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When does an Exchange Traded Fund (ETF) take out expenses (for example 0,3% on a yearly basis)? Does it happen daily, or once yearly or according to some other scheme? Where does it take them from?

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In general, it depends on the particular ETF, and should be checked in the prospectus, but one standard way (e.g. SPY) is to do it on a daily basis based on NAV published after the close. E.g. NAV per share = X$, so the expenses taken out would be X*0.03/(100*252). Again usually ETF's have cash component (with aggregated dividends etc), so there's no problem with taking out the expenses.

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