  In this note, we investigate possible relationships between the bivariate
Hurst exponent $H_{xy}$ and an average of the separate Hurst exponents
$\frac{1}{2}(H_x+H_y)$. We show that two cases are well theoretically founded.
These are the cases when $H_{xy}=\frac{1}{2}(H_x+H_y)$ and
$H_{xy}<\frac{1}{2}(H_x+H_y)$. However, we show that the case of
$H_{xy}>\frac{1}{2}(H_x+H_y)$ is not possible regardless of stationarity
issues. Further discussion of the implications is provided as well together
with a note on the finite sample effect.
