Simple Uni V2 Tree (Part 2)

Assumptions:
- Uses Simple Tree
- Uses stablecoins (ie, USDC and USDT) to control for impermanent loss
- Includes state machine to handle finite supply of index tokens
LPs include:
- USDC-USDT
- USDC-iUSDC
Medium Article: Liquidity Tree Performance using Stablecoins: Part 2

[1]:

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 *

Script params

[2]:

init_tkn_lp = 100000
tkn_delta_param = 1000
tkn_invest_amt = 100
tkn_nm = 'USDC'
itkn_nm = 'iUSDC'
usd_nm = 'USDT'
iusd_nm = 'iUSDT'

Simulate price data

[3]:

# *************************
# *** 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}/{usd_nm})', fontsize=20)
USD_ax.set_ylabel('Price (USD)', size=20)
USD_ax.set_xlabel('Date', size=20)

[3]:

Text(0.5, 0, 'Date')

../_images/tutorials_simple_tree_pt2_5_1.png

Initialization Params

[4]:

user_nm = 'user0'
tkn_amount = init_tkn_lp
dai_amount = p_arr[0]*tkn_amount

Initialize DEX Tree

[5]:

dai1 = ERC20(usd_nm, "0x111")
tkn1 = ERC20(tkn_nm, "0x09")
exchg_data = UniswapExchangeData(tkn0 = tkn1, tkn1 = dai1, symbol="LP", address="0x011")

TKN_amt = TokenDeltaModel(tkn_delta_param)
TKN_amt_arb = TokenDeltaModel(100)

lp1_state = MarkovState(stochastic = True)
iVault1 = IndexVault('iVault1', "0x7")

factory = UniswapFactory(f"{tkn_nm} pool factory", "0x2")
lp = factory.deploy(exchg_data)
Join().apply(lp, user_nm, tkn_amount, dai_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, dai1, user_nm, lp.get_reserve(tkn1) - lp.get_reserve(dai1))

lp.summary()
lp1.summary()

Exchange USDC-USDT (LP)
Reserves: USDC = 110000.0, USDT = 110000.0
Liquidity: 109983.64230441394

Exchange USDC-iUSDC (LP1)
Reserves: USDC = 9972.071706380651, iUSDC = 4843.286073492405
Liquidity: 6949.647186683727

Take an investment position

[6]:

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'])
lp1_state.next_state(mint_itkn1_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: 110033.5484278999

Exchange USDC-iUSDC (LP1)
Reserves: USDC = 9972.071706380651, iUSDC = 4893.1921969783725
Liquidity: 6985.30700316561

99.700 USDC redeemed from 49.906 LP tokens if 100.0 invested USDC immediately pulled from parent
99.403 USDC redeemed from 35.660 LP1 tokens if 100.0 invested USDC immediately pulled from tree

Simulate trading

[7]:

arb = CorrectReserves(lp, x0 = 1)
arb1 = Arbitrage(lp1, lp1_state)

TKN_amt = TokenDeltaModel(tkn_delta_param)

lp_direct_invest_arr = []; lp1_direct_invest_arr = []; lp1_tree_invest_arr = [];
pTKN_DAI_arr = []; pTKN_iTKN_arr = []
fee_lp_arr  = []; fee_lp1_arr  = [];

for k in range(n_sim_runs):

    #if(k % 100 == 0 and k != 0): print(f'Processing event {k}')

    # *****************************
    # ***** Parent Arbitrage ******
    # *****************************
    arb.apply(p_arr[k])

    # *****************************
    # ***** Child Arbitrage ******
    # *****************************
    amt_arb1 = TKN_amt_arb.delta()
    arb1.apply(1, user_nm, amt_arb1)
    arb1.update_state(itkn1)

    mint_tkn1_amt = 0.5*TKN_amt.delta()
    SwapIndexMint(iVault1, opposing = False).apply(lp, tkn1, user_nm, mint_tkn1_amt)
    mint_itkn1_deposit = lp1.convert_to_human(iVault1.index_tokens[itkn_nm]['last_lp_deposit'])
    lp1_state.next_state(mint_itkn1_deposit)
    vault_lp1_amt = lp1_state.get_current_state('dVault')
    burned_itkn1_amt = lp1_state.get_current_state('dBurned')

    ## WithdrawSwap burned token from parent LP
    if(burned_itkn1_amt > 0):
        total_tkn_w_swap = LPQuote(False).get_amount_from_lp(lp, tkn1, burned_itkn1_amt)
        amt_out = RemoveLiquidity().apply(lp, tkn1, user_nm, total_tkn_w_swap/2)

    ## Balance LP1: TKN/iTKN
    if(vault_lp1_amt > 0):
        # A portion of aquired token is coming from newly minted, while the remainder is coming from held
        amt_tkn = LPQuote(False).get_amount_from_lp(lp, tkn1, vault_lp1_amt)
        price_tkn = amt_tkn/vault_lp1_amt
        AddLiquidity(price_tkn).apply(lp1, itkn1, user_nm, vault_lp1_amt)
    elif(vault_lp1_amt < 0):
        # A portion of removed token is getting held, while the remainder is getting burned
        RemoveLiquidity().apply(lp1, itkn1, user_nm, abs(vault_lp1_amt))

    # *****************************
    # ***** Random Swapping ******
    # *****************************
    Swap().apply(lp, tkn1, user_nm, TKN_amt.delta())
    Swap().apply(lp, dai1, user_nm, TKN_amt.delta())

    # conservatively assume 10% of tokens held outside vault are traded
    held_tokens = lp1_state.get_current_state('Held')
    if(held_tokens > 0):
        tradable_itkn1_amt = 0.1*held_tokens
        Swap().apply(lp1, tkn2, user_nm, LPQuote(False).get_amount_from_lp(lp, tkn1, tradable_itkn1_amt))
        Swap().apply(lp1, itkn1, user_nm, tradable_itkn1_amt)

    # *****************************
    # ******* Data Capture ********
    # *****************************

    # price
    pTKN_DAI_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(LPQuote(True).get_amount_from_lp(lp1, itkn1, 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(dai1)))
    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 = 172270.47986192277, USDT = 169688.0597961738
Liquidity: 162921.9244399491

Exchange USDC-iUSDC (LP1)
Reserves: USDC = 27958.351361224384, iUSDC = 13816.083802580026
Liquidity: 16591.87575875552

105.365 USDC redeemed from 49.906 LP tokens if 100.0 invested USDC pulled from parent (lp)
125.058 USDC redeemed from 35.660 LP1 tokens if 100.0 invested USDC pulled from tree (lp + lp1)

[8]:

lp1_state.check_states()
lp1_state.inspect_states(tail = True, num_states = 5)

Amount of tokens retained across states: PASS

[8]:

	Mint	Held	Vault	Burned	dHeld	dVault	dBurned
1996	18.462873	4498.676195	16526.816957	74539.337534	-1058.336332	1078.992156	50.057808
1997	91.074019	4844.185571	16148.921866	74590.186122	345.509377	-377.895092	50.848588
1998	7.415598	4362.801913	16671.573778	74639.991887	-481.383659	522.651913	49.805765
1999	30.026816	5818.449418	15149.357511	74713.976247	1455.647506	-1522.216268	73.984360
2000	2.262046	5238.183496	15686.906375	74786.720122	-580.265923	537.548864	72.743875

[9]:

fig, (TKN_ax, DAI_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_DAI_arr[strt_pt:], color = 'b',linestyle = '-', linewidth=0.7, label=f'{tkn_nm}/{usd_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()

DAI_ax.plot(dates[strt_pt:], pTKN_iTKN_arr[strt_pt:], color = 'b',linestyle = 'dashed', label=f'{tkn_nm}/{itkn_nm} (LP1)')
DAI_ax.set_ylabel('prices', size=20)
DAI_ax.set_ylabel('Price (USD)', size=20)
DAI_ax.legend(fontsize=12)
DAI_ax.grid()

../_images/tutorials_simple_tree_pt2_15_0.png

[10]:

y1_samp = stats.gamma.rvs(a=2000, scale=0.0005, size=10000)

fig, ax = plt.subplots(1, 2, figsize=(12,5))

sns.distplot(pTKN_DAI_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}/{usd_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')

[10]:

Text(0, 0.5, 'Frequency')

../_images/tutorials_simple_tree_pt2_16_1.png

[11]:

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_ylabel("$100 USD Investment", fontsize=14)

[11]:

Text(0, 0.5, '$100 USD Investment')

../_images/tutorials_simple_tree_pt2_17_1.png

[12]:

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 104.700 TKN after direct investment into parent (lp)
100.000 TKN before is worth 119.797 TKN after direct investment into child (lp1)
100.000 TKN before is worth 124.390 TKN after investment into simple tree (lp + lp1)

[13]:

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}/{usd_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 (Direct Investment, Simple Tree, Uni V2)', fontsize = 20)
plt.xlabel("Time unit", fontsize=12)
plt.ylabel("Collected Fees (USD)", fontsize=14)

plt.legend(fontsize=12)

[13]:

<matplotlib.legend.Legend at 0x28b82fe50>

../_images/tutorials_simple_tree_pt2_19_1.png