A Generalization of the CAPM Based on a Property of the Covariance Operator

Losq, Etienne; Chateau, John Peter D.

doi:10.2307/2330862

Cited by 12 publications

(4 citation statements)

References 15 publications

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“…Losq and Chateau 1982) extend the result to the case when g (· ) is a function of n random variables. (Wei and Lee 1988) extend this further to the case where both variables are functions of multivariate normal random variables (Siegel 1993…”

mentioning

confidence: 81%

Combining Dimension Reduction, Distance Measures and Covariance (Presentation Slides)

Kashyap

2017

SSRN Journal

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mentioning

confidence: 81%

Combining Dimension Reduction, Distance Measures and Covariance (Presentation Slides)

Kashyap

2017

SSRN Journal

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“…Central to our proof is a mathematical property of the covariance operator often referred to as Stein's Lemma [see e.g. Losq and Chateau (1982)]. …”

Section: Appendix Dmentioning

confidence: 99%

Market Timing and Security Market Line Analysis

Kempf

Kreuzberg

2003

SSRN Journal

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It seems to be widely accepted that Jensen alpha fails to detect successful market timing funds spuriously indicating poor fund performance. Jensen (1972), Admati and Ross (1985), Dybvig and Ross (1985), and Titman (1989), (1995) attribute that to an upwards biased estimate of the systematic risk of successful market timers. Therefore, they recommend not to use alpha in external performance evaluation. In this paper, we show that this conclusion is misleading. We set up a theory of delegated portfolio management in a mean variance framework with asymmetric information. Within this model we prove that alpha is an unbiased performance measure even for market timing funds. We show that the systematic risk for a fund investor consists of two parts: benchmark risk and management risk resulting from the uncertainty about the skills of the fund manager. We show that the extent of management risk depends on what fund investors know about the fund manager's trade record. Therefore, the performance of mutual funds depends not only on the skills of the fund managers, but also on whether they publish their trade record or not. (JEL classification: G11, G23). * We are grateful to Olaf Korn, Christoph Memmel, and Eric Theissen for their helpful comments. Both authors are from the

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“…ProofofCorollary 2. We provide an alternative to the proof by Losq and Chateau (1982). Since X, Y I , ••• , Y" are normally distributed, QxvQ y y -I = LXVL y y -I in equation (7).…”

Section: Appendixmentioning

confidence: 99%

“…Losq and Chateau (1982) derive the discrete‐time multibeta CAPM under the assumption of normality. Here we generalize the model to the LCE distribution family.…”

Section: Linear Asset Pricing and The Lce Distribution Familymentioning

confidence: 99%

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

Lee

1999

J of Financial Research

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We show thatE[X(g(f" .. , f.»)(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, f l , . . ., f. 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, ofwhich 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 ofthe LCE family to Ross's (1978) separating distribution family.

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A Generalization of the CAPM Based on a Property of the Covariance Operator

Cited by 12 publications

References 15 publications

Combining Dimension Reduction, Distance Measures and Covariance (Presentation Slides)

Combining Dimension Reduction, Distance Measures and Covariance (Presentation Slides)

Market Timing and Security Market Line Analysis

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

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