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')

../_images/tutorials_simple_tree_pt1_5_1.png

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()

../_images/tutorials_simple_tree_pt1_14_0.png

[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')

../_images/tutorials_simple_tree_pt1_15_1.png

[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')

../_images/tutorials_simple_tree_pt1_16_1.png

[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>

../_images/tutorials_simple_tree_pt1_18_1.png