Standard optimal capital tax theory abstracts from modeling asset prices, making it unsuitable for thinking about capital gains and wealth taxation. We study optimal redistributive taxation in an environment with asset price changes, adopting the modern finance view that asset prices fluctuate not only because of changing cash flows, but also due to other factors (“discount rates”). We show that the optimal tax base (i) generally differs from the case with constant asset prices, and (ii) depends on the sources of asset-price changes. Whenever asset prices fluctuate, and are not exclusively driven by cash flow changes, taxes must target realized trades and generally involve a combination of realization-based capital gains and dividend taxes. This result stands in contrast to the classic Haig-Simons comprehensive income tax concept, as well as recent proposals for wealth or accrual-based capital gains taxes.