> For the complete documentation index, see [llms.txt](https://docs.keikofinance.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.keikofinance.com/redemption-mechanism/ars-simulations.md).

# ARS Simulations

We did simulations with a big dataset of random Keiko vaults to explore the Adjusted Redemption Score (ARS), a metric that builds upon the traditional Normalized Collateral Ratio (NCR) by incorporating additional risk factors.\
\
You can run the simulations yourself and modify the parameters used by executing the 'simulations.py' python script that you can find on this github repo:

> <https://github.com/KeikoFinance/keiko-data>

### Key Insights

1. **Risk Sensitivity**: The ARS provides a more sensitive measure of redemption risk. While the NCR might suggest similar risk levels for vaults with the same collateral-to-debt ratio, the ARS can differentiate based on the specific MCR requirements.
2. **System Adaptability**: The MCR Component in the ARS allows the system to adapt to changing market conditions or risk preferences by adjusting how the MCR influences the overall score.
3. **Risk Distribution**: The ARS creates a wider spread of risk scores compared to NCR alone. This allows for more granular risk categorization and potentially more precise liquidation or incentive mechanisms.
4. **Collateralization Incentives**: By incorporating the MCR into the risk score, the ARS may encourage users to maintain higher collateralization ratios relative to their specific vault requirements, potentially increasing overall system stability.
5. **Complex Risk Factors**: The ARS can potentially incorporate more complex risk factors through adjustments to the MCR Component calculation, allowing for a more sophisticated risk assessment model.

### 100 Vaults Sample Data (simulation.py)

<figure><img src="/files/Nv8P8HJjpzXqT9jMD7uk" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/8YcbjT1QxG0BLtv7LX1Q" alt=""><figcaption></figcaption></figure>

With an MCR\_Factor of 0.2, we obtain the following results:

* Average Impact: 21.11%
* Median Impact: 19.22%
* Minimum Vault Impact: 0.97%
* Maximum Vault Impact: 52.23%

In this context, "Impact" refers to the relative weight of the MCR (Minimum Collateralization Ratio) component in the ARS (Adjusted Redemption Score) compared to the NCR (Normalized Collateralization Ratio) component. Our current goal is to achieve an average impact of approximately 20%. Given these results, an MCR\_Factor of 0.2 appears to be an appropriate choice.

This factor allows for a balanced influence of both MCR and NCR components in the ARS Score calculation, with the MCR component contributing, on average, about one-fifth of the total score.&#x20;

###

### Data Visualization

<figure><img src="/files/W0ZQ2aEYmswa8lSQkCjy" alt=""><figcaption><p>collateral_debt_ratio_vs_mcr_impact</p></figcaption></figure>

<figure><img src="/files/0QDwP2hCHt3wotiycckm" alt=""><figcaption><p>correlation_heatmap</p></figcaption></figure>

<figure><img src="/files/5KikSQeC9wYVbuW6LvGa" alt=""><figcaption><p>mcr_impact_distribution</p></figcaption></figure>

<figure><img src="/files/wKB7a3RISERoZjXjcoQw" alt=""><figcaption><p>ncr_vs_ars_impact_zoomed</p></figcaption></figure>


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