A Class of Exact F-Tests for Capital Asset Pricing Models

• Activity Number: 521
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Jiajuan Liang*+
• Companies: University of New Haven
• Keywords: Capital asset pricing ; Dimension reduction ; Exact F-test ; Monte Carlo method ; Portfolio efficiency

Abstract

The tradeoff between risk and expected return in the formation of an investment portfolio is a central focus of modern financial theory. The Capital Asset Pricing Model has been widely employed to study the efficiency of a portfolio. Testing whether a portfolio is efficient was proved to reduce to testing a statistical hypothesis on a parameter constraint in a multivariate linear regression model. In this article we develop a class of F-tests to evaluate the portfolio efficiency and compare the new tests with existing ones in the case of high dimension with small sample sizes by using the Monte Carlo method. Empirical results show that the new tests outperform the classical ones in the circumstances where the number of observation time points is close to the number of assets (securities) in the portfolio and they still work effectively even if the number of observation time points is less than the number of assets (securities) in the portfolio. We illustrate the result by using real data and test the circumstances where the number of data points is small and classical tests have no power.