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Abstract
We introduce a methodology which deals with possibly integrated variables in the specification of the betas of conditional asset pricing models. In such a case, any model which is directly derived by a polynomial approximation of the functional form of the conditional beta will inherit a nonstationary right hand side. Our approach uses the cointegrating relationships between the integrated variables in order to maintain the stationarity of the right hand side of the estimated model, thus, avoiding the issues that arise in the case of an unbalanced regression. We present an example where our methodology is applied to the returns of funds-of-funds which are based on the Morningstar mutual fund ranking system. The results provide evidence that the residuals of possible cointegrating relationships between integrated variables in the specification of the conditional betas may reveal significant information concerning the dynamics of the betas.
Highlights
The Capital Asset Pricing Model (CAPM), proposed by Treynor (1962), Sharpe (1964) and Lintner (1965), has been a cornerstone of the modern asset pricing theory. This model postulates that the expected excess return, E(Rj − Rf), on asset j, is linearly related to the ‘beta’, βj, of asset j, βj ≡ Cov(Rj, Rm)/Var(Rm) where Rm denotes the returns on the market portfolio and E(Rj − Rf) = βjE(Rm − Rf)
This in turn implies that the relationship between the excess returns of the portfolio j and the excess returns of the market factor is given by the relationships (1)–(3), where, rj,t = Rtj* Rf,t, j = 1, 2, ..., 5, Rf,t is the return of a one-month Treasury bill, Zt = [Z1,t, Z2,t, ..., Zn,t]′ is an n-vector of state variables observable by the managers at time t, and rm,t = Rtm Rf,t where Rtm stands for the returns of the market factor
We introduced a methodology that allows for the estimation of models that derive from polynomial approximations of the time varying betas in conditional asset pricing models
Summary
The Capital Asset Pricing Model (CAPM), proposed by Treynor (1962), Sharpe (1964) and Lintner (1965), has been a cornerstone of the modern asset pricing theory. Collins et al (1987), Bos and Fetherston (1992), Bos and Fetherston (1995) and Faff et al (1992) The findings of these studies motivated the examination of models of time varying betas (see, e.g., Shanken, 1990; Jagannathan and Wang, 1996; Ferson and Schadt, 1996; Lettau and Ludvigson, 2001). If n = 1 and Zt is I(1), we will face the problem of an unbalanced regression because both conditional and unconditional variances of the right hand side of the model will be explosive This may be the case if some (or all) of the variables in Zt are integrated.
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