . 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).

Suggested Citation

  • Wolfgang Karl Härdle & Léopold Simar & Matthias R. Fengler, 2024. "Applications in Finance," Springer Books, in: Applied Multivariate Statistical Analysis, edition 0, chapter 0, pages 487-499, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-63833-6_19
    DOI: 10.1007/978-3-031-63833-6_19
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