Linear Conditional Expectation, Return Distributions, and Capital Asset Pricing Theories

Posted: 20 Aug 1999

See all articles by Cheng-Few Lee

Cheng-Few Lee

Rutgers University, Newark, School of Business-Newark, Department of Finance & Economics

K.C. John Wei

Hong Kong Polytechnic University

Alice C. Lee

PriceWaterhouseCoopers LLP - Arlington Office

Abstract

We show that E[Xxg(Y1, .., Yn)] (where E[.] is the expectation operator) can be decomposed into a product of two expected values plus a sum of n co-movement 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 separating distribution family.

JEL Classification: G12

Suggested Citation

Lee, Cheng-Few and Wei, Kuo-Chiang (John) and Lee, Alice C., Linear Conditional Expectation, Return Distributions, and Capital Asset Pricing Theories. Available at SSRN: https://ssrn.com/abstract=168593

Cheng-Few Lee (Contact Author)

Rutgers University, Newark, School of Business-Newark, Department of Finance & Economics ( email )

111 Washington Avenue
Newark, NJ 07102
United States
732-445-3907 (Phone)
732-445-5927 (Fax)

Kuo-Chiang (John) Wei

Hong Kong Polytechnic University ( email )

11 Yuk Choi Rd
Hung Hom
Hong Kong

Alice C. Lee

PriceWaterhouseCoopers LLP - Arlington Office ( email )

1616 N. Fort Myer Drive
Arlington, VA 22209
United States
703-516-8441 (Phone)
703-741-1616 (Fax)

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