Simple Uni V2 Tree (Part 1)
Assumptions:
Uses Simple Tree
Uses stablecoins (ie, USDC and USDT) to control for impermanent loss
Infinite supply of index tokens
LPs include:
USDC-USDT
USDC-iUSDC
Medium Article: Liquidity Tree Performance using Stablecoins: Part 1
[8]:
import os
import numpy as np
import pandas as pd
import datetime
import matplotlib.pyplot as plt
import scipy.stats as stats
import statsmodels.api as sm
import seaborn as sns
from uniswappy import *
cwd = os.getcwd().replace("notebooks/medium_articles","")
os.chdir(cwd)
Script params
[9]:
init_tkn_lp = 100000
tkn_delta_param = 1000
tkn_invest_amt = 100
tkn_nm = 'USDC'
itkn_nm = 'iUSDC'
usdt_nm = 'USDT'
iusdt_nm = 'iUSDT'
Simulate price data
[10]:
# *************************
# *** Simulation
# *************************
n_sim_runs = 2000
seconds_year = 31536000
shape = 2000
scale = 0.0005
p_arr = np.random.gamma(shape = shape, scale = scale, size = n_sim_runs)
n_runs = len(p_arr)-1
dt = datetime.timedelta(seconds=seconds_year/n_sim_runs)
dates = [datetime.datetime.strptime("2024-09-01", '%Y-%m-%d') + k*dt for k in range(n_sim_runs)]
x_val = np.arange(0,len(p_arr))
fig, (USD_ax) = plt.subplots(nrows=1, sharex=False, sharey=False, figsize=(18, 5))
USD_ax.plot(dates, p_arr, color = 'r',linestyle = 'dashdot', label='initial invest')
USD_ax.set_title(f'Price Chart ({tkn_nm}/{usdt_nm})', fontsize=20)
USD_ax.set_ylabel('Price (USD)', size=20)
USD_ax.set_xlabel('Date', size=20)
[10]:
Text(0.5, 0, 'Date')

Initialization Params
[11]:
user_nm = 'user0'
tkn_amount = init_tkn_lp
usdt_amount = p_arr[0]*tkn_amount
Initialize Simple DEX Tree
[12]:
usdt1 = ERC20(usdt_nm, "0x111")
tkn1 = ERC20(tkn_nm, "0x09")
exchg_data = UniswapExchangeData(tkn0 = tkn1, tkn1 = usdt1, symbol="LP", address="0x011")
TKN_amt = TokenDeltaModel(tkn_delta_param)
iVault1 = IndexVault('iVault1', "0x7")
factory = UniswapFactory(f"{tkn_nm} pool factory", "0x2")
lp = factory.deploy(exchg_data)
Join().apply(lp, user_nm, tkn_amount, usdt_amount)
tkn2 = ERC20(tkn_nm, "0x09")
itkn1 = IndexERC20(itkn_nm, "0x09", tkn1, lp)
exchg_data1 = UniswapExchangeData(tkn0 = tkn2, tkn1 = itkn1, symbol="LP1", address="0x012")
lp1 = factory.deploy(exchg_data1)
JoinTree().apply(lp1, user_nm, iVault1, 10000)
# Re-balance LP price after JoinTree
SwapDeposit().apply(lp, usdt1, user_nm, lp.get_reserve(tkn1) - lp.get_reserve(usdt1))
lp.summary()
lp1.summary()
Exchange USDC-USDT (LP)
Reserves: USDC = 110000.0, USDT = 110000.0
Liquidity: 109983.31666575832
Exchange USDC-iUSDC (LP1)
Reserves: USDC = 9972.071706380653, iUSDC = 4833.211949992264
Liquidity: 6942.415727789479
Take an investment position
[13]:
tkn_invest = 100
invested_user_nm = 'invested_user'
SwapIndexMint(iVault1, opposing = False).apply(lp, tkn1, invested_user_nm, tkn_invest)
mint_itkn1_deposit = lp1.convert_to_human(iVault1.index_tokens[itkn_nm]['last_lp_deposit'])
SwapDeposit().apply(lp1, itkn1, invested_user_nm, mint_itkn1_deposit)
lp.summary()
lp1.summary()
lp_invest_track = lp.get_liquidity_from_provider(invested_user_nm)
lp1_invest_track = lp1.get_liquidity_from_provider(invested_user_nm)
# Redeem from parent
tkn_redeem_parent = LPQuote(False).get_amount_from_lp(lp, tkn1, lp_invest_track)
# Redeem from tree (child + parent)
itkn_redeem_child = LPQuote(False).get_amount_from_lp(lp1, itkn1, lp1_invest_track)
tkn_redeem_tree = LPQuote(False).get_amount_from_lp(lp, tkn1, itkn_redeem_child)
print(f'{tkn_redeem_parent:.3f} USDC redeemed from {lp_invest_track:.3f} LP tokens if {tkn_invest:.1f} invested USDC immediately pulled from parent')
print(f'{tkn_redeem_tree:.3f} USDC redeemed from {lp1_invest_track:.3f} LP1 tokens if {tkn_invest:.1f} invested USDC immediately pulled from tree')
Exchange USDC-USDT (LP)
Reserves: USDC = 110100.0, USDT = 110000.0
Liquidity: 110033.22264148264
Exchange USDC-iUSDC (LP1)
Reserves: USDC = 9972.071706380653, iUSDC = 4883.117925716595
Liquidity: 6978.1123931422935
99.700 USDC redeemed from 49.906 LP tokens if 100.0 invested USDC immediately pulled from parent
99.403 USDC redeemed from 35.697 LP1 tokens if 100.0 invested USDC immediately pulled from tree
Simulate trading
[14]:
arb = CorrectReserves(lp, x0 = 1)
arb1 = CorrectReserves(lp1, x0 = lp1.reserve1/lp1.reserve0)
TKN_amt = TokenDeltaModel(n_sim_runs)
lp_direct_invest_arr = []; lp1_direct_invest_arr = []; lp1_tree_invest_arr = [];
pTKN_USDT_arr = []; pTKN_iTKN_arr = []
fee_lp_arr = []; fee_lp1_arr = [];
for k in range(n_sim_runs):
# *****************************
# ***** Parent Arbitrage ******
# *****************************
arb.apply(p_arr[k])
# *****************************
# ***** Child Arbitrage ******
# *****************************
#p_lp1 = SettlementLPToken().apply(lp, tkn1, lp1.reserve0)/lp1.reserve0
p_lp1 = LPQuote().get_lp_from_amount(lp, tkn1, lp1.get_reserve(tkn2))/lp1.get_reserve(tkn2)
arb1.apply(p_lp1)
# *****************************
# ***** Random Swapping ******
# *****************************
Swap().apply(lp, tkn1, user_nm, TKN_amt.delta())
Swap().apply(lp, usdt1, user_nm, TKN_amt.delta())
# conservatively assume 20% of parent trading by volume
Swap().apply(lp1, tkn2, user_nm, 0.2*TKN_amt.delta())
#Swap().apply(lp1, itkn1, user_nm, SettlementLPToken().apply(lp, tkn1, 0.2*TKN_amt.delta()))
Swap().apply(lp1, itkn1, user_nm, LPQuote().get_lp_from_amount(lp, tkn1, 0.2*TKN_amt.delta()))
# *****************************
# ******* Data Capture ********
# *****************************
# price
pTKN_USDT_arr.append(LPQuote().get_price(lp, tkn1))
pTKN_iTKN_arr.append(LPQuote().get_price(lp1, tkn1))
# investment performance
tkn_redeem_parent = LPQuote(False).get_amount_from_lp(lp, tkn1, lp_invest_track)
itkn_redeem_child = LPQuote(False).get_amount_from_lp(lp1, itkn1, lp1_invest_track)
tkn_redeem_tree = LPQuote(False).get_amount_from_lp(lp, tkn1, itkn_redeem_child)
lp_direct_invest_arr.append(tkn_redeem_parent)
lp1_direct_invest_arr.append(RebaseIndexToken().apply(lp1, tkn2, lp1_invest_track))
lp1_tree_invest_arr.append(tkn_redeem_tree)
# DEX Fees
fee_lp_arr.append(TreeAmountQuote().get_tot_y(lp, lp.get_fee(tkn1), lp.get_fee(usdt1)))
fee_lp1_arr.append(TreeAmountQuote().get_tot_y(lp1, lp1.get_fee(tkn2), lp1.get_fee(itkn1)))
lp.summary()
lp1.summary()
# Redeem from parent
tkn_redeem_parent = LPQuote(False).get_amount_from_lp(lp, tkn1, lp_invest_track)
# Redeem from tree (child + parent)
itkn_redeem_child = LPQuote(False).get_amount_from_lp(lp1, itkn1, lp1_invest_track)
tkn_redeem_tree = LPQuote(False).get_amount_from_lp(lp, tkn1, itkn_redeem_child)
print(f'{tkn_redeem_parent:.3f} USDC redeemed from {lp_invest_track:.3f} LP tokens if {tkn_invest:.1f} invested USDC pulled from parent (lp)')
print(f'{tkn_redeem_tree:.3f} USDC redeemed from {lp1_invest_track:.3f} LP1 tokens if {tkn_invest:.1f} invested USDC pulled from tree (lp + lp1)')
Exchange USDC-USDT (LP)
Reserves: USDC = 147284.7509076092, USDT = 142910.2586404444
Liquidity: 136970.6876694417
Exchange USDC-iUSDC (LP1)
Reserves: USDC = 12290.555766155601, iUSDC = 5486.217037846741
Liquidity: 7507.116283763606
107.147 USDC redeemed from 49.906 LP tokens if 100.0 invested USDC pulled from parent (lp)
111.584 USDC redeemed from 35.697 LP1 tokens if 100.0 invested USDC pulled from tree (lp + lp1)
[15]:
fig, (TKN_ax, USDT_ax) = plt.subplots(nrows=2, sharex=False, sharey=False, figsize=(15, 8))
strt_pt = 5
TKN_ax.plot(dates[strt_pt:], p_arr[strt_pt:], color = 'g',linestyle = 'dashed', linewidth=1, label=f'{tkn_nm} Price (Market)')
TKN_ax.plot(dates[strt_pt:], pTKN_USDT_arr[strt_pt:], color = 'b',linestyle = '-', linewidth=0.7, label=f'{tkn_nm}/{usdt_nm} (LP)')
TKN_ax.set_title('Price comparison: parent vs child LPs', fontsize=20)
TKN_ax.set_ylabel('Price (USD)', size=20)
TKN_ax.legend(fontsize=12)
TKN_ax.grid()
USDT_ax.plot(dates[strt_pt:], pTKN_iTKN_arr[strt_pt:], color = 'b',linestyle = 'dashed', label=f'{tkn_nm}/{itkn_nm} (LP1)')
USDT_ax.set_ylabel('prices', size=20)
USDT_ax.set_ylabel('Price (USD)', size=20)
USDT_ax.legend(fontsize=12)
USDT_ax.grid()

[16]:
fig, ax = plt.subplots(1, 2, figsize=(15,5))
sns.distplot(pTKN_USDT_arr, hist=True, kde=True, bins=int(30), color = 'darkblue',
hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2}, ax=ax[0])
sns.distplot(pTKN_iTKN_arr, hist=True, kde=True, bins=int(30), color = 'darkblue',
hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2}, ax=ax[1])
ax[0].set_title(f'Distribution: {tkn_nm}/{usdt_nm} LP price (parent)')
ax[0].set_xlabel('Price')
ax[0].set_ylabel('Frequency')
ax[1].set_title(f'Distribution: {tkn_nm}/{itkn_nm} LP1 price (child)')
ax[1].set_xlabel('Price')
ax[1].set_ylabel('Frequency')
[16]:
Text(0, 0.5, 'Frequency')

[17]:
lowess = sm.nonparametric.lowess
x = range(0,n_sim_runs)
res = lowess(lp_direct_invest_arr, x, frac=1/15); sm_lp_direct = res[:,1]
res = lowess(lp1_direct_invest_arr, x, frac=1/15); sm_lp1_direct = res[:,1]
res = lowess(lp1_tree_invest_arr, x, frac=1/15); sm_lp1_tree= res[:,1]
strt_ind = 3
fig, (p_ax) = plt.subplots(nrows=1, sharex=True, sharey=False, figsize=(15, 8))
fig.suptitle('Simple Tree (USDC / USDT) performance ', fontsize=20)
p_ax.plot(dates[strt_ind:], lp_direct_invest_arr[strt_ind:], linestyle='dashed', linewidth=0.5, color = 'g')
p_ax.plot(dates[strt_ind:], sm_lp_direct[strt_ind:], color = 'g', label = 'Expected return from parent (LP)')
p_ax.plot(dates[strt_ind:], lp1_direct_invest_arr[strt_ind:], linestyle='dashed', linewidth=0.5, color = 'b')
p_ax.plot(dates[strt_ind:], sm_lp1_direct[strt_ind:], color = 'b', label = 'Expected return from child (LP1)')
p_ax.plot(dates[strt_ind:], lp1_tree_invest_arr[strt_ind:], linestyle='dashed', linewidth=0.5, color = 'r')
p_ax.plot(dates[strt_ind:], sm_lp1_tree[strt_ind:], color = 'r', label = 'Expected return from tree (LP+LP1)')
p_ax.legend( fontsize=12)
p_ax.set_ylim(80, 140)
p_ax.set_ylabel("$100 USD Investment", fontsize=14)
[17]:
Text(0, 0.5, '$100 USD Investment')

[18]:
print(f'{tkn_invest:.3f} TKN before is worth {sm_lp_direct[-1]:.3f} TKN after direct investment into parent (lp)')
print(f'{tkn_invest:.3f} TKN before is worth {sm_lp1_direct[-1]:.3f} TKN after direct investment into child (lp1)')
print(f'{tkn_invest:.3f} TKN before is worth {sm_lp1_tree[-1]:.3f} TKN after investment into simple tree (lp + lp1)')
100.000 TKN before is worth 105.524 TKN after direct investment into parent (lp)
100.000 TKN before is worth 111582716410069549056.000 TKN after direct investment into child (lp1)
100.000 TKN before is worth 114.471 TKN after investment into simple tree (lp + lp1)
[19]:
t = np.arange(0,len(fee_lp_arr))
fee_lpB = np.array(fee_lp1_arr)
fee_lpA = fee_lpB+np.array(fee_lp_arr)
fig = plt.figure(figsize=(15, 5))
plt.plot(dates, fee_lpA, color = 'r', label = f'Parent LP ({tkn_nm}/{usdt_nm})')
plt.fill_between(dates, fee_lpB, fee_lpA, alpha=0.3, color='r')
plt.plot(dates, fee_lpB, color = 'b', label = f'Child LP1 ({tkn_nm}/{itkn_nm})')
plt.fill_between(dates, np.repeat(0,len(fee_lp_arr)), fee_lpB, alpha=0.3, color='b')
plt.title('Cumulative Arbitrage Fees (Stablecoin Simple Tree, Uni V2)', fontsize = 20)
plt.ylabel("Collected Fees (USD)", fontsize=14)
plt.legend(fontsize=12)
[19]:
<matplotlib.legend.Legend at 0x1666d0040>
