# Interest Rate Risk

### Interest Rate Risk

#### Definition

**Interest rate risk** is the risk that changes in market interest rates reduce the value of USD0’s underlying collateral.

When interest rates rise, the market value of fixed-income securities (e.g., US Treasury Bills) typically falls. Their fixed cash flows become less attractive compared to newly issued, higher-yield instruments, which pushes prices down. If collateral must be liquidated before maturity during such a period, the protocol may realize capital losses.

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### Impact on Usual’s Collateral

In an ideal setup, collateral would be held at a central bank to earn risk-free daily interest. Because the US Federal Reserve does not accept crypto stablecoins, Usual instead holds collateral in tokenized Real-World Assets (RWAs)—primarily **US Treasury Bills** and **reverse repurchase agreements (overnight repos)** via providers such as **Hashnote USYC**.

This approach exposes the collateral portfolio to interest rate movements. Usual quantifies and manages this exposure using **duration**, a traditional finance metric that approximates the expected percentage price change of a bond for a given change in interest rates. **Longer duration = higher sensitivity** to rate changes.

> **Example:**
>
> * A bond with a **5-year duration** would decrease in value by approximately **5%** if interest rates rise by **1%**.
> * A bond with a **0.33-year duration** would decrease in value by approximately **0.33%** under the same rate shock.

Because Usual restricts collateral to **ultra-short-duration** instruments, interest rate risk is structurally minimized.

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### Historical Stress Test Context

Based on a historical review of the most extreme interest rate moves observed over the last 30 years:

| Stress Scenario                 | Rate Increase | Period    |
| ------------------------------- | ------------: | --------- |
| 2022 extreme (two-week window)  |       +75 bps | \~2 weeks |
| 2022 extreme (one-month window) |      +100 bps | \~1 month |

With a maximum portfolio **average duration of 0.33 years**, even these extreme scenarios would imply a temporary collateral value decline of approximately **0.33%**, which is intended to remain within the insurance fund’s capacity.

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### Risk Monitoring and Management

Usual applies a **three-line-of-defense** framework with defined limits, monitoring, and escalation paths.

#### 1) First Line of Mitigation: Duration Limits (Structural Constraints)

* **Per-asset limit:** Each accepted RWA must have a duration **< 0.5 years**.
* **Portfolio average limit:** The weighted average duration of the full collateral portfolio must not exceed **0.33 years** (≈ 4 months).
* **Eligibility enforcement:** Any collateral that would cause the portfolio duration to exceed **0.33 years** is **ineligible** for onboarding, regardless of other characteristics.

These hard constraints limit interest rate exposure before any operational monitoring is applied.

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#### 2) Second Line of Mitigation: Continuous Monitoring (Detection & Alerts)

* **Ongoing duration monitoring:** Portfolio duration is computed as the **weighted average duration** of all reserve assets and monitored continuously.
* **Passive deviation handling:** Deviations caused by user activity (deposits/redemptions) or market-driven changes in RWA duration are tracked. A **tolerance threshold of 0.25 years** is allowed for minor, passive fluctuations without immediate corrective action.
* **Rate monitoring:** The protocol computes a **daily weighted sum of collateral rates** and maintains a **180-day rolling weighted average**. Alerts trigger when:
  * The rolling average moves more than **±5%** versus the prior day’s value.
  * The weighted average deviates by more than **±20%** from **SOFR** on any day.
* **Missing data handling:** Weekend and holiday gaps are filled by carrying forward the last available business-day values to preserve continuity.

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#### 3) Third Line of Mitigation: Corrective Measures (Response Actions)

If deviations exceed tolerated thresholds, corrective actions are initiated in increasing order of severity:

* **Duration adjustment:** Reduce portfolio duration by selling/redeeming higher-duration RWAs and reallocating into shorter-duration instruments.
* **Withdrawal restrictions:** Limit or remove an RWA from eligible collateral if its duration profile deteriorates beyond acceptable bounds.
* **Insurance fund increase:** Increase the insurance fund size (subject to available capital) to absorb potential losses from rate-driven collateral value declines.

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### Insurance Fund Protection

Usual maintains a dedicated **insurance fund per Liquid Deposit Token (LDT)** to hedge against collateral losses, including those driven by interest rate movements.

| Parameter              |                                             Value |
| ---------------------- | ------------------------------------------------: |
| **Accrual rate**       |                       \~20% of yield (set by DAO) |
| **Minimum fund cap**   |                            0.33% of all USD0 LDTs |
| **Maximum fund cap**   |                            5.33% of all USD0 LDTs |
| **Replenishment time** | \~24 days (at 0.33-year avg. duration, 5% coupon) |

This cap range is calibrated using historical Value-at-Risk (VaR) analysis across the most extreme interest rate environments observed over the past three decades.

The fund operates through the **Counter Bank Run Mechanism (CBR)**, which burns LDT tokens held in reserve to increase the salvageable redemption value per outstanding token:

$$
S\_{LDT} = \min \left( \frac{\sum\_{i=1}^n P\_{Collateral\_i} \times C\_{Collateral\_i}}{Supply\_{LDT} - Insurance\_{LDT}}, F\_{LDT} \right)
$$

If the salvageable redemption value falls below 1, the DAO can temporarily pause the minting engine and route activity through the secondary market to prioritize re-pegging.

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### Multi Collateral Controller

The **Multi Collateral Controller** adds another layer of interest rate risk management through dynamic portfolio optimization. It computes optimal collateral weights by maximizing a risk-adjusted objective function that explicitly penalizes duration:

$$
\max \left( \lambda\_3 \sum\_{i} w\_i^\* E\[R\_i] + \lambda\_4 \sum\_{i} w\_i^\* S\_i - \lambda\_1 \sum\_{i} w\_i^\* D\_i - \lambda\_2 \sum\_{i} w\_i^\* \sigma\_i \right)
$$

Where:

* $D\_i$ is the duration of collateral type $i$
* $\lambda\_1$ is the duration risk-aversion coefficient

This construction encourages the portfolio to rebalance toward lower-duration assets as duration risk rises, and it triggers automatically when the maximum weight deviation exceeds the threshold $\epsilon$.

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### Future Enhancements

* **Automated reallocations:** Implement automatic reallocations among collateral types to preserve optimal risk-adjusted exposure and reduce manual intervention.
* **Collateral aggregator/diversifier:** Evolve toward a more advanced collateral management layer to improve duration and rate risk controls across an expanding set of RWA providers.
* **Community governance:** Using USUAL governance, the community may update duration limits, insurance fund parameters, and risk thresholds as market conditions change.

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#### Note on Parameters (KB Alignment)

The draft references specific thresholds and caps (e.g., duration limits, tolerances, insurance fund caps, alert thresholds). If you share the KB values, I can update this page to match them precisely while keeping GitBook-compatible markdown.