TLDR:
- Proof-of-Stake protocols have higher security when the numeraire value of the token is “high” and a large majority of tokens are staked.
- Derivatives may be introduced to PoS protocols via synthetic asset creation where a validator can use their staked assets to borrow the synthetic asset.
- The implementation of derivatives to a PoS protocol can decrease the inequality of wealth distribution in the system, increasing security.
- ROI for validators may decrease with the implementation of derivatives as part of the monetary supply must be burned to compensate for borrowing defaults and slashes.
Core Research Questions:
How do staking derivatives affect network security for PoS and DeFi?
Citation:
Chitra, Tarun, and Alex Evans. “Why Stake When You Can Borrow?.” Available at SSRN 3629988 (2020).
Background:
- Proof-of-Stake (PoS): a Sybil-protection mechanism with a corresponding consensus protocol where validators lock (stake) their coins and the protocol mechanism randomly assigns the validator the right to mine the next block. The probability of a validator being selected to mine the next block is typically proportional to the value of the coins they have staked. In other words, the more a validator stakes the more likely they are to be randomly chosen to mine the next block and receive the reward.
- Staking: a version of mining where one “locks” their cryptocurrency in a wallet to support the security/operations of the PoS protocol and is rewarded for doing so with payouts in either the native cryptocurrency or a different, related cryptocurrency (depends on the protocol).
- Proof-of-Work (PoW): a Sybil-protection mechanism with a corresponding consensus protocol where participants called miners use computational power to identify the correct “hash” for the current mining block. The more miners competing to identify the correct hash, the more secure the network is.
- Smart contracts: a contract that is executed automatically depending on the criteria of the contract being met. In terms of asset settlement, DvP can be ensured using the autonomous nature of smart contracts.
- Slashing: a mechanism designed to protect PoS networks from malicious validators. If the validator is found acting against the network, some amount of their stake will be removed, causing a gradual loss of capital over time if the validator continues to act maliciously. In terms of DeFi, actors who borrow against their staked assets will be penalized.
- Derivatives: traditionally, a financial security with a value derived from an underlying asset or asset group. In DeFi, market derivatives can be thought of as future/short contracts as well as “synthetic” tokens.
- Agent-Based Model: a class of computational models simulating the actions/interactions of autonomous agents to view how their actions/interactions affect the system as a whole.
- Constant Function Market Maker (CFMM): a smart contract that allows for the exchange of coins and derivative assets. It employs a convex function that maps asset quantities to implied prices abiding by the principle of supply and demand. Read about other automated market makers
- Algorithmic Stablecoins: have dynamic monetary policies which adjust to maintain the coin’s pegged value. For example, if supply is low, potentially resulting in a value of the synthetic version of the stablecoin increasing in value, more of the coin may be issued. If the synthetic asset is below the equilibrium price, tokens may be “burned” to decrease supply, thus, increasing the value of the synthetic asset back to equilibrium.
- Pólya Urn Model: a way to theoretically map real-world scenarios. For example, determining who receives a block reward and who doesn’t by using colored balls that are hidden in an urn to represent individuals, groups, or outcomes. One picks out a colored ball to represents an outcome, then puts the ball back in the urn with an additional ball of the same color. Now, there is one more ball of the previously picked color in the urn than before, increasing the probability of the same color being picked again. Many use the Pólya Urn Model as a way to show the rich get richer idea.
Figure 2: Figure of a Pólya Urn Model, (pg 11)
- Gini Coefficient: a measurement of inequality within a tested group. The higher the coefficient the higher the inequality.
- Monte Carlo Simulation: a statistical modeling technique relying on repeated random sampling to obtain results. The idea is to run models over-and-over to find numerical results which adequately represent the randomness of the tested variables.
Summary:
- The researchers give an overview of PoS and PoW staking models, agent-based models, staking, and derivatives outside of PoS, and outline their key findings in the paper.
- The general functions of staking derivatives are explored using Tezos (XTZ) and a synthetic XTZ (sXTZ) as an example. Specifically, the four main properties of what makes staking solvent are defined:
- If a validator borrows more than the collateral factor allows, the network can reclaim the validator’s staked tokens.
- If a validator mints x amount of the synthetic asset, they will always be required to pay at least x of the synthetic asset to reclaim their collateral.
- The more the synthetic asset is slashed, the more the validator who minted said asset will need to pay to reclaim their collateral.
- An on-chain market connecting synthetic assets to real assets must exist, allowing for the purchase of the synthetic asset.
- How derivative pricing functions are used to close out liens is defined.
- The derivative pricing functions of Synthetix, Tezos, Polkadot, and AAVE are outlined in broad terms.
- Using a Pólya Urn Model via Monte Carlo simulations, wealth concentrations in PoS derivative markets are explored, primarily focusing on how borrowing demand and slash probability affect wealth concentration.
- Potential derivatives returns, i.e. staking rewards, are modeled through the derivative return process.
Method:
- The researchers introduce derivative pricing functions for CFMMs to model different instances of derivatives and lending practices and the effects on the security/wealth distribution of a PoS system.
- Using both an Urn Model and Portfolio Risk Model to model different outcomes.
- The Urn Model is used to show wealth concentration/distribution using Monte Carlo simulations. The Urn Model allows for the following:
- “Measur(ing) the concentration of wealth and inequality in the stake distribution.” (pg. 5)
- The authors create a proxy for the Gini coefficient to measure inequality.
- The Portfolio Risk Model is used to map potential “safe” and “unsafe” derivative usage for different protocols when manipulating aspects of derivative pricing functions.
- Using agent-based models, a scenario where an agent aims to maximize their wealth using a two-component portfolio composed of staked and derivative assets is developed.
- Changes in mean returns and time duration are the main drivers of the portfolio.
- A third component to the agent’s portfolio is added allowing for on-chain lending, where staking and derivative returns are independent of lending returns.
- The authors add a third component to the previous Monte Carlo simulation to account for lending and risk preferences.
- Using agent-based models, a scenario where an agent aims to maximize their wealth using a two-component portfolio composed of staked and derivative assets is developed.
Results:
Wealth Concentration
- When borrowing demand and slashing probability increase the Gini Coefficient decreases implying the equality of the system increases (Figure 3).
- When borrowing demand increases, even larger participants mint staking derivatives which, when slashed, effectively act as a redistribution of wealth to smaller validators.
- When this occurs a sizable variance of the levels of wealth concentration exists as well.
- If borrowing demand is high and the probability of slashing is non-trivial then staking derivatives can reduce inequality.
Figure 3: Heat map indicating the Gini Coefficient under different assumptions
The color bar on the right side of the map indicates the Gini Coefficient, remember, when the Gini Coefficient = 1 there is perfect inequality and when the Gini Coefficient = 0 there is perfect equality within the system.
Returns and Portfolio Selection
- If a protocol wants to change a borrower’s risk level there are two main tools that can be leveraged to potentially rebalance a validator’s ratio of staked-to-derivative assets:
- Charge a higher “interest rate” increasing the base returns.
- Increase the cost of convexity, i.e. increase the collateral requirements.
- The returns of a portfolio consisting of derivatives and staked assets resembles that of a portfolio of bonds and options on bonds.
- Inequality can be reduced with the introduction of derivatives
- However, the ROI for validators is reduced as portions of the money supply (tokens) must be burned to compensate for defaults of the derivatives.
Discussion:
- If PoS protocol designers want to design a system with more equal token distribution, they should consider adopting staking derivatives and ensure the probability of slashing is non-negligible.
- More equally distributed tokens within a PoS protocol can lead to higher security for the network.
- The use of the Pólya Urn Model may open new avenues for research regarding how concentrations of wealth are distributed in PoS, and other protocol designs, using realistic scenarios.
- When the derivative pricing curve was smooth and in a ‘safe’ region far away from liquidation it was possible to compute the expected returns.
- This implies the possibility for implementing multiple protocol management options such as collecting fees on derivative contracts, rewarding honest validators, and can be used to mitigate capital flight (especially if the derivatives market becomes the primary borrowing market for the staked assets.)
- To guard against capital flight, protocol designers must choose a viable derivative pricing function that promotes the derivative as being the primary borrowing market.
- The variability of designs different PoS derivatives utilize make it difficult to use traditional credit models to price in credit risk for PoS derivative markets.
- Given the ability for the PoS derivative to handle defaulting validators is completely dependent on the design of the derivative traditional credit models may not be appropriate, but newer models utilizing the Pólya Urn Model structure may be able to model the effects credit risk has on PoS derivative security and pricing.
Applicability:
The results indicating that the introduction of derivatives to PoS networks may decrease the concentration of wealth within the network have far-reaching security implications. With more of the wealth in the PoS network being distributed amongst more validators, it becomes harder for malicious actors to successfully attack the network. Furthermore, if individuals perceive the network to have a more equal distribution of rewards, more validators may be incentivized to join the network, thus increasing the security of the network. It is important for protocol designers who wish to include derivatives in the PoS network, to choose a viable derivative pricing function as slash probabilities are shown to significantly impact the wealth distribution in the network and the ratio of staking-to-lending within a users portfolio.