Linear conditional expectation, return distributions, and capital asset pricing theories

K. C.John Wei, Cheng F. Lee, Alice C. Lee

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We show that E[X(g(Y1, …, Yn)] (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, Y1, …, Yn 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.

Original languageEnglish (US)
Pages (from-to)471-487
Number of pages17
JournalJournal of Financial Research
Issue number4
StatePublished - Dec 1999

All Science Journal Classification (ASJC) codes

  • Accounting
  • Finance


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