# A Crypto Yield Model for Staking Return

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## Abstract

**:**

## 1. Introduction

## 2. On the Staking Reward Calculation

- Mining rewards: Miners receive newly minted coins for successfully validating and adding new blocks to the blockchain. The miners are also compensated for protecting the network from spam attacks.
- Staking rewards: In addition to the rewards mentioned above, the stakers receive opportunities to vote on protocol upgrades (e.g., staking reward amount) and changes in addition to partaking in the overall governance of the blockchain.

## 3. Main Results

**Result 1**(Claim 1).

**Result 2**(Claim 2).

**Result 3**(Claim 3).

## 4. Formal Derivation of the Staking Rate

- $\mathbb{N}=\{0,1,2,\cdots \}$ and ${\mathbb{N}}^{*}=\mathbb{N}\setminus \left\{0\right\}=\{1,2,\cdots \}$;
- The discrete set $\u301a1,n\u301b$ is $\{1,2,\cdots ,n\}$, for any $n\in {\mathbb{N}}^{*}$;
- $\mathbb{R}$ is the set of real numbers and ${\mathbb{R}}_{+}^{*}=\{x\in \mathbb{R},x>0\}$;
- ${1}_{X}$ is the indicative function associated with the event X (i.e., it is 1 if the event X occurs, and 0 otherwise).

#### 4.1. Probabilistic Definition of Staking

#### 4.2. Staking Rate Derivation

- 1.
- The staker i;
- 2.
- The blockchain pool, regularly rewarding staker i.

**Definition 1.**

**Claim 1.**

**Proof.**

#### 4.3. Slash Rate Inclusion

**Claim 2.**

**Proof.**

#### 4.4. MEV for Estimating the Reward

**Definition 2**

**Claim 3.**

**Proof.**

#### 4.5. The Ethereum 2.0 Staking Rate

#### 4.5.1. Rate Estimation

#### 4.5.2. Electricity Cost Addon

#### 4.5.3. Annual Percentage Yield

#### 4.5.4. Implementation

#### 4.6. Mining Rate Derivation

**Claim 4.**

**Proof.**

## 5. Discussion

#### 5.1. Time-Dependency

#### 5.2. General Discussion on the Approach

#### 5.3. Adding Maturity

#### 5.4. Assumptions and Healthy Blockchain

#### 5.5. Model Limitations

#### 5.6. Slashing

#### 5.7. Memoryless Property for Slashing Events

#### 5.8. Slashing Event Independent of Staker

#### 5.9. MEV and Total Income

#### 5.10. Transaction Fee—Exponential Assumption

#### 5.11. Mining Rate

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Disclaimer

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**Figure 1.**Staking gains (blue arrows) of an investor who is staking coins (red arrow representing deposit), i.e., committing some of their cryptocurrencies to support its validation and construction. In this case, the staker is rewarded at times ${t}_{1}$, ${t}_{2}$, ${t}_{4}$, ${t}_{5}$, and ${t}_{7}$.

**Figure 2.**Annual percentage yield with respect to time. The process should be continuous and can be updated each time a block is added to the blockchain.

**Figure 3.**Exponential and log-normal fits of the daily average transaction fees (in ETH) for the Ethereum blockchain—from 7 November 2022 to 7 November 2023 (source: Blockchair). KS test Pval(exponential at the tail) = 0.45; KS test Pval(lognormal) = 0.033; KS test Pval(lognormal at the tail) = 0.57.

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**MDPI and ACS Style**

Riposo, J.; Gupta, M.
A Crypto Yield Model for Staking Return. *FinTech* **2024**, *3*, 116-134.
https://doi.org/10.3390/fintech3010008

**AMA Style**

Riposo J, Gupta M.
A Crypto Yield Model for Staking Return. *FinTech*. 2024; 3(1):116-134.
https://doi.org/10.3390/fintech3010008

**Chicago/Turabian Style**

Riposo, Julien, and Maneesh Gupta.
2024. "A Crypto Yield Model for Staking Return" *FinTech* 3, no. 1: 116-134.
https://doi.org/10.3390/fintech3010008