Imp Loss V2

Impermanent Loss

from uniswappy import *
import numpy as np
import datetime
import matplotlib.pyplot as plt

GBM

# Instantiation Parameters
n_steps = 2000     # Number of steps
start_price = 10 # Initial price SYS/USD
mu = 0.1; sigma = 0.5
n_paths = 1      # Number of simulationed paths
seconds_year = 31536000

# Brownian Model
bm = BrownianModel(start_price)
p_arr = bm.gen_gbms(mu, sigma, n_steps-1, n_paths).flatten()

dt = datetime.timedelta(seconds=seconds_year/n_steps)
dates = [datetime.datetime.strptime("2024-09-01", '%Y-%m-%d') + k*dt for k in range(n_steps)]

user_nm = 'user0'
tkn1_amount = 1000
tkn2_amount = p_arr[0]*tkn1_amount

tkn1_nm = 'TKN1'
tkn2_nm = 'TKN2'

tkn1 = ERC20('TKN1', "0x111")
tkn2 = ERC20('TKN2', "0x09")
exchg_data = UniswapExchangeData(tkn0 = tkn1, tkn1 = tkn2, symbol="LP", address="0x011")

factory = UniswapFactory("pool factory", "0x2")
lp = factory.deploy(exchg_data)
Join().apply(lp, user_nm, tkn1_amount, tkn2_amount)

lp.summary()

Exchange TKN1-TKN2 (LP) Reserves: TKN1 = 1000.0, TKN2 = 10000.0 Liquidity: 3162.2776601683795

out = AddLiquidity().apply(lp, tkn1, user_nm, 10)
lp.summary()

dL = lp.get_last_liquidity_deposit()
iLoss = UniswapImpLoss(lp, dL)

Exchange TKN1-TKN2 (LP) Reserves: TKN1 = 1010.0, TKN2 = 10100.0 Liquidity: 3193.900436770063

tkn1_init_amt = iLoss.get_init_amt(tkn1)
tkn2_init_amt = iLoss.get_init_amt(tkn2)
tkn1_hold_amt = iLoss.hold_value(tkn1)
tkn2_hold_amt = iLoss.hold_value(tkn2)

print(f'Initial {tkn1.token_name} amount: {tkn1_init_amt:.2f}, Initial {tkn2.token_name} amount: {tkn2_init_amt:.2f}')
print(f'Hold {tkn1.token_name} amount: {tkn1_hold_amt:.2f}, Hold {tkn2.token_name} amount: {tkn2_hold_amt:.2f}')

Initial TKN1 amount: 10.00, Initial TKN2 amount: 100.00 Hold TKN1 amount: 20.00, Hold TKN2 amount: 200.00

Simulate AMM

arb = CorrectReserves(lp, x0 = p_arr[0])
TKN_amt = TokenDeltaModel(100)
pTKN1_TKN2_arr = [];

for k in range(n_steps):

    # *****************************
    # ***** Random Swapping ******
    # *****************************
    Swap().apply(lp, tkn1, user_nm, TKN_amt.delta())
    Swap().apply(lp, tkn2, user_nm, p_arr[k]*TKN_amt.delta())

    # *****************************
    # ***** Rebalance ******
    # *****************************
    arb.apply(p_arr[k])

    # *****************************
    # ******* Data Capture ********
    # *****************************
    pTKN1_TKN2_arr.append(LPQuote().get_price(lp, tkn1))

lp.summary()

Exchange TKN1-TKN2 (LP) Reserves: TKN1 = 1771.3573494134228, TKN2 = 18219.61113048574 Liquidity: 4952.847449768049

Plot

n_steps = 1000
alphas = np.linspace(0, 5, num=n_steps)
alpha_deltas = alphas-1

imp_loss = np.array([iLoss.calc_iloss(alpha) for alpha in alphas])

m0 = 10; m1 = 100
fig, (lp_ax) = plt.subplots(nrows=1, sharex=True, sharey=False, figsize=(12, 5))
fig.suptitle(f'Impermanent Loss: Uni V2', fontsize=20)
lp_ax.plot(100*alphas[m0:-m1]-100, 100*imp_loss[m0:-m1], label = f'Uni V2')
lp_ax.set_xlabel("Price Chg (%)", fontsize=12)
lp_ax.set_ylabel("Impermanent Loss (%)", fontsize=14)
lp_ax.legend(fontsize=10, facecolor="lightgray", loc='lower right')

<matplotlib.legend.Legend at 0x146ff0fa0>

Calculate Imp. Loss

tkn1_hold_amt = iLoss.hold_value(tkn1)
tkn2_hold_amt = iLoss.hold_value(tkn2)
tkn1_pos_amt = iLoss.current_position_value(tkn1)
tkn2_pos_amt = iLoss.current_position_value(tkn2)

print(f'{tkn1.token_name} hold amt: {tkn1_hold_amt:.2f}, {tkn2.token_name} hold amt: {tkn2_hold_amt:.2f}')
print(f'{tkn1.token_name} position amt: {tkn1_pos_amt:.2f}, {tkn2.token_name} position amt: {tkn2_pos_amt:.2f}')
print(f'Start price: {p_arr[0]:.2f}, End price: {p_arr[1]:.2f}')

TKN1 hold amt: 19.72, TKN2 hold amt: 202.86 TKN1 position amt: 22.51, TKN2 position amt: 231.57 Start price: 10.00, End price: 9.91

iloss_calc = iLoss.apply(fees = False)
returns_calc = iLoss.apply(fees = True)

print(f'Imp Loss: {100*iloss_calc:.2f}%, returns: {100*returns_calc:.2f} %')

Imp Loss: -0.01%, returns: 14.15 %