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From Investopedia:

Assume an ETF has a stated annual expense ratio of 0.75%. On an investment of $50,000, the expected expense to be paid over the course of the year is $375. If the ETF returned precisely 0% for the year, the investor would slowly see his $50,000 move to a value of $49,625 over the course of the year.

How exactly is this $50,000 reduced to $49,625? Does my # shares decrease, is the price decreased by the fee amount (which means the tracking to the index deviates over time ?), or something else?

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When you buy shares you either buy them second hand or you get them from the market maker. The market maker then goes to the fund manager and either delivers underlying securities that form the creation unit (in order for new shares to be issued) or delivers cash. The fund manager will therefore hold some securities and some cash. Every day the fund administrator will calculate the daily net asset value (the administrator is a different entity typically from the manager). They will then take their daily fee and take it straight out of the fund holdings (in your case approximately 0.0075 / 260 * NAV).

The price of the fund will track the NAV (after fees have been subtracted). This is ensured by the mechanism through which the shares of the fund are created and redeemed. Since the market maker needs to deliver either cash or securities for the creation unit, they will ensure that this matches the value of the NAV (otherwise they'd make a loss on the transaction). As the fee goes straight out of NAV, this ensures the price is automatically adjusted by the market to take account of fees.

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