Applications in Finance

Wolfgang Karl Härdle, Leopold Simar and Matthias Fengler
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Wolfgang Karl Härdle: Humboldt-Universität zu Berlin, Ladislaus von Bortkiewicz Chair of Statistics

Chapter Chapter 19 in Applied Multivariate Statistical Analysis, 2024, pp 487-499 from Springer

Abstract: 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).

Date: 2024
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Chapter: Applications in Finance (2019)
Chapter: Applications in Finance (2015)
Chapter: Applications in Finance (2003)
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DOI: 10.1007/978-3-031-63833-6_19

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