# Pharo GreenPaper: Tokenomics

# Pharo Tokenomics

The $PHRO tokenomics is designed to incentivize new markets and early adopters. $PHRO is a utility token designed to incentivize the discovery of a market’s event rate by rewarding users’ event rate estimate performance. Each new market creates a constant buy-pressure as premiums must be paid in $PHRO, and early market adopters earn $PHRO by accurately predicting market events. To earn $PHRO rewards from any market, a user must stake $PHRO and give their event rate estimate for that market, whether they’re a liquidity provider or cover buyer. This staking requirement creates a consistent deflation mechanism that can be actively managed by the Pharo DAO.

**Ticker:** PHRO

**Chain:** Polygon, Optimism & Ethereum

**Contract Address: Kovan **0xD0F30A471826AAf7970eB35d8409E88CB8BA5370

**Max Supply:** Unlimited

# Deflationary Mechanism

Each Pharo market begins with inflation, then transitions to deflation as the market stabilizes. Deflation happens naturally as $PHRO is required to participate on either side of each Pharo market, putting constant buy pressure on $PHRO as new premiums and new liquidity must be paid using $PHRO. $PHRO staked in a market could be:

- Redistributed as rewards
- Added to the reinsurance liquidity pool (reserve pool)
- Added to DEX liquidity pools
- Burned

# Rewards Distribution

$PHRO rewards decrease when the underlying data, user and event, matches Pharo’s estimated Probability Distribution Function (PDF) according to its p-value. When a Pharo market stabilizes, the rewards are minimal as the p-value indicates little value in new estimates. The p-value therefore limits the inflationary rewards period, the time and number of estimates required to characterize the event rate and reliably predict market events.

## Stable Market

A stable market is defined as a market whose event rate is “predictable”. Predictable means the event occurs within known statistical uncertainty. A market event rate’s statistics are calculated from the market’s users who submit their event rate estimates when they stake their $PHRO in the market.

# Reinsurance

Events happen, payouts will be made, but in the long run liquidity providers will earn money if they re-stake and stay in the game. To support this, Pharo collects 5% of $PHRO staked into a reinsurance pool, which liquidity providers can pay an additional premium to access; The 5% is managed by the Pharo DAO. This reinsurance pool makes it easy to stay in a market, maintaining liquidity in that market, and thereby supporting the deflationary process.

# DEX or Burn

The Pharo DAO can vote to invest or burn $PHRO locked in any given market. When investing, minimum liquidity in any or all pools will be maintained by selling the locked $PHRO. The Pharo DAO can burn the locked $PHRO to avoid creating sell pressure and lowering the token value too much.

# Limits of Inflation and Deflation

# Maximum Market Inflation aka Kickstart Inflation

Inflation of $PHRO occurs by design in an unstable market, this is how users are incentivized to participate early: when event rates are unknown and uncertainty is highest. An inflation period is shortest lived if users’ estimates have a p-value of 0 (zero), and perfectly predict the arrival time, aka Pharo cycles, of the next event, which can occur with as little as 33 user estimates; A Pharo cycle being the unit of measure defined by that market’s event rate discovery question.

# Maximum Perpetual Inflation

## TL;DR

Chaotic markets → Consistent Inflation → Inflation / Cycle < Kickstart Inflation → Deflation / Cycle >=< Inflation / Cycle → Deflation is DAO controlled.

## Rabbit Hole

**Chaotic Markets**

Some markets will have crowds that fundamentally disagree about the true event rate, either because of an unfalsifiable assumption, or because the event distribution is multi-modal or chaotic. These disagreements will result in irregular event rate estimates, estimates that collectively do not match Pharo’s assumption of a gamma distribution, likely resulting in p-values anywhere between 0.5 and 1 depending.

**Consistent Inflation**

Usually after the “kickstart” inflation period, incentives go to zero once users have discovered the market event rate, however in our chaotic market the rewards will never go to zero, there is no good simplification or analytical characterization of the users’ estimates, and the market will consistently inflate $PHRO with each observed event.

**Inflation / Cycle < Kickstart Inflation**

This inflation rate will be less than the kickstart minimum rate as, 1) the p-value cuts rewards in half due to an imperfect statistical characterization, and 2) users’ estimates must be statistically further from observed events than a ‘perfect’ kickstart period. Whether this inflation is 7% or 0.1%, there is consistent inflation as $PHRO is awarded to users that correctly estimate the event rate, it just may be that the object whose events we’re observing doesn’t have a regular pattern, and may even be chaotic in nature.

**Deflation / Cycle >=< Inflation / Cycle**

Each market’s potential deflation rate per cycle is greater than the kickstart inflation rate as rewards are designed to be capped at 100% of $PHRO staked in each cycle.

**Deflation is DAO controlled**

The Pharo DAO has three deflationary actions that can be managed manually via the Pharo DAO multisig wallet, or automatically via the Pharo DAO smart contract. The real question is how can the Pharo DAO ensure long term stability of the $PHRO token price as markets are added and as market TCL changes.

Pharo uses its own internal definition of time, which we call a cycle and is based on that market’s question for gathering event rate estimates and determining the wisdom of the crowd. Let’s say we have a market collecting $10K in premiums each cycle, paid in $PHRO. Let’s also say one (1) $PHRO = one (1) $USDC, then a DEX with $1MM in $PHRO / $USDC paired liquidity has equal amounts $PHRO and $USDC, 500K / 500K respectively. We can calculate the deflation rate for each cycle using the change in the DEX’s liquidity ratio, in our case purchasing $10K in $PHRO changes the $USDC / $PHRO ratio from 500K / 500K to 500K / 490K, which is a 2% $PHRO price increase due to buy pressure. If we instead use $100K in premiums, we’ll see a 25% price increase each cycle. As liquidity pools are created and/or increase their TVL, Pharo will track the average deflation rate across all markets and determine how to best control the price of $PHRO by adjusting the rates of:

- Minting new $PHRO,
- Selling back into the market,
- Adding liquidity to $PHRO liquidity pools, or
- Burning $PHRO

The average of these various rates are maintained at any positive inflation or negative deflation rate the DAO chooses for whatever reason. With such precise control over the price of $PHRO, each new market both stabilizes the overall rates while allowing each market to behave organically.

Next we’ll be breaking down the Pharo IDO, scheduled for 2022Q1, stay tuned 📻