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As indicated by @AlexC and @amdopt, the formula is exact for log returns and approximate for discrete returns. Define the factor by which a price changes as $k$ so that price tomorrow $P_{t+1}$ is the price today times $k$ : $P_{t}*k$.Then the change in the price over a business year is $$\prod_{i \in [1, 252]}{k}$$ The log of the change is by properties of ...

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