After-the-fact rate of return often consider as realized or actual can be denoted

The correct answer is $\boxed{\text{A}}$.

The after-the-fact rate of return, often considered as realized or actual, can be denoted as $\hat{r}_s$. This is because the superscript $\hat{*}$ is used to denote a realized or actual value, and the subscript $s$ denotes the security.

The other options are incorrect because:

• Option $\text{B}$, $r_{\bar{s}}$, is the expected rate of return.
• Option $\text{C}$, $r_{\hat{s}}$, is the ex ante rate of return.
• Option $\text{D}$, $s_{\bar{r}}$, is the standard deviation of the return.