Theoretical approach for building a risk-free atom delegation token

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Introduction

Hello everyone, this is Meher, co-founder of Chorus One.

In this post, I consider the question of whether a risk-free interest rate exists for the Cosmos Hub. I got interested in this question because Hyung from BHarvest wants to create a validator independent delegation token. Such a token would allow its holders to make some amount of validator-independent risk free interest from the delegation economy. Here is my proposal to make such a risk-free interest-delivering token for the users of the Cosmos Hub. This proposal is in addition to a separate design, based on delegation tranching, being worked on concurrently by BHarvest.

Naively, the expectation would be one cannot make any amount of risk-free interest in atoms. The impression is that the choice is between holding liquid atoms at zero interest or delegating to a validator and making ~10% interest. Delegations incur risk, therefore the interest made via delegations to a validator are not risk-free.

The next section summarizes all of the parameters used in the example to follow. The section thereafter demonstrates a particular delegation portfolio, christened “The Ideal Delegator’s portfolio”, that presents a third option.

Please bear in mind that this post discussed a theoretical portfolio, not a real world construction. Real world constructions can be built from this concept, but they are likely to be low-risk tokens, rather than zero-risk tokens.

Parameters used in example

  • Total atom supply: 240 million
  • Total atom supply bonded: 168 million
  • Percentage atom supply bonded: 70%
  • Staking yield rate without commission: 12%
    • This is the amount of annual interest a delegator would make delegating to a perfect validator, that never suffers downtime or slashing, with zero commission.
    • Also referred to as staking yield rate in the post
  • Double signing penalty percentage: 5%
  • Certus’ voting power weight: 5.64%

The Ideal Delegator’s portfolio

Let’s think of Alice, who has 100 atoms that need to be delegated. She constructs her portfolio thus:

  1. 30% of her atoms are kept undelegated / free. This equals 30 atoms. The 30% number is derive from the percentage of free atoms in the protocol.
  2. 70% of her atoms are delegated to the validator set in proportion to the amount of voting power held by the particular validators
  3. For example, Certus currently has a voting power percentage of 5.64%. Hence, Alice would delegate (5.64% X 70 atoms =) 3.948 atoms to Certus.
  4. In effect, all validators get a delegation.
  5. The portfolio is updated continuously in lockstep with changing validator voting powers.

My position is the above portfolio is risk-free, and will produce an approximate interest rate of ~7.56%, if the staking yield rate is 12%. This approximate yield was calculated back of the envelope. It is possible to calculate this exactly from the voting powers and commission rates of all of the validators at this link.

What happens when a particular validator double signs, and Alice is penalized 5% of her delegation to that particular validator? Assume, Certus double signs 10 minutes after Alice executes her portfolio. In this case, Alice’s total penalty is 0.1974 ( = 3.948 * 0.05), and the total number of atoms in her possession decline to 99.8026.

(I am using Certus as an example, because the scenario of them double signing is outlandish!)

Meanwhile, the total number of atoms in existence has also fallen, as a result of being burned. In totality, 0.47376 million (= 168 million * 0.0564 * 0.05) atoms will be burned in this episode, resulting in a final supply of 239.52624 million atoms. Hence, atoms become scarcer overall. The interesting thing is that the percentage ownership of Alice in the network remains unchanged. You can verify this by comparing her earlier ownership ratio 100/240 million, by her later ownership ratio 99.8026/(239.52624 million). Both of these ratios are exactly equal to 4.166 X 10-7.

This mathematical behavior is independent of the type of punishment suffered by a validator - it will be the same even if the validator suffered an availability punishment, or if the network changed the slashing penalty amounts.

Intuitively, any punishment will be reflected in Alice’s part of the portfolio corresponding to that validator. But the other portions of her portfolio will benefit from the punishment by having Alice own an asset that has become scarcer. These two effects cancel each other out, resulting in Alice preserving the same ownership percentage of the network as before.

Hence, Alice stands to make an upside of 7.56% from this delegation portfolio, while suffering no down side at all. In other words, this portfolio is a risk-free interest bearing portfolio.

This article christens it “The Ideal Delegator’s Portfolio”, and the rewards made by the ideal delegator’s portfolio “The Network Risk Free Rate”.

Properties of the Network Risk Free Rate

Here are some properties that can be inferred for the network risk-free rate:

  1. The risk-free rate is correlated to total bonded supply of the network: Greater the bonded supply on the network, higher is the risk free rate and vice versa.

  2. The risk-free rate is negatively correlated to the average commission rate levels of the validator in the network: Higher the average commission rate of the validator set, lower is the risk-free rate of the network and vice versa.

  3. The risk-free rate is independent of individual validators: The rate is independent of individual validators, but each validator contributes (indirectly) to the risk-free rate setting by setting their commission rates. Because of this independence, a risk-free rate delivering token could become very liquid and attractive for follow-on staking derivative applications.

  4. The incremental risk and reward, over the risk-free rate, obtained by a concentrated validator delegation is the idiosyncratic rate of the validator: If a particular user delegates purely to Chorus One, they stand to make an incremental interest of 2.64% above the risk-free rate, by assuming this 5% slashing downside of Chorus One. it should be somehow possible to convert this idiosyncratic risk into a purer validator token. That is, some token that has only a face value of the actual slashing downside (5 atoms or 5%), while delivery an interest rate of the extra 2.64%. The design of such an idiosyncratic validator token can be considered in a later article.

  5. (Speculative) All PoS networks will have a risk-free rate: While this example was conceived for Cosmos, all other proof of stake networks ought to have an analogous risk-free rate. (Question to ponder: Under what conditions will a proof of stake network not have a risk free rate?)

  6. Mathematically, the risk-free rate can be derived from the formulae:

  • Risk-free rate = (Staking yield) X (atoms bonded fraction) X (1 - average validator commission rate)
  • Risk-free rate = (Network inflation rate) X (1 - average validator commission rate)

Constructing a low-risk interest delivering atom

Staking indexes should allow us the construction of validator independent, low-risk interest delivering token. Such a token would ultimately a voucher of delegation vouchers; with the basket of delegation vouchers chosen as per the voting powers of the different validators. It will have utility as reliable interest-bearing collateral for DeFi applications in the Cosmos ecosystem.