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By Berhane K., Thomas D. C.

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TORBEN G. ANDERSEN ET AL. 100 3 6 PG (AR2) 100 2 2 MRK (AR5) 100 1 5 20 1 100 0 4 JNJ (AR1) 60 2 1 IP (AR1) 80 1 3 20 1 100 0 2 GM (AR3) 100 2 1 GE (AR2) 100 1 26 100 27 Realized Beta: Persistence and Predictability derive the limiting distribution of realized beta. In particular, as N ! 1; where b^ it À bit r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ) Nð0; 1Þ, PN t 2 À2 g^ it j¼1 rmjt g^ it ¼ Nt X a2ij À j¼1 N t À1 X (11) (12) aij aijþ1 j¼1 and aij ¼ rijt rmjt À b^ it r2mjt . À2 u N t u X t 2 ^ r (14) b 2b Æz g^ , it it a=2 mjt it j¼1 where za/2 denotes the appropriate critical value of the standard normal distribution.

Fourth, theoretical and empirical inquiries in asset pricing are often undertaken in conditional, as opposed to unconditional, frameworks, the essence of which is to allow for time-varying betas, presumably because doing so is viewed as necessary for realism. The motivation for the conditional CAPM comes from at least two sources. 4 Second, from a different and empirical perspective, the financial econometric volatility literature (see Andersen, Bollerslev, & Diebold, 2005, for a recent survey) has provided extensive evidence of wide fluctuations and high persistence in asset market conditional variances, and in individual equity conditional covariances with the market.

The CAPM) to suspect that the cointegrating function is the ratio of the covariance to the variance. This provides great simplification. In the integer-cointegration framework with known cointegrating vector under the alternative, for example, one could simply test the cointegrating combination for a unit root, or test the significance of the error-correction term in a complete errorcorrection model, as in Horvath and Watson (1995). We proceed in analogous fashion, examining the integration status (generalized to allow for fractional integration) of the realized market variance, realized individual equity covariances with the market, and realized market betas.

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