Research Summary - Why Stake When You Can Borrow?


  • 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?


Chitra, Tarun, and Alex Evans. “Why Stake When You Can Borrow?.” Available at SSRN 3629988 (2020).


  • 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.


  • 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.


  • 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.


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.


  • 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.


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.


This paper highlights that both high market cap and high staking participation are necessary for PoS network security and that, under the right conditions, an endogenous staking derivatives market can be the primary lending market for a given staked asset. This is a particularly relevant concept in the present DeFi ecosystem of high demand for borrowing as well as increased market capitalization (due to rising prices).

This environment creates the risk for capital flight in order to maximize yield if there are attractive off-platform lending opportunities available. In this paper, the researchers present conditions under which staking derivatives help to address this problem by redistributing wealth in a PoS system. However, there is a balancing act of parameterization between creating conditions that help preserve stake equality versus leading to excessive liquidations. Finding this ‘optimal region’ can be a narrow margin depending on system configuration.


Well put. This is perhaps the best paper to frame a discussion on the intersection between PoS financialization and network security. I agree with the authors’ analysis that staking derivatives have the potential to mitigate wealth centralization in a PoS network’s validator set, much like the advent of mining pool protocols increased miner decentralization (albeit via a substantially different mechanism).


As far as the parallel between mining pools and staking derivatives, I think risk is a key lens through which we can examine this problem. Mining pools allow for pooled risk, which reduces an economic cost on participants, making it more efficient to engage with the system. This is somewhat similar to how staking derivatives reduce the capital cost inefficiency on validators. However, these staking derivatives do have to compete with the exogenous lending markets in order to have some effect on equality and the PoS systems have to contend with potential credit risk, creating more economic cost, reducing efficiency for all participants.

It is also worth mentioning that there is a potential for parasitic markets or other economically dangerous constructs to emerge if this minting occurs off-platform. In this context, a parasitic market means a market that issues a derivative asset tied to the value of some staked quantity but where the PoS protocol is unable to slash the derivative holder for failure to meet participation criteria.

Given the magnitude of capital needed for secure PoS operation, these derivatives have the potential to represent significant value. It would be potentially risky for the system if these validators were able to sell or lend these derivatives privately in order to then obtain more capital to stake and further mint in a loop. This could potentially allow a validator to accumulate an outsized stake (if unnoticed). This is a non-zero risk and potentially more likely in a frothy, bullish market where stake is consistently increasing in value.


The analogy of a bond seems fitting here. Stakers lend capital to the network so it can disincentivize attacks and reach stable Nash equilibrium. In return, they receive a yield that is
risk-free as it is algorithmically paid if stakers honor loan terms, such as liveliness requirements. Following the same analogy, staking derivatives are what transform staked assets into fixed income instruments that can be freely traded.

Previous work by Tarun showed PoS deflationary systems are unstable and unlikely to work as DeFi has introduced high opportunity costs. In the event of a network-wide rebalance driven by better risk-adjusted returns in DeFi, a “bank run” might take place where lenders can overrun the “Time to Maturity” of a staked asset by selling the derivative, thereby synthetically draining a network’s security budget.


DeFi staking protocols represent a blend of inflationary, constant, and deflationary monetary policies. In this paper, Tarun highlights how 1) completely deflationary currencies are particularly vulnerable to large rebalances, 2) having fewer coins than system participants leads to high borrowing demand and subsequently large rebalances and 3) the worst-case rebalancing rate for deflationary currencies depends on the terminal money supply unlike exponentially inflationary systems (where it only depends on initial money supply). As such, the money supply policy plays an important role in determining the ability for a PoS network to find this ‘safe’ balance.

One self-identified gap in this paper’s scope is how validators and other ecosystem participants price credit risk into these staking derivatives. It is interesting and potentially important to consider to what extent credit risk changes the estimation of the impact staking derivatives have on PoS network security. Unfortunately, it is difficult to model this risk and there are a number of nuances that limit the ability for researchers to directly apply traditional credit risk models to PoS derivatives.

As you mentioned, Lucas, one of the requirements for validators to ensure that staking derivative yields remain “risk-free” is generally liveliness. This threat of slashing having an impact on derivative profitability is critical as it is the ‘stick’ to measure against the ‘carrot’ that is leverage on staked capital. This assumption, however, only holds when the endogenous market is the locus for minting these derivatives.


I wonder the extent to which indirect deflationary mechanisms like EIP1559 could change this analysis. EIP1559 enables polynomial inflation at the block level, but also introduces a fee-burning heuristic that may lead to deflation in the long run. One hypothesis is that, if coupled EIP1559, inflationary PoS protocols with “in-protocol borrowing” could reduce supply dilution while also decreasing the impact of bank runs.


Though EIP1559 introduces a deflationary mechanism, it is not clear that this would outpace traditional Ethereum inflation and it is entirely possible that the system would remain largely inflationary (though less predictably so). That said, if a PoS protocol’s own monetary supply policy is broadly inflationary then the risk of ‘bank runs’ is mitigated as mentioned in the paper. EIP1559 does not appear like it would represent a significant and predictable impact in the underlying protocol’s security, at least vis a vis staking derivatives.


This has been an awesome conversation to follow! It did raise a few questions that maybe people could help me out with. When @Vishesh says:

Have we ever seen this optimal region in the wild (or at least something getting close to it)? It would be interesting to see examples if anything has approached this balancing point.

Similarly, I’m curious about the nature of that balancing point. Are the concerns about network security or concerns about excessive liquidation equally valued? Or is one concern slightly more important than the other?

Then later in the conversation @cipherix claims:

and that got me wondering if there is a cost here (as fixed income) that is then worth it to the protocol for the increase in network security that the original paper is talking about? Or maybe more what factors should be considered for that network and how do we get to a price point for security balance?

This discussion has highlighted that balancing points are needed, and I’m interested in what more we might be able to elaborate on where those balancing points are/how do we compare the balancing factors.


Direct from the paper–> “We highlight the main results that are relevant for DeFi and PoS protocol designers. First, the results of §3 show that one can reduce inequality amongst stakers by adding staking derivatives. However, the portfolio returns estimated in §4.5.2 show that this inequality comes at the cost of burning a significant fraction of the money supply. These two results describe a trade-off between the number of liquidations of a derivative position and the amount of inequality in the system.”

I don’t know that there is a live case where a protocol designer has taken this body of work and explicitly used it to inform the design of a staking derivatives system.

What this means is that one of the drawbacks of these staking derivatives can be excessive liquidation of derivative positions. If there is excessive liquidation, then there would be significant 1) gas cost, 2) token burn, 3) Gini coefficient redistribution. For different reasons, each of these can present security risks for a PoS system.


Since the release of this paper in June 2020 Aave have published V2 of their whitepaper. With this update from V1 to V2 of the Aave protocol we’re able to see a few key changes involving collateral swapping, how loans can be repaid using collateralized assets, and changes to the risk parameters. I want to take a look at how collateral swapping may impact the ecosystem in terms of the conclusions found in the summary above as well as with some of the claims made in the subsequent discussion.
V2 allows for users to trade their deposited assets, this includes any assets they’re using as collateral. In a medium post Stani Kulechov states the following:

“Collateral swapping can be a useful tool to avoid liquidations.” (1)

One of the key outcomes of this new feature is users are able to better manage positions that may contain high fluctuating asset valuations. If a user is concerned their position(s) may be liquidated due to price fluctuations they can swap their collateralized assets for a stablecoin to secure their position. Another benefit to users is they are able to change their position to potentially a higher yielding one in one step.

Given the described benefits of implementing collateral swapping on Aave V2 I wanted to bring up a point discussed in the conversation above. In the conversation between @Vishesh and @cipherix it was stated:

“In the event of a network-wide rebalance driven by better risk-adjusted returns in DeFi, a “bank run” might take place where lenders can overrun the “Time to Maturity” of a staked asset by selling the derivative, thereby synthetically draining a network’s security budget.”

This brings me to the following question:

Does the implementation of collateral swapping increase the risk of the aforementioned “bank run” and/or draining of a liquidity pool?

From my interpretation, if yields in position A significantly outweigh those in position B then any rational actor would swap their deposited assets, even if it is already being used as collateral, to switch from A to B. If enough users do this is it possible to see the distribution of assets on the platform becoming significantly weighted one way or another, potentially destabilizing it? This is a little bit of a turn from the initial paper but given the implications of collateral swapping on the potential distribution of assets I believe some of the conlcusions found in the summary may be pertinent to this situation.

@Vishesh and @cipherix would either of you be able to touch on this?


It’s hard to say whether collateral swapping inherently increases this risk.

It is probably equivalent to consider selling versus collateral swapping, though it is not clear to me that collateral swapping would even be mechanically feasible for most platforms where the derivative is minted by the primary platform which would likely prevent ownership transfers of staked positions. This means that derivatives would have to be paid back in order to unlock stake wouldn’t it? If so, any “swap” of positions from one owner to another would be explicitly priced in by the system, diluting the value of the staked asset or potentially incurring slashing penalties.

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