Abstract - The CAPM Relation for Inefficient Portfolios

Following empirical evidence that—contrary to CAPM predictions—found little relation between expected rates of return and betas, the relation has been investigated extensively. Roll (1977), Roll and Ross (1994) (RR) Kandel and Stambaugh (1995), and Jagannathan and Wang (1996) are seminal works. In this context, within a Markowitz world (finite number of nonredundant risky securities with finite first two moments), we generally and simply write the theoretical CAPM relation for inefficient (non-frontier) portfolios (CAPMI). We demonstrate that the CAPMI is a well-specified alternative for the widely implemented misspecified CAPM for use with inefficient portfolios. We identify three
sources for this misspecification: i) the omission of an addend in the pricing relation, ii) the use of an incorrect risk premiums/beta coefficients (due to of the existence of infinitely many “zero beta” portfolios at all expected returns), and iii) the use of unadjusted betas. We suggest the use of incomplete information equilibria to overcome unobservability of moments of returns. Our results are robust to regressions that produce positive explanatory beta power, including extensions such as multiperiod, multifactor, and the conditioning on time and various attributes.

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