💣Case Studies - Liquidation

Examples and calculations

To help users better understand the cause and process of liquidation, we've prepared two sets of examples, one with a single position and the other one with multiple open positions. In both examples, we further list down all possible cases when liquidation is triggered.

General setting:

Alex deposits 1,000 USDC into Symmetry Trade and wants to open positions. The oracle price of BTC is $25,000 and the oracle price of ETH is $2,000 now.

Case 1: Single Open Position

Alex opens +0.2 BTCUSDC position at the execution price of $25,200, $Keeperfee_{min} = \$1$, $UserInputfee = \$10$, trading fee rate 0.1%. Minimum margin deposit $50.

Scene 1: BTC Oracle price drops from $25,000 to $24,000, Funding = $-20, .

Now,

Keeper fee is $10.

Alex PnL is $0.2 \times (24,000-25,200 \times (1+0.1\%))-10 = \$-255.04$.

Margin balance is $1000-255.04-20=\$724.96$.

Available margin is $724.96-\frac {0.2 \times 24,000} {25} -50=\$ 482.96$.

Buying power is $(482.96+50)\times 25 = \$13,324$.

Maintenance margin is $0.2 \times 24,000 \times 2\% = \$96$.

Maintenance margin ratio is $\frac {724.96} {96}=7.55 > 1$.

Scene 2: BTC Oracle price drops from $25,000 to $20,500, $Funding = $50, $\sum FinancialCosts = \$0$.

Now,

Alex PnL is $0.2 \times (20,500-25,200\times (1+0.1\%)) -10= \$-955.04$.

Margin balance is $1000-955.04+50=\$94.96$.

$94.96-\frac {0.2 \times 20,500} {25}-50<0$, therefore available margin is 0, trader could not withdraw any money.

Buying power is 0.

Maintenance margin is $0.2 \times 20,500 \times 2\% = \$82$.

Maintenance margin ratio is $\frac {94.96} {82}=1.16 > 1$.

Scene 3: BTC Oracle price drops from $25,000 to $20,500, Funding = $30, $\sum FinancialCosts = \$0$.

Now,

Alex PnL is $0.2 \times (20,500-25,200\times (1+0.1\%)) -10= \$-955.04$.

Margin balance is $1000-955.04+30=\$74.96$.

$74.96-\frac {0.2 \times 20,500} {25}-50<0$, therefore available margin is 0, trader could not withdraw any money.

Buying power is 0.

Maintenance margin is 0.2 \times 20,500 \times 2\% = \$82.

Maintenance margin ratio is $\frac {74.96} {82}=0.91 <1$.

Out of the three possibilities listed above, Scene 3 would trigger the liquidation process. For the process, we have four different scenarios, categorized by the price at which all BTC/USDC positions are closed:

at $20,450

Then,

Liquidation keeper fee is $0.2 \times 20,500 \times 0.35\% = \$14.35<\$1000$ .

Alex PnL is $0.2 \times (20,450\times (1-0.1\%)-25,200\times (1+0.1\%))-10-14.35 = \$-983.48$.

Margin balance is $1000-983.48+30=\$46.52$.

Penalty fee is $0.2 \times 20,500 \times 1\% =\$41$.

User asset is $46.52 -41 = \$5.52.$ $\$5.52$ will be returned to user.

at $20,300

Then,

Liquidation keeper fee is $0.2 \times 20,500 \times 0.35\% = \$14.35<\$1000$.

Alex PnL is $0.2 \times (20,300\times (1-0.1\%)-25,200\times (1+0.1\%)) -10-14.35= \$-1013.45$.

Margin balance is $1000-1013.45+30=\$16.55$.

Penalty fee is $0.2 \times 20,500 \times 1\% =\$41$.

After paying all fees, only $16.55 will be credited to the insurance account, user asset is 0.

at $20,200

Then,

Liquidation keeper fee is $0.2 \times 20,500 \times 0.35\% = \$14.35<\$1000$.

Alex PnL is $0.2 \times (20,200\times (1-0.1\%)-25,200\times (1+0.1\%))-10-14.35 = \$-1033.43$.

Margin balance is $1000-1033.43+30=\$-3.43<0$.

Penalty fee is $0.2 \times 20,500 \times 1\% =\$41$.

Insurance account pay $3.43 to LP, user asset is 0.

at $20,000

Then,

Liquidation keeper fee is $0.2 \times 20,500 \times 0.35\% = \$14.35<\$1000$.

Alex PnL is $0.2 \times (20,000\times (1-0.1\%)-25,200\times (1+0.1\%))-10-14.35 = \$-1073.39$.

Margin balance is $1000-1073.39+30=\$-43.39 <0$.

Then insurance account will pay $43.39 to the keeper bot, LP and protocol, user asset is 0.

Case 2: Multiple Open Positions

Alex opens +0.2 BTC/USDC position at the execution price of $25,200 and opens -2 ETH/USDC position at the execution price of $1,990. For each trade, $Keeperfee_{min} = \$1$, $UserInputfee = \$10$. Trading fee rate 0.1\%. Minimum margin deposit $50.

Scene 1: BTC Oracle price drops from $25,000 to $24,000, and ETH Oracle price drops from $2,000 to $1,900, $\sum Funding = \$-50$, $\sum FinancialCosts = \$0$.

Now,

Alex PnL is $0.2 \times (24,000-25,200\times (1+0.1\%)) - 2 \times(1,900-1,990\times (1-0.1\%))-20 = \$-89.02$

Margin balance is $1000-89.02-50=\$860.98$.

Available margin is $860.98-\frac {0.2 \times 24,000+2 \times 1,900} {25}-50=\$ 466.98$.

Buying power is $(466.98+50)\times 25 = \$12,924.5$.

Maintenance margin is $(0.2 \times 24,000 + 2 \times 1,900) \times 2\% = \$172$.

Maintenance margin ratio is $\frac {860.98} {172}=5.0 > 1$

Scene 2: BTC Oracle price drops from $25,000 to $24,000, and ETH Oracle price increases from $2,000 to $2,300, $\sum Funding = \$70$, $\sum FinancialCosts = \$0$.

Now,

Alex PnL is $0.2 \times (24,000-25,200\times (1+0.1\%)) - 2 \times(2,300-1,990\times (1-0.1\%)) -20= \$-889.02$

Margin balance is $1000-889.02+70=\$180.98$.

$180.98-\frac {0.2 \times 24,000+2 \times 2,300} {25}-50<0$, therefore available margin is 0, trader could not withdraw any money.

Buying power is 0.

Maintenance margin is $(0.2 \times 24,000 + 2,300 \times 2) \times 2\% = \$188$.

Maintenance margin ratio is $\frac {180.98} {188}=0.96 < 1$.

Out of the two possibilities listed above, Scene 2 would trigger the liquidation process. For the process, we have two different scenarios, categorized by the price at which all BTC/USDC positions are closed (as BTC/USDC would be the first position to close, ETH/USDC follows):

at $24,000

Then,

Liquidation keeper fee is $0.2 \times 24,000 \times 0.35\% = \$16.8<\$1000$.

Alex PnL is $0.2 \times (24,000\times (1-0.1\%)-25,200\times (1+0.1\%)) - 2 \times(2,300-1,990\times (1-0.1\%)) -20 -16.8= \$-910.62$

Penalty fee is $0.2 \times 24,000 \times 1\% =\$48$.

Margin balance is $1000-910.62+70 -48 = \$111.38$.

Maintenance margin is $2 \times 2,300 \times 2\% = \$92$.

Maintenance margin ratio is now $\frac {111.38} {92}=1.21 > 1$ .

No need to further liquidate the ETH/USDC positions now.

at $23,500

Then,

Liquidation keeper fee is $0.2 \times 24,000 \times 0.35\% = \$16.8<\$1000$.

Alex PnL is $0.2 \times (23,500\times (1-0.1\%)-25,200\times (1+0.1\%)) - 2 \times(2,300-1,990\times (1-0.1\%))-20-16.8 = \$-1,010.52$

Penalty fee is $0.2 \times 24,000 \times 1\% =\$48$.

Margin balance is $1000-1,010.52+70-48 = \$11.48$.

Maintenance margin is $2 \times 2,300 \times 2\% = \$92$.

Maintenance margin ratio is $\frac {11.48} {92}=0.12< 1$.

Because the maintenance margin ratio is still below 1, the ETH/USDC position also needs to be liquidated.

All ETH/USDC positions are closed at $2,300. Assume all funding incomes come from BTC/USDC position.

After closing BTC/USDC position, USDC deposit is $1000-0.2 \times (23,500\times (1-0.1\%)-25,200\times (1+0.1\%))-10-16.8+70-48 = \$645.46$

Liquidation keeper fee is $2 \times 2,300 \times 0.35\% = \$16.1<\$1000$.

Alex PnL is $- 2 \times(2,300\times (1+0.1\%)-1,990\times (1-0.1\%)) -10-16.1= \$-654.68$.

ETH position penalty fee is $2 \times 2,300 \times 1\% =\$46$.

Margin balance is $645.46-654.68-46 = -\$55.22<0$.

Therefore, insurance account needs to pay $|645.46-654.68| = \$9.22$ to keeper bot, LP & protocol, taker has no asset left.