Abstract
The chapter focuses on multifactor models. It begins with an analysis of their simplified version: the exact factor model. To examine it, the no-arbitrage hypothesis is introduced. The main result is the exact factor pricing theorem, which is proved by using this hypothesis. The highlight of the chapter is the Ross-Huberman Arbitrage Pricing Theory dealing with a model of a “large” asset market and establishing an “approximate” factor pricing theorem. The main assumption under which this result is obtained is an asymptotic version of the no-arbitrage hypothesis.
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Notes
- 1.
The distance between two vectors \(a = (a_{1},\ldots,a_{N})\) and \(b = (b_{1},\ldots,b_{N})\) is equal to \(\Vert a - b\Vert\), where \(\Vert \cdot \Vert\) stands for the norm of a vector. The norm (the length) of a vector \(c = (c_{1},\ldots,c_{N})\) is defined by \(\Vert c\Vert = \sqrt{c_{1 }^{2 } + \ldots + c_{N }^{2}}\). For these and other mathematical notions involved in this chapter see Appendix A.
- 2.
Two vectors a and b are called orthogonal if \(\langle a,b\rangle = 0\). Geometrically, this means that the angle between a and b is the right angle 90∘.
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Evstigneev, I.V., Hens, T., Schenk-Hoppé, K.R. (2015). Factor Models and the Ross-Huberman APT. In: Mathematical Financial Economics. Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-16571-4_9
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DOI: https://doi.org/10.1007/978-3-319-16571-4_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16570-7
Online ISBN: 978-3-319-16571-4
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