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Let's say I want to invest in some Index which contains 30 stocks. I can just buy and ETF which tracks the index, but I guess I can also simply buy the 30 individual stocks of the index with their appropriate weight and thus remove the management fees of the ETF (if there are any). If the final result is the same, what reason would I have in buying an ETF?

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what reason would I have in buying an ETF?

Apart from the efforts, the real reason is the ticket size. One can't buy shares in fraction. To truly reflect the index in equal weight, the amount to invest will be in multiples of millions [depending on the Index and the stock composition]

This related question should help you understand why it is difficult even for large fund house to exactly mimic the index. Why do passive ETFs require so much trading (and incur costs)?

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To add to Dheer's point, the vast majority of retail investors will have to pay fees and use up a large amount of valuable time on the entrance and exit of each stock, and each and every time you rebalance as the index weightings change.

These also add up extremely fast vs the few basis points the large and liquid ETFs charge for this service.

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