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LINEAR CONDITIONAL EXPECTATION, RETURN DISTRIBUTIONS, AND CAPITAL ASSET PRICING THEORIES
Author(s) -
Wei K. C. John,
Lee Cheng F.,
Lee Alice C.
Publication year - 1999
Publication title -
journal of financial research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.319
H-Index - 49
eISSN - 1475-6803
pISSN - 0270-2592
DOI - 10.1111/j.1475-6803.1999.tb00706.x
Subject(s) - capital asset pricing model , distribution (mathematics) , capital asset , asset (computer security) , econometrics , capital (architecture) , arbitrage pricing theory , operator (biology) , mathematics , consumption based capital asset pricing model , relation (database) , product (mathematics) , economics , mathematical economics , finance , computer science , mathematical analysis , biochemistry , chemistry , computer security , archaeology , repressor , gene , history , transcription factor , geometry , database
We show that E [ X ( g ( Y 1 , …, Y n )] (where E [.] is the expectation operator) can be decomposed into a product of two expected values plus a sum of n comovement terms, if X, Y 1 , …, Y n follow a distribution that admits linear conditional expectation (LCE). We then apply this relation to show that if each asset return is LCE distributed with the market and/or the factors, many capital asset pricing models and the mutual fund separation theorem can be obtained. A well‐known example of a class of distributions that admits LCE is the elliptical distributions, of which the normal is a special case. A larger family, not mentioned in the existing literature, that admits LCE is the Pearson system. As a result, the distribution assumption to derive the capital asset pricing theories can be relaxed to the wider LCE family. We also present the relation of the LCE family to Ross's (1978) separating distribution family.