1. The Managed Uniswap V3 Pool

The core strategy behind the managed Uniswap V3 pool is to buy under Spot’s fmv and sell over Spot’s fmv. For this reason, outsized gains are realized each time Spot’s price goes through the process of 1) dipping below fmv, 2) rising above fmv, and then 3) returning to fmv. We call this 1-2-3 process a “mean-reversion cycle.”

The managed UniV3 pool provides concentrated liquidity effectively buying low and selling high around Spot’s fmv. Broadly when:

• spot_price < fmv — the pool buys more than it sells ("buying low").
• spot_price > fmv — the pool sells more than it buys ("selling high").

This strategy can be replicated (and fine tuned) by manually setting and updating concentration bands on Uniswap V3, but we recommend using the managed vault because it allows users to benefit by “setting and forgetting.”

2. Analyzing APY

Typically Spot’s mean-reversion cycle takes ~30 days to complete and volumes spike when Spot’s price deviates from the FMV of 1 Spot. For this reason, we can best evaluate APY using 30-day rolling averages. Here's a table comparing average 30-day APY to average 30-day volatility.

By contrast, it would not make sense to expect annualized daily APYs to accurately reflect year-over-year gains. To illustrate, we can simply look at examples of 1-day APY overestimation and 1-day APY underestimation.

• 1-Day Overestimate: Annualizing the (1/17/25) daily fees incorrectly suggests an APY of 8305.56%.
• 1-Day Underestimate: Annualizing the (2/23/25) daily fees incorrectly suggests an APY of 2.80%.

When analyzing the performance of this pool, the minimum recommended lookback window is 1 cycle period (30 days) and the minimum recommended lookback window for calculating an average is 2-3 cycle periods (or 60-90 days). Generally, the longer the lookback window, the less noisy your APY value.

3. Mean Reversion

Spot is a perpetual senior tranche of AMPL. To explain how Spot's mean-reversion works, in this section we’ll briefly provide context on AMPL’s mean reverting characteristic and then expand on how this translates to Spot.

3.1. Context on AMPL Mean Reversion

AMPL, launched in 2019, has a mean-reverting price around its target. It executes a simple protocol that increases or decreases the quantity of tokens in user wallets — such that the price of AMPL reverts to 1 2019 CPI-adjusted dollar. And it has been demonstrated extensively now that the price of AMPL always returns to target, even through extreme market conditions.

Given this, you might expect that it would be profitable to apply the simple counter cyclical strategy of purchasing AMPL under its price target and selling over its price target. But it’s not that straightforward.

Although it’s clear that AMPL’s price will eventually revert to its 2019 dollar target, holders cannot precisely know how long this process of finding an equilibrium will take. And in the meantime, they are exposed to volatility through supply rebasing. The case is slightly different with Spot.

3.2. Context on Spot Mean Reversion

Spot is a derivative of AMPL that insulates holders from AMPL's supply volatility, but not its price volatility. For this reason, Spot inherits AMPL's mean-reverting price distribution. Thus under all typical operating conditions it is straightforward for market actors to execute the strategy of:

• Buying SPOT under its redeemable AMPL value
• Selling SPOT over its redeemable AMPL value

This is the core strategy employed by the managed Uniswap v3 pools discussed above.

4. FMV Calculation

SPOT is a freely redeemable asset. It has a fair-market-value (fmv) that can be calculated as:

• fmv = spot_exchange_rate * ampl_target

Example Calculation — Let’s say the current exchange rate between SPOT and senior AMPL tranches is: 1.00 and the AMPL price target is 1.19. In this case we would compute the FMV as: fmv = 1.00 * 1.19 = 1.19

This fair-market-value exists because at any time, SPOT can be redeemed for senior AMPL tranches and then sold. When:

• spot_price > fmv — market actors buy AMPL, mint SPOT, and sell to capture the difference.
• spot_price < fmv — market actors buy SPOT redeem for AMPL and sell to capture the difference.

Arbitrage between the live market price of SPOT and its redeemable AMPL value, causes SPOT prices to revert to this fmv.

4.1. FMV Over Time

You might have noticed that the fmv curve shown in the time series chart above isn’t a straight line. This is because fmv can change gradually over time. That is to say, the spot_exchange_rate above changes over time.

Broadly, the Spot protocol functions by reorganizing the volatility of AMPL into high and low volatility derivatives. The system balances demand for stability and volatility using a bi-directional funding rate.

• When there’s more demand for volatility than stability: spot_exchange_rate increases
• When there’s more demand for stability than volatility: spot_exchange_rate decrease

See the spot primer for more details.

5. APY & Volatility Calculation

To calculate the 30-day APY we first calculate 30 day yields and then annualize.

5.1. Calculate Daily Fee Yield

For each day, calculate the fee yield by dividing the swap fees generated on that day by the total value locked (TVL) at the start of that day. Formally, this is represented as:

5.2. Aggregate Fee Yields over 30 days

Sum the daily fee yields over a contiguous 30-day period to obtain a cumulative 30-day fee yield:

5.3. Annualize 30-day Fee Yield to Derive APY

To extrapolate the 30-day cumulative yield to an annual figure, the cumulative yield is annualized. This is achieved by raising the sum to the power of the ratio of the number of days in a year (365) to the period length (30), then subtracting 1:

5.4. Volatlity Calculation Methodology

Volatility is calculated as the standard deviation of 30-day returns for holding an LP token accross an n-day window. LP tokens are assumed to be (50% spot / 50% usd).

6. Equilibrium Yield in Efficient Markets

It's natural to wonder: "What happens when all arbitrage opportunities are extracted from the system?" We can imagine the scenario where an overwhelming amount of demand for staking in the managed Uniswap V3 pools enters the market, deep concentration bands are put up around Spot's fmv, and Spot's price distribution narrows; making the gains equivalent to a traditional (stable:stable) pool.

Let's first note that:

1. Spot's price volatility is inherited from AMPL
2. Spot will always be smaller in marketcap than AMPL
3. Countercyclical demand for Spot translates into countercyclical demand for AMPL.

In a vaccum AMPL's default price volatility is related to general market volatility for altcoins; and the general market volatiltiy of altcoins today is increasingly driven by macroeconomic factors.

The ambient volatiliy AMPL is exposed to, creates price-volatility for Spot. And although Spot's marketcap can become meaningful relative to AMPL's marketcap it will always be smaller because new demand for SPOT expands AMPL commensurately. For this reason we expect the arbitrage opportunity to last pretty long.

6.1. Yield Equilibrium in Efficient Markets

Let's imagine Spot's liquidity is 1/5 of AMPL's. And let's imagine that AMPL experiences 20% monthly volatility in a vacuum. All of this volatility is margin for Spot/USDC arbitragers — until it's not. At which point arbitragers would deem the cost of capital too high and find their yield elsewhere. This movement in and out of an arbitrage opportunity would eventually orient around a market competitive equilibrium yield.

6.2. Countercyclcial Demand in Efficient Markets

Concentrated demand to buy below Spot's fmv and sell above Spot's fmv is countercyclical in nature. That is to say, when AMPL's marketcap goes down, Spot's price goes down, causing actors to buy (below fmv), which translates into upward pressure on AMPL — and vice versa.

Sufficient countercyclical demand would eventually inspire market makers to directly arbitrage AMPL, buying under its price target and selling over its target, further stabilizing the collateral. And the protocol would have bootstrapped an even more resilient, stable, decentralized, store of value. Both Spot and AMPL would have the strong tendency to remain where they are; until structual changes in demand for stability are observed one way or another. Spot would behave more like an inflation resistant decentralized stablecoin. And AMPL would grow in times of fear, changing the market irrevocably.