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Published in:
2012 | OriginalPaper | Chapter
Applications in Finance
Authors : Wolfgang Karl Härdle, Léopold Simar
Published in: Applied Multivariate Statistical Analysis
Publisher: Springer Berlin Heidelberg
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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
)
⊤
. 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).