R_{base} = \sum_{i \in L} (w_i \cdot r_i)
* *L* - The set of approved Lending Tier sources (e.g., Aave V3, Compound V3). * *r**i* - The current annualized supply APY for USDC on source $i$. * *w**i* - The governed weight of source $i$ based on total liquidity depth (\sum *w**i* = 1). *Example:* If Aave is yielding 1.97% (60% weight) and Compound is yielding 2.56% (40% weight), the Base Rate is established at **2.20%**. *** ### 2. Deriv Spread (Market Sentiment) While the Base Rate moves slowly, the demand for leverage moves in milliseconds. To capture this, we measure the **Deriv Spread ($S\_{deriv}$)**. The system analyzes the **Derivatives Tier** (e.g., Hyperliquid funding rates, Ethena basis yields) to calculate the aggregate secured yield ($R\_{deriv}$). The Deriv Spread is simply the difference between the fast-moving synthetic rate and the slow-moving spot rate:S_{deriv} = R_{deriv} - R_{base}
**Interpreting the Spread:** * **Positive Spread ($S\_{deriv} > 0$):** The market is "Risk-On" (Greedy). Traders are willing to pay massive funding rates to maintain leveraged long positions. The cost of synthetic leverage exceeds the cost of spot borrowing. * **Negative Spread ($S\_{deriv} < 0$):** The market is "Risk-Off" (Fear/Neutral). Demand for long leverage has collapsed, or shorts are aggressively paying longs. *** ### 3. Risk Premium If we added the raw Deriv Spread directly to the Base Rate, the ISFR would be too volatile to serve as a reliable benchmark. A 10-minute flash crash on a single exchange could distort the rate by 50%. To solve this, ISFR v2 introduces the **Risk Premium (`P`*****`risk`*****)**, utilizing an alpha scalar to dampen extreme noise.P_{risk} = S_{deriv} \cdot \alpha
* Alpha scalar: A governed parameter (currently set to `0.25`). This acts as a shock absorber. It ensures that the ISFR captures the *trend* of the derivative market without being hijacked by short-term *wicks*. *Example:* If the Deriv Spread is aggressively negative at -86.9 bps, applying the 0.25 alpha dampens the shock, resulting in a calculated Risk Premium of **-21.7 bps**. *** ### 4. Final ISFR Calculation The final ISFR v2 is computed by combining the slow-moving Base Rate with the real-time, dampened Risk Premium. $$\text{ISFR} = R\_{base} + P\_{risk}$$ Or, fully expanded: $$\text{ISFR} = R\_{base} + \alpha(R\_{deriv} - R\_{base})$$ #### **Live Example Calculation** Based on the live dashboard parameters: 1. **Base Rate (R*****base*****):** 1.97% (Anchored by Aave/Compound) 2. **Deriv Spread (S*****deriv*****):** -86.9 bps (Derivatives are cheaper than spot) 3. **Risk Premium (P*****risk*****):** -21.7 bps (Dampened by alpha = 0.25) **Final ISFR:** `1.97% + (-0.217%)` = **1.75%** *** ### Index Goals 1. **Manipulation Resistance:** To manipulate the ISFR, an attacker cannot just spoof a single orderbook. They would have to simultaneously manipulate billions of dollars in Aave spot liquidity *and* the funding rates across major perpetual exchanges. 2. **TradFi Compatibility:** By separating the "Risk-Free" component from the "Credit Spread" component, the ISFR structurally mirrors how traditional finance calculates SOFR and LIBOR. 3. **Mean-Reversion:** Because the alpha scalar dampens extreme volatility, the ISFR naturally mean-reverts, making it the perfect benchmark for pricing fixed-rate loans and yield swaps within the Nunchi ecosystem.