Dealing with Non-Normality When Estimating Abnormal Returns and Systematic Risk of Private Equity: A Closed-Form Solution

52 Pages Posted: 1 Jul 2015

See all articles by Axel Buchner

Axel Buchner

University of Passau; CEPRES - Center of Private Equity Research

Date Written: June 1, 2015


The paper develops a novel econometric approach to estimate abnormal returns and systematic risk of private equity investments from observable investment cash flows. A unique feature of the method is that it gives closed-form estimators for systematic risk and abnormal returns. In addition, unlike previous studies that derive estimates based on the standard CAPM, the method employs a generalized CAPM that is based on the equilibrium model of Rubinstein (1976).This generalized CAPM accurately takes into account that private equity returns typically deviate from a normal distribution. The methodology is validated using numerical examples and is applied to a unique and comprehensive sample of 12,565 (7,732 venture capital and 4,833 buyout) fully realized portfolio company investments by private equity funds. The outperformance of venture capital investments documented is lower than found in previous studies that estimate a standard CAPM, which is consistent with the theory that investors require an additional premium for the negative coskewness reported for the sample investments. In contrast, we find a similar outperformance and systematic risk of buyout investments than previously documented, which is in line with the observation that the sample buyout investments do not exhibit significant coskewness. In addition, the results highlight that the log-utility CAPM, which provides estimates that are consistent with the standard PME, typically overstates the alpha from large beta assets, like venture capital investments, whereas it provides a good approximation for assets that have betas relatively close to one, like buyout investments.

Keywords: private equity, venture capital, abnormal returns, systematic risk, coskewness, generalized CAPM

JEL Classification: C51, G12, G23, G24

Suggested Citation

Buchner, Axel, Dealing with Non-Normality When Estimating Abnormal Returns and Systematic Risk of Private Equity: A Closed-Form Solution (June 1, 2015). Available at SSRN: or

Axel Buchner (Contact Author)

University of Passau ( email )

Innstraße 27
Passau, 94030

CEPRES - Center of Private Equity Research ( email )

Max-Joseph-Strasse 7
Munich, 80333

Register to save articles to
your library


Paper statistics

Abstract Views
PlumX Metrics