On ex-dividend days, the percent change in the adjusted closing price is \[\frac{P_{t}}{P_{t-1}-D_t} - 1\] rather than what we might prefer: \[\frac{P_{t} + D_t}{P_{t-1}} - 1\] but this is a minor issue (small difference 4 days a year).
If we want returns at a different frequency, for example annual returns, then we can either