  Applying the dynamical coherent potential approximation to a simple model, we
have theoretically studied the behavior of the optical bandedge in diluted
magnetic semiconductors (DMSs). For $A^{\rm II}_{1-x}$Mn$_{x}B^{\rm VI}$-type
DMS, the present study reveals that the linear relationship between
exchange-spitting $\mit\Delta E_{ex} $ and the averaged magnetization $|x < S_z
>|$ widely holds for different values of $x$. The ratio, $\mit\Delta E_{ex}/x <
S_z>$, however, depends not only the exchange strength but also the band
offset. Furthermore, the present study reveals that in the low dilution of
Ga$_{1-x}$Mn$_x$As the optical bandedge exists not at the bandedge of the
impurity band but near the bottom of host band. The optical bandedge behaves as
if the exchange interaction is ferromagnetic although the antiferromagnetic
exchange interaction actually operates at Mn site. We conclude that the
spin-dependent shift of the carrier states between the impurity band and host
band accompanying with the change of magnetization causes the apparently
ferromagnetic behavior of the optical bandedge which was reported in the
magnetoreflection measurement of Ga$_{1-x}$Mn$_x$As.
