Systematic Risk and Empirical Research
证明，在标准条件下，包含会计和非会计风险因素的收益生成过程使CAPM的贝塔成为充分统计量，并推导出基于无效指数组合的贝塔与市场组合贝塔的参数关系，解释了多因子模型与CAPM的一致性。
We show here that risky asset returns generating processes stated in terms of factors which include both accounting and non‐accounting based measures of risk (e.g. book to market ratios) imply, under fairly standard regularity conditions, that the Sharpe‐Lintner‐Black asset pricing model beta is a ‘sufficient’ statistic in the sense that it captures all important attributes of the returns generating process in a single number. We then derive the parametric relationship between betas based on inefficient index portfolios and betas based on the market or tangency portfolio. We demonstrate that the relationship between risky asset expected returns and betas computed on the basis of inefficient index portfolios is both consistent with the predictions of the Capital Asset Pricing Model and the multi‐factor asset pricing models of Fama and French (1992, 1993, 1995 and 1996). The ‘trick’ is to realise that inefficient index portfolios are composed of the market portfolio and a collection of inefficient but self financing ‘kernel’ or ‘arbitrage’ portfolios. It then follows that there is a perfect linear cross sectional relationship between risky asset expected returns, betas based on inefficient index portfolios and the arbitrage portfolios. Hence, if we happen to stumble across variables that span the same subspace as the vectors representing the arbitrage portfolios, it is easy to create the illusion that risky asset expected returns depend on variables other than ‘beta’.