The Arbitrage Theory of Capital Asset Pricing

The purpose of this paper is to examine rigorously the arbitrage model of capital asset pricing developed in Ross [13, 14]. The arbitrage model was proposed as an alternative to the mean variance capital asset pricing model, introduced by Sharpe, Lintner, and Treynor, that has become the major analytic tool for explaining phenomena observed in capital markets for risky assets. The principal relation that emerges from the mean variance model holds that for any asset, i, its (ex ante) expected return$E_i = p + \lamdba b_i, \kern+100pt (1)$where ρ is the riskless rate of interest, is the expected excess return on the market, Em − ρ, and$ b_i - \,\sigma _{im}^2 /\sigma _m^2 , $is the beta coefficient on the market, where σm2 is the variance of the market portfolio and $ \sigma _{im}^2 $ is the covariance between the returns on the ith asset and the market portfolio. (If a riskless asset does not exist, ρ is the zero-beta return, i.e., the return on all portfolios uncorrelated with the market portfolio)…