Free Collateral

The free collateral calculation calculation is a two part process.
1.Collect local currency collateral surplus/requirement figures for each supported currency
2.Aggregate local currency collateral figures into one ETH-denominated free collateral figure
Local Currency Collateral Calculation
An account has four possible types of assets per currency: cTokens, nTokens fCash, and Liquidity Tokens. Calculating local currency collateral figures requires converting the value of these assets to a common denominator - local currency - applying relevant haircuts, and then summing the values together. Here is a step by step walk-through of this process.
Example Account Holdings in Local Currency
cTokens: +100
nTokens: +100
Maturity
fCash
Liquidity Tokens
June 1 2021
+100
0
September 1 2021
-50
+150
March 1 2022
-150
0
Step 1: Decompose Liquidity Tokens into Claims on cTokens and fCash
Liquidity tokens are freely exchangeable for their constituent cTokens and fCash. The first step in this calculation is to aggregate these claims with the account's cTokens and fCash holdings.
Step 2: Apply Liquidity Token Haircut to cToken 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 cTokens and fCash derived from liquidity tokens for the purposes of calculating their value as collateral. The liquidity token haircut will be unique to each active tenor and will reflect the fact that longer dated liquidity tokens are riskier than shorter dated liquidity tokens.
Step 3: Merge Liquidity Token Claims
Add the liquidity token claims on cTokens and fCash to the account's cToken balance and fCash ladder.
cTokens: +220
nTokens: +100
Maturity
fCash
June 1 2021
+100
September 1 2021
+70
March 1 2022
-150
Step 4: Get Present Value of fCash and Apply Haircut/Buffer
We get the present value of fCash by discounting the face value of that fCash to the present via the oracle rate which corresponds to the fCash asset's maturity. See more detail on this here. In order to account for the riskiness of fCash (the likelihood that its present value decreases) we adjust the oracle rate used to discount the face value of the fCash back to the present. 
If the face value of the fCash is positive we adjust the oracle rate higher, such that the collateral value of the fCash is diminished. If the face value is negative, we adjust the oracle rate lower such that the collateral value of the debt is magnified in this calculation.
if fCash>0:adjustedOracleRate=oracleRate+fCashHaircut if fCash<0:adjustedOracleRate=oracleRate−fCashBuffer collateralValue(fCash)=fCash∗e−adjustedOracleRate ∗ timeToMaturityif \text{ } fCash > 0: adjustedOracleRate = oracleRate + fCashHaircut \\~\\ if\text{ } fCash < 0: adjustedOracleRate = oracleRate - fCashBuffer \\~\\ collateralValue(fCash) = fCash * e^{-adjustedOracleRate \text{ }* \text{ } timeToMaturity}if fCash>0:adjustedOracleRate=oracleRate+fCashHaircut if fCash<0:adjustedOracleRate=oracleRate−fCashBuffer collateralValue(fCash)=fCash∗e−adjustedOracleRate ∗ timeToMaturity
cTokens: +220
nTokens: +100
Maturity
fCash Collateral Value
June 1 2021
+85
September 1 2021
+52
March 1 2022
-140
Step 5: Get Present Value of nTokens and Apply Haircut
To get the collateral value of an account's nToken holdings, we first need to get the present value of a single nToken. The present value of one nToken is equal to the present value of all the assets in the nToken account (ignoring any haircuts) divided by the total supply of nTokens. 
PV(nToken)=PV(nTokenAccount)/nTokenSupplyPV(nToken) = PV(nTokenAccount) / nTokenSupplyPV(nToken)=PV(nTokenAccount)/nTokenSupply
The present value of an account's nTokens is then just the present value of one nToken multiplied by the account's nToken balance.
PV(nTokens)=PV(nToken)∗nTokenBalancePV(nTokens) = PV(nToken) * nTokenBalancePV(nTokens)=PV(nToken)∗nTokenBalance
To get a collateral value for an account's nTokens we apply a haircut after getting the present value of their nTokens. Applying the haircut after the present value calculation is more practical than deriving a present value of their nTokens that includes haircuts on the constituent fCash and liquidity tokens in the nToken account. 
collateralValue(nTokens)=PV(nTokens)∗nTokenHaircutcollateralValue(nTokens) = PV(nTokens) * nTokenHaircutcollateralValue(nTokens)=PV(nTokens)∗nTokenHaircut
cTokens: +220
nToken Collateral Value: +800
Maturity
fCash Collateral Value
June 1 2021
+85
September 1 2021
+52
March 1 2022
-140
Step 6: Convert cToken Value to Local Currency
localCurrencycTokenValue=cTokenBalance∗cTokenExchangeRatelocalCurrencycTokenValue = cTokenBalance * cTokenExchangeRatelocalCurrencycTokenValue=cTokenBalance∗cTokenExchangeRate
cToken Collateral Value: +2200
nToken Collateral Value: +800
Maturity
fCash Collateral Value
June 1 2021
+85
September 1 2021
+52
March 1 2022
-140
Step 7: Sum cToken Value with Collateral Values of nTokens and fCash
localCurrencycTokenValue+collateralValue(nTokens)+collateralValue(fCash) localCurrencyCollateral=2200+800+85+52−140 localCurrencyCollateral=2997localCurrencycTokenValue + collateralValue(nTokens) + collateralValue(fCash) \\~\\localCurrencyCollateral = 2200 + 800 + 85 + 52 - 140 \\~\\ localCurrencyCollateral = 2997localCurrencycTokenValue+collateralValue(nTokens)+collateralValue(fCash) localCurrencyCollateral=2200+800+85+52−140 localCurrencyCollateral=2997
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 Haircuts/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 adjust the local currency collateral figure by either a buffer or a haircut when we convert it to ETH. We use a haircut (value less than 1) if the local currency figure is positive and a buffer (value greater than 1) if the figure is negative. Each currency type has its own haircut and buffer for use in this calculation.
Step 1: Convert Local Currency Collateral Values to ETH
if localCurrencyCollateral>0 ethDenominatedCollateral=localCurrencyCollateral∗exchangeRate∗haircut if localCurrencyCollateral<0 ethDenominatedCollateral=localCurrencyCollateral∗exchangeRate∗bufferif \text{ } localCurrencyCollateral > 0 \\~\\ ethDenominatedCollateral = localCurrencyCollateral * exchangeRate * haircut \\ ~ \\ if \text{ } localCurrencyCollateral < 0 \\~\\ ethDenominatedCollateral = localCurrencyCollateral * exchangeRate * bufferif localCurrencyCollateral>0 ethDenominatedCollateral=localCurrencyCollateral∗exchangeRate∗haircut if localCurrencyCollateral<0 ethDenominatedCollateral=localCurrencyCollateral∗exchangeRate∗buffer
Currency
ETH
DAI
USDC
Local Currency Collateral
+1
+140
-100
ETH/DAI exchangeRate=400ETH/USDC exchangeRate=400ETH Haircut=.8DAI Haircut=.8USDC Buffer=1.25ETH/DAI \text{ } exchange Rate = 400 \\ETH/USDC \text{ } exchangeRate = 400 \\ ETH \text{ }Haircut = .8 \\ DAI \text{ }Haircut = .8 \\ USDC \text{ }Buffer = 1.25ETH/DAI exchangeRate=400ETH/USDC exchangeRate=400ETH Haircut=.8DAI Haircut=.8USDC Buffer=1.25
Currency
ETH
DAI
USDC
Local Currency Collateral
+1
+140
-100
ETH-Denominated Collateral
+.8
+.28
-.3125
Step 2: Sum ETH Denominated Collateral Values
FreeCollateral=sum(EthDenominatedCollateral) FreeCollateral=.8+.28−.3125 FreeCollateral=+.7675 ETHFreeCollateral = sum(EthDenominatedCollateral) \\~\\ FreeCollateral = .8 + .28 - .3125  \\ ~ \\ FreeCollateral = +.7675 \text{ } ETHFreeCollateral=sum(EthDenominatedCollateral) FreeCollateral=.8+.28−.3125 FreeCollateral=+.7675 ETH
Last modified 1yr ago
Maturity	fCash	Liquidity Tokens
June 1 2021	+100	0
September 1 2021	-50	+150
March 1 2022	-150	0
Maturity	fCash Collateral Value
June 1 2021	+85
September 1 2021	+52
March 1 2022	-140
Currency	ETH	DAI	USDC
Local Currency Collateral	+1	+140	-100
ETH-Denominated Collateral	+.8	+.28	-.3125