Divergent Rates, Financial Restrictions and Relative Prices in Capital Market Equilibrium

Abstract

The mean-variance capital asset pricing model (CAPM) of Sharpe and Lintner was extended by Brennan [3] to incorporate divergent borrowing and lending rates. He found that in equilibrium the security market line (SML) has the same structure as the SML under the single-rate CAPM of Sharpe and Lintner. That is, the expected return of a security or a portfolio remains linear in its systematic risk, with the intercept replaced by an equivalent risk-free return, which is an average of the divergent borrowing and lending rates weighted by the investors' taste parameters. The equivalent risk-free return is larger than the riskless lending rate and, hence, does not represent an inconsistency with the empirical findings by Friend and Blume [4] and by Black, Jensen and Scholes [1[ that the intercept of empirical SML estimated for the single-rate CAPM is larger than the riskless rate. Moreover, Brennan attempted to show that his construct can be extended to the extreme case where there are no riskless opportunities. The case of no riskless opportunities was of course investigated by Black [2], who generalized the CAPM and SML by inventing the concept of zero-beta port-folio to account for the same empirical problem encountered in the traditional SML tests of CAPM. Since the Sharpe-Lintner single-riskless-rate CAPM implies a perfect loan market, we may view the attempts by Black and Brennan as generalizing the CAPM by incorporating financial restrictions and loan market imperfections. Their primary motive, however, is empirical, i.e., to reconcile the results from the traditional SML tests with their generalized CAPM.