The Rise and Fall (and Rise and Fall) of Ampleforth — Part I

By Derek Schloss and Stephen McKeon

Ampleforth has received a lot of attention lately from both market participants as well as new projects that are incorporating similar features into their own protocols. We’ve been following Ampleforth for a long time so we wrote this two-part article as an explainer and a framework for thinking about how it may evolve. Part I (below) covers Ampleforth’s design and pricing mechanics. Part II covers Ampleforth’s psychology and demand drivers.

AMPL is a “supply-elastic” cryptocurrency. This means the total number of AMPL changes in response to the price per unit. Here are the basics:

• Every night at 7:00pm (Pacific), Ampleforth’s smart contract expands or contracts the total AMPL supply. This nighty supply adjustment is called a rebase.
• The supply adjustments each night are applied universally and proportionally across each wallet’s balance. After a rebase, all holders own the same share of the network as they did before the rebase. The rebases (both positive and negative) are non-dilutive because they affect all balances pro-rata.
• There is no airdrop or transaction associated with the change in units in your wallet, it’s just a function of the AMPL token smart contract.
• The nightly rebase is determined by the market price of AMPL. If the price of AMPL is trading 5% or more above the target, the rebase will expand supply to wallets holding AMPL. If the price of AMPL is trading 5% or more below the target, the rebase will decrease units in wallets holding AMPL.
• The target price is a 2019 dollar. In 2019, the target was $1.00, but now in 2020, since there has been some inflation (as measured by the CPI), the target is $1.011. This means that the equilibrium band is $0.96 to $1.06 (+/- 5%). When the market price (as reported by oracles) is within this band, then no rebasing occurs that night.

Rebase analogies: Stock Splits, Cows, Gold, and Dollars

To understand how an investor’s wealth might respond to rebasing, analogies are often a useful mental model. We’ll examine supply expansions in four other asset types: stocks, cows, gold, and U.S. dollars. Let’s start with a model from equity markets — a stock split.

In order to manage the price per share, companies will occasionally split their stock to reduce the price (or increase the price in the case of a reverse split). Let’s say a company doesn’t want the price of their stock to be over $100. When it reaches a price close to that level, say $90, they execute a 2:1 split. If I had 100 shares before the split, I now have 200 shares. This pro rata distribution of new units is similar to AMPL. If I hold 100 units of AMPL, and there is a 10% rebase, I now hold 110 units of AMPL. Every balance in every wallet is increased pro rata.

But what happens to the price?

It turns out that this is not a simple question to answer. In the case of a 2:1 stock split, the price of each share is cut in half (from $90 to 45) when trading reopens, so the total value of my shares is unchanged (100*$90=200*$45). When I teach stock splits in class, I always use the analogy of a pie — you don’t make the pie bigger by cutting it into more pieces, just like you don’t change the fundamentals of a company by slicing the equity into more shares. Intrinsically, there is no effect on the market value of corporate equity by altering the number of shares.

But, and this is important, commodity money like AMPL is not equity and the protocol is not a company. The value of corporate equity is a function of the discounted value of future cash flows, which is not an applicable framework to value commodity money, so the stock split analogy fails to paint the full picture. Our framework for thinking about the response of price to quantity adjustments is a little different when we consider commodities.

For example, if we own 100 cows and the herd gives birth to 25 calves, we don’t immediately assume that every cow is worth 20% less. A supply expansion of cows creates new value, if it didn’t then farmers wouldn’t breed them. Then again, if every farmer’s herd expands by 20% and there is an oversupply in the market for cows, then perhaps the market price per cow would decrease, but it depends on what the market expects both in terms of the supply expansion and the degree to which that supply expansion is sent to market. If market participants anticipated a flood of cows into the market, then the price would adjust in advance and we’d expect to see no reaction to the supply increase itself. The problem with this analogy is that cows are a consumable commodity, not a commodity money (at least not anytime recently). While there are digital versions of consumable commodities, AMPL isn’t one of them. Thinking about supply adjustments in consumable commodities adds something to our understanding beyond stock splits, because it introduces the notion that the additional units have value above and beyond the aggregate value of units in existence, but the analogy is still not perfect.

Let’s try again with one of the oldest commodity monies in the world. How do supply increases work for gold? Here, supply increases accrue to those that perform work to expand supply (i.e. miners). If gold miners expand supply by 1% by digging up more gold, this supply increase doesn’t cause the gold bar in my closet to magically expand by 1%. The amount of gold I own is unchanged by the supply expansion. All things equal, for a given level of demand, supply expansions that are sent to market translate to a lower equilibrium market price, which reduces my wealth if I don’t receive a share of the supply increase. Investors analyze stock-to-flow ratios for most commodity-monies because current holders (i.e. the “stock”) are negatively impacted by supply expansions (i.e. the “flow”). AMPL holders are not hurt by supply expansions because the stock receives the flow, so the analogy doesn’t fit.

Last try: fiat money. When the Federal Reserve prints USD, do you end up with a share of the increase? Maybe. For example, the money they print could be mailed out in the form of a stimulus check. If you’re a recipient, that would cause the number of units you hold to increase. But, the increase in the number of dollars was not distributed pro rata to all holders of dollars, for example, the foreign investor who holds dollars probably didn’t receive a distribution. You could argue that the government printing money causes interest rates to rise, which in turn generates an increase in the number of dollars you hold, but now we’re moving towards the idea of holding currency in the form of investable assets. The paper dollars under your mattress do not respond to interest rates, although it will be interesting to see whether the advent of CBDCs alter our thinking on this topic. On top of all of this, expansions in the money supply may induce price inflation, meaning that the purchasing power of each unit decreases. The effect of fiat supply expansion is far too vast a topic to fully address here, but in the spirit of moving on let’s agree that increases in fiat currency are not distributed perfectly pro rata to all holders of that currency, so the analogy to AMPL fails us.

So there you have it. Ampleforth’s supply model is somewhere between stock splits and cows, but dissimilar to gold and dollars. There’s nothing quite like it.

Pricing Mechanics

Let’s look at some numbers around rebasing events.

• The nightly rebase is determined by (Oracle price-Target price)/10. For example, if the oracle price on a given day is $2.00 and the target is $1.01, then the rebase that night would add 9.9% [(2.00–1.01)/10] to the AMPL balances in everyone’s wallets.
• By construction, negative rebases are capped at about 10%, positive rebases are uncapped.

Mechanically, rebases move the price in the direction of the target on geometric mean market makers like Uniswap. These systems hold the weighted geometric mean of the reserves constant. This means X does not change in the equation below:

A positive rebase causes the pool to contain more units of AMPL, therefore the price of AMPL must decrease so that X remains constant, and vice versa for a negative rebase.

A numerical example: Say that the price on Uniswap is 200 AMPL for 1 ETH just prior to a rebase. Then a 10% rebase happens so you now have 220 AMPL. You might think you can game the system by entering a trade on Uniswap one millisecond after the rebase to get 1.1 ETH. Wrong. Since the number of AMPL inside the pool rebased (just like your wallet), the price instantly went from 200 AMPL per ETH, to 220 AMPL per ETH. In other words, the price of AMPL decreased in terms of ETH (and therefore $, holding ETH constant). This did not require arbitrage trading, the rebase itself moved the price in the direction of the target by altering the composition of the pool.

It’s important to acknowledge that the Uniswap price is not AMPL’s oracle price and we’ve drawn up the following example to illustrate why that matters. For a moment, assume no one buys or sells following a rebase and we’ll use the Uniswap price to dictate the rebases. If you spend $1,000 to buy 500 AMPL at $2.00, and then all trading stopped and we just let the rebases take their course, you would have about 942 AMPL 22 days later by the time it rebased back to $1.06, or in other words, still $1,000.

But here’s where the psychology part comes in. The Uniswap price isn’t the oracle price. The Uniswap price is treating it like a stock split, not like an expansion of commodity money.

If there are market participants who believe the new units have value that does not proportionally decrease the value of their holdings prior to the rebase, then what we would observe is the asset trading at a higher price on centralized exchanges versus the instantly adjusted price on Uniswap. This leads arbitrage activity that pushes up the price on Uniswap and pushes down the price on centralized exchanges until they meet.

Turning back to stock splits, it’s important to note that the rationale wasn’t solely around cost frictions, it was also psychological friction. Back in the day, a stock price over $100 was deemed to be “expensive” and we know from a plethora of academic literature that investor psychology responds to reference points. $100/share was a reference point for 20th century equity investors, and stock splits were issued in part to manage investor psychology around that reference point.

Ampleforth’s adjustments also work towards a reference point: one 2019 dollar. Reactions to reference points are considered a behavioral bias, but the economic outcomes are real. It’s yet another case where the programmable nature of cryptocurrencies offer a feature that is implausible in traditional assets and therefore the psychological effects of daily rebasing are not well studied or understood. It’s one of the most fascinating experiments in crypto today because it’s testing the design space around the intersection of psychology and economics.

Reasonable people can debate whether increases in network value corresponding to increases in the supply of a money commodity is justified or not, but at the end of the day the value of money is a social construct. It has value because we collectively believe it does (or does not) and network value is a market outcome that aggregates beliefs.

In the case of AMPL, since price and supply are constantly being adjusted, the focus from an investment perspective is primarily on network value. Our view is that demand is a much stronger determinant of network value relative to supply. Within Ampleforth, supply is a function of demand.

So the real question is what drives demand? And that is exactly what we explore in Part II, available here.