Functional Forms and the Capital Asset Pricing Model

The Heterogeneous Investment Horizon and the Capital Asset Pricing Model: Theory and Implications

“…The observed investment horizon associated with the return data reported is most likely to be different from the true single-period horizon. Under this circumstance, further transformation on return data is necessary (see Lee (1976) and McDonald (1983)). Denote \, = h t /N, X fi = h fi /N, and \ mi = Hj/N.…”

“…The explicit consideration of heterogeneous investment horizons generates several important implications on the empirical estimation of systematic risk and tests of the risk-return relationship. Jensen (1969), Hasty and Fielitz (1975), Lee (1976), Levhari and Levy (1977), McDonald (1983), and Gilster (1983) investigated the empirical implications of heterogeneous investment horizons. 1 While these studies have substantially contributed to our understanding of multi-period investments, none of them has provided a generalized asset pricing model for the equilibrium risk-return relationship under heterogeneous investment horizons.…”

“…2 It shows that the functional form of the CAPM is nonlinear when the true investment horizon is unknown. Unlike the studies by McDonald (1983), Hasty and Fielitz (1975), and Lee (1976), the generalized CAPM is derived from the optimal selection of portfolio sequences. Thus, this paper provides a theoretical foundation for the nonlinearity in the CAPM.…”

Misspecification testing and robust estimation of the market model: estimating betas for the FT-SE industry baskets

“…For example, the market model, which posits a linear relationship between the returns from a given security and the returns from some market portfolio, has been used widely, particularly in event study methodology (see, for example, the seminal work of Brown and Warner, 1980; the survey by Strong, 1992; and recent applications by Mitra and Owers, 1995;and Rippington and Tafler, 1995), but also as a basis for testing the CAPM (Gibbons, 1982). It is noticeable, however, that in many typical applications the statistical assumptions underlying the market model are often only asserted, rather than tested for: given the findings of, for example, McDonald (1983) and McDonald and Lee (1988) on the extent of empirical misspecification in the market model, such assertions must be highly questionable.…”