Abstract
A portfolio is a linear combination of assets. Each asset contributes with a weight cj to the portfolio. The performance of such a portfolio is a function of the various returns of the assets and of the weights c = (c1, . . ., 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).
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Applications in Finance. In: Applied Multivariate Statistical Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72244-1_17
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DOI: https://doi.org/10.1007/978-3-540-72244-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72243-4
Online ISBN: 978-3-540-72244-1
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