BY Kevin Dowdon May 6, 2015
(Note: check original article for actual equations)
In his ground-breaking work, Denationalisation of Money: the Argument Refined, F.A. Hayek proposed that open competition among private suppliers of irredeemable monies would favor the survival of those monies that earned a reputation for possessing a relatively stable purchasing power.
One of the main problems with Bitcoin has been its tremendous price instability: its volatility is about an order of magnitude greater than that of traditional financial assets, and this price instability is a serious deterrent to Bitcoin’s more widespread adoption as currency. So is there anything that can be done about this problem?
Let’s go back to basics. A key feature of the Bitcoin protocol is that the supply of bitcoins grows at a predetermined rate.1 The Bitcoin price then depends on the demand for bitcoins: the higher the demand, the higher the price; the more volatile the demand, the more volatile the price. The fixed supply schedule also introduces a strong speculative element. To quote Robert Sams (2014: 1):
If a cryptocurrency system aims to be a general medium-of-exchange, deterministic coin supply is a bug rather than a feature. . . . Deterministic money supply combined with uncertain future money demand conspire to make the market price of a bitcoin a sort of prediction market [based] on its own future adoption.
To put it another way, the current price is indicative of expected future demand. Sams continues:
The problem is that high levels of volatility deter people from using coin as a medium of exchange [and] it might be conjectured that deterministic money supply rules are self-defeating.
One way to reduce such volatility is to introduce a feedback rule that adjusts supply in response to changes in demand. Such a rule could help reduce speculative demand and potentially lead to a cryptocurrency with a stable price.
Let’s consider a cryptocurrency that I shall call “coins,” which we can think of as a Bitcoin-type cryptocurrency but with an elastic supply schedule. Following Sams, if we are to stabilize its price, we want a supply rule that ensures that if the price rises (falls) by X% over some period, then the supply increases (decreases) by X% to return the price back toward its initial or target value. Suppose we measure a period as the length of time needed to validate n transactions blocks. For example, a period might be a day; if takes approximately 10 minutes to validate each transactions block, as under the Bitcoin protocol, then the period would be the length of time needed to validate 144 transactions blocks. Sams posits the following supply rule:
Here Pt is the coin price, Qt is the coin supply at the end of period t, and ∆Qt is the change in the coin supply over period t. There is a question as to how Pt is defined, but following Ferdinando Ametrano (2014a), let’s assume that Pt is defined in USD and that the target is Pt=$1. This assumed target provides a convenient starting point, and we can generalize it later to look at other price targets, such as those involving price indices. Indeed, we can also generalize it to targets specified in terms of other indices such as NGDP.
Another issue is how the change in coin supply (∆Qt) is distributed. The point to note here is that there will be occasions when the coin supply needs to be reduced, and others when it needs to be raised, depending on whether the coin price has fallen or risen over the preceding period.
Ametrano proposes an elegant solution to this distribution problem, which he calls ‘Hayek Money.’ At the end of each period, the system should automatically reset the price back to the target value and simultaneously adjust the number of coins in each wallet by a factor of Pt/Pt-1. Instead of having k coins in a wallet that each increase or decrease in value by a factor of Pt/Pt-1, a wallet holder would thus have k×Pt/Pt-1, coins in their wallet, but the value of each coin would be the same at the end of each period.
This proposal would stabilize the coin price and achieve a stable unit of account. However, it would make no difference to the store of value performance of the currency: the value of the wallet would be just as volatile as it was before. To deal with this problem, both Ametrano (2014b) and Sams propose improvements based on an idea they call ‘Seigniorage Shares.’ These involve two types of claims on the system—coins and shares, with the latter used to support the price of the former via swaps of one for the other. Similar schemes have been proposed by Buterin (2014a),2 Morini (2014),3 and Iwamura et al. (2014), but I focus here on Seigniorage Shares as all these schemes are fairly similar.
The most straightforward version of Seigniorage Shares is that of Sams, and under my interpretation, this scheme would work as follows. If ∆Qt is positive and new coins have to be created in the t-th period, Sams would have a coin auction 4 in which ∆Qt coins would be created and swapped for shares, which would then be digitally destroyed by putting them into a burning blockchain wallet from which they could never be removed. Conversely, if ∆Qt is negative, existing coins would be swapped for newly created shares, and the coins taken in would be digitally destroyed.
At the margin, and so long as there is no major shock, the system should work beautifully. After some periods, new coins would be created; after other periods, existing coins would be destroyed. But either way, at the end of each period, the Ametrano-style coin quantity adjustments would push the price of coins back to the target value of $1.
Rational expectations would then come into play to stabilize the price of coins during each period. If the price of coins were to go below $1 during any such period, it would be profitable to take a bullish position in coins, go long, and profit when the quantity adjustments at the end of the period pushed the price back up to $1. Conversely, if the price of coins were to go above $1 during that period, then it would be profitable to take a bear position and sell or short coins to reap a profit at the end of that period, when the quantity adjustments would push the price back down to $1.
These self-fulfilling speculative forces, driven by rational expectations, would ensure that the price during each period would never deviate much from $1. They would also mean that the length of the period is not a critical parameter in the system. Doubling or halving the length of the period would make little difference to how the system would operate. One can also imagine that the period might be very short—even as short as the period needed to validate a single transactions block, which is less than a minute. In such a case, very frequent rebasings would ensure almost continuous stability of the coin price.
The take-home message here is that a well-designed cryptocurrency system can achieve its price-pegging target—provided that there is no major shock.
Ametrano, F.A. “Hayek Money: The Cryptocurrency Price Stability Solution.” August 19, 2014. (a)
Ametrano, F. M “Price Stability Using Cryptocurrency Seigniorage Shares.” August 23 2014. (b)
Buterin, V. “The Search for a Stable Cryptocurrency.” November 11, 2014. (a)
Buterin, V. “SchellingCoin: A Minimal-Trust Universal Data Feed.” March 28, 2014. (b)
Iwamura, M., Kitamura, Y., Matsumoto, T., and Saito, K. “Can We Stabilize the Price of a Cryptocurrency? Understanding the Design of Bitcoin and Its Potential to Compete with Central Bank Money.” October 25, 2014.
Morini, M. “Inv/Sav Wallets and the Role of Financial Intermediaries in a Digital Currency.” July 21, 2014.
Sams, R. “A Note on Cryptocurrency Stabilisation: Seigniorage Shares.” November 8, 2014.
 Strictly speaking, the supply of bitcoins is only deterministic when measured in block-time intervals. Measured in real time, there is a (typically) small randomness in how long it takes to validate each block. However, the impact of this randomness is negligible, especially over the longer term where the law of large numbers also comes into play.
 Buterin (2014b) examines three schemes that seek to stabilize the cryptocurrency price: BitAsset, the SchellingCoin (first proposed by Buterin (2014b)) and Seigniorage Shares. He concludes that each of these is vulnerable to fragility problems similar to those to be discussed in my next post.
 In the Morini system, participants would have a choice of Inv and Sav wallets, the former for investors in coins and the other for savers who want coin-price security. The Sav wallets would be protected by the Inv wallets, and participants could choose a mix of the two to meet their risk-aversion preferences.
 In fact, Sams’ auction is unnecessarily complicated and not even necessary. Since shares and coins would have well-defined market values under his system, it would suffice merely to have a rule to swap them as appropriate at going market prices without any need to specify an auction mechanism.