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Suppose you wanted to create a token representing an index fund for various cryptocurrencies and you made sure that you held enough cryptocurrency reserves for each currency represented in the fund. Would it be possible to adjust the circulation of the token or use some other programmatic means to keep the cost of the token pegged to the index?

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This is an economic question. You could define an economic model in which you control the token's supply, so you will provide more tokens when it is needed. Technically, this is possible through your token's smart contract. You could supply more tokens to lower the price or buy the tokens from the market to raise up the price.

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