In order to hold the peg you need to collateralize your coin ether in full (sound but suboptimal), fractionally (that's what banks do) or not at all (that's fraudulent).
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There's a large twitterature out there on "why pegcoins don't work" (usually mislabeled as stablecoin), so I can skip that and talk about actual stablecoins. Short version: thin collateral makes pegs explode. (Also, pegging against fiat makes you an exchange.)
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3. To create a stablecoin that's endogenous to the underlying value creation process you have *in principle* two levers: 1. the issuance scheme, and 2. the allocation scheme.
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In practice you're running against a bunch of taboos and more technical obstacles. Taboo #1 is that you can't (and shouldn't) commit to a fixed cap bc you have to adjust issuance ad hoc acc to an external signal, which leads directly to taboo #2, the dilution/debasement scare.
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But while by default new coins are allocated to in-kind efforts that secure the network (read: mining), in theory new coins could also be allocated to current coin holders as a kind of automated dividend. Some algorithmic stablecoins propose to do that.
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That still leaves pretty steep technical problems: How to create (or work around) an unimpeachable external signal of purchasing power, how to withdraw coins from circulation, how to parametrize issuance and allocation, etc.
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But there's already a bunch of algorithmic stablecoins out there that attempt to implement such a scheme. How well they achieve this is likely more an empirical than a theoretical problem, so there's certainly space for more.
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Blockchain space like startup space is about parallelizing the taking of wrong turns.

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Replying to @oliverbeige @ecoinomia
I need to add my 2 cents and mention that interest rates are an integral part of any stable currency. As well, market signal can be utilized to create stability in a currency while integrating the time value of money.https://www.sap.com/canada/documents/2017/11/382d86c5-e07c-0010-82c7-eda71af511fa.html …
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Replying to @james_zdralek
Indeed, although I haven't seen that being incorporated into "automated central bank" type stablecoins yet. Let me know if you're aware of one, I'm not necessarily up to speed on that topic.
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interest rates will have to be decided by the market itself, otherwise the Impossible Trinity will be broken. Algorithmic stablecoins choose: Free capital flow - YES Fixed exchange rate - YES Sovereign Monet Policy (e.g. rates) - NO you can’t do all three, as Asia 1998 showed
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