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Notional
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Notional Basics
Risk and Collateralization
Technical Topics
Free Collateral Calculation
The free collateral calculation calculation is a two part process.
1. 1.
Collect local currency collateral surplus/requirement figures for each supported currency
2. 2.
Aggregate local currency collateral figures into one ETH-denominated free collateral figure

## Local Currency Collateral Calculation

An account has three possible types of assets per currency: cash, fCash, and Liquidity Tokens. Calculating local currency collateral figures requires converting the value of these assets to a common denominator - cash - and then summing them together. Here is a step by step walk-through of this process.

Cash: +100
Maturity
fCash
Liquidity Tokens
December 1 2020
+100
0
March 1 2021
-50
+150
June 1 2021
-150
0

## Step 1: Decompose Liquidity Tokens into Claims on Cash and fCash

Liquidity tokens are freely exchangeable for their constituent cash and fCash. The first step in this calculation is to aggregate these claims with the account's cash and fCash holdings. ## Step 2: Apply Liquidity Token Haircut to Cash and fCash Claims

Liquidity Tokens are risk assets because their net value can decrease. To account for this risk, we apply a haircut to the claims on cash and fCash derived from liquidity tokens for the purposes of calculating their value as collateral. The current liquidity token haircut is 20%. ## Step 3: Merge Liquidity Token Claims

Add the liquidity token claims on cash and fCash to the account's cash balance and fCash ladder.
Cash: +220
Maturity
fCash
December 1 2020
+100
March 1 2021
+70
June 1 2021
-150

## Step 4: Get Present Value of fCash

We take a conservative approach to valuing fCash as collateral. We do not currently refer to Notional's on-chain liquidity pools for market prices of fCash - instead we apply a significant haircut to positive fCash balances and value negative fCash balances at their full face value. We may choose to upgrade our risk framework to incorporate market prices in the future after evaluating the risks of doing so.

### Haircutting Positive fCash

We value positive fCash at a punitive implied annual interest rate that we are confident will be significantly less than its market value. Currently we value fCash at an implied annual interest rate of 50%. Additionally, we cap the collateral value of fCash at 95% of face value.
$fCashPV = min(fCashAmount* .95,\\ fCashAmount / (1+.5*(timeToMaturity / One Year)))$
Maturity
fCash Present Value
December 1 2020
+85
March 1 2021
+52
June 1 2021
-150

## Step 5: Sum Cash and Present Value of fCash

$CollateralValue = cashBalance + sum(fCash PV) \\ ~\\ CollateralValue = 220 + 85 + 52 - 150 \\ ~\\CollateralValue = 207$

## Aggregating Local Currency Collateral Values

Once we have local currency collateral values for each supported currency we aggregate them into a single ETH-denominated free collateral figure.

### Exchange Rate Buffers

Notional allows users to hold collateral in one currency against debts in another currency. This introduces exchange rate risk. To account for this risk, we add a buffer to any net debt position in a currency when we convert it to ETH. Currently this buffer is 140%.

## Step 1: Convert Local Currency Collateral Values to ETH

$If \text{ } LocalCurrencyCollateral > 0 \\~\\ EthDenominatedCollateral = LocalCurrencyCollateral * ExchangeRate \\ ~ \\ If \text{ } LocalCurrencyCollateral < 0 \\~\\ EthDenominatedCollateral = LocalCurrencyCollateral * ExchangeRate * Buffer$
Currency
ETH
DAI
USDC
Local Currency Collateral
+1
+140
-100
$ETH-DAI \text{ } Exchange Rate = 400 \\ETH-USDC \text{ } ExchangeRate = 400 \\ Buffer = 1.4$
Currency
ETH
DAI
USDC
Local Currency Collateral
+1
+140
-100
ETH-Denominated Collateral
+1
+.35
-.35

## Step 2: Sum ETH Denominated Collateral Values

$FreeCollateral = sum(EthDenominatedCollateral) \\~\\ FreeCollateral = 1 + .35 - .35 \text { } ETH \\ ~ \\ FreeCollateral = +1 \text{ } ETH$