In the formula for the beta of $r_t$ with respect to $x_t$, what is represented by $COV_{\frac{1}{2}} r_t; x_t$?
$COV_{\frac{1}{2}} r_t; x_t$ is equivalent to the covariance of $(\frac{1}{2} r_t + \frac{1}{2} r_{t1})$ and $x_t$.