Affiliations: Institute of Mathematics, Actuarial and Computer Sciences, Jamaica. E-mail: [email protected] | Department of Finance, Eastern Carolina University, NC, USA. E-mail: [email protected] | Jindal School of Management, The University of Texas at Dallas, Richardson, TX, USA
Note: [] Corresponding author: Sandun Perera, Jindal School of Management, The University of Texas at Dallas, Richardson, TX 75080, USA. Tel.: +1 972 883 4422; E-mail: [email protected]
Abstract: We show that Black Capital Asset Pricing Model (Black CAPM) is extremely sensitive to the choice of the market portfolio and becomes unstable as market portfolios approach the Global Minimum-Variance portfolio. When market portfolios approach the minimum-variance portfolio, the expected return on the zero beta asset approaches negative infinity and its variance increases rapidly. Moreover, expected return on a fixed portfolio becomes indefinite (i.e., takes infinitely many values), and betas of all portfolios approach one. Unlike the Sharpe–Lintner CAPM, the market risk premium in the Black CAPM always has a positive minimum, while beta may have a negative minimum value, dependent on the underlying covariance matrix.
Keywords: Asset pricing, Black CAPM, global minimum variance asset, zero-beta asset
