Abstract
The chapter continues the study of the Markowitz model. The reader will learn how to compute an efficient portfolio with the given risk tolerance. The highlight is an explicit formula for efficient portfolios, rigorously derived and comprehensively discussed. The chapter analyses the minimum variance portfolio and the return-generating self-financing portfolio involved in the solution to the Markowitz optimization problem. It concludes with explaining the linear structure of the set of efficient portfolios.
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- 1.
By the definition of an inverse matrix, we have \(\mathit{WV} = \mathit{VW} = \mathit{Id}\), where Id is the identity matrix. The inverse matrix V −1 exists when the equation Vx = 0 has the unique solution x = 0 (e.g. if V is positive definite).
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Evstigneev, I.V., Hens, T., Schenk-Hoppé, K.R. (2015). Solution to the Markowitz Optimization Problem. In: Mathematical Financial Economics. Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-16571-4_3
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DOI: https://doi.org/10.1007/978-3-319-16571-4_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16570-7
Online ISBN: 978-3-319-16571-4
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