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It is pretty clear; if you hold a share of a distributing ETF, which is replicating a stock market index like S&P 500 for example, then you can count on regular dividends paid by the the distributing ETF — so there is clearly a value in that. By buying a distributing ETF's share, you buy yourself these future income flows for the years to come, as long as you hold this share. This expected future income flow justifies the price of a single ETF's share.

But what makes an accumulating ETF's share valuable? Is it only the hope, that somebody in the future buys the ETF share from the investor for a higher price, corresponding the value of the shares held by the fund? Of course, I can see the current net asset value per share of an ETF's share on the page of the ETF provider, but what guarantees that there is going to be a buyer in the future, who is actually willing to pay the net asset value per share in the future for the accumulating ETF share, if there are no distributions, since we are talking about accumulating ETFs?

What makes this investment different than buying gold or cryptocurrencies? Do we actually buy only this future hope of being able to sell for a higher price in case of accumulating ETFs as well? In other words: Why do the paid prices for an accumulating ETF share follow the current net asset value per share?

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Why do the paid prices for an accumulating ETF share follow the current net asset value per share?

The creation and redemption mechanism of ETFs ensures this. The share prices of ETFs (including accumulating ETFs) will follow the net asset value (NAV) per share because "authorized participants" will conduct arbitrage when the price and NAV deviate. This arbitrage will narrow the gap between price and NAV. I explain in detail here: Understanding how an ETF works.

The concerns in the rest of your question are not relevant to the main question, because the mechanism explained above does not rely on "hope" to keep the price in line with the NAV.

While not relevant to answering your question, your concerns suggest that this might interest you: If a stock doesn't pay dividends, then why is the stock worth anything?

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