Portfolio optimization on Dirac

Device: Dirac-1

Introduction

This approach seeks to identify a sub-portfolio of stocks that have superior risk-return profiles compared to the full portfolio. This identifies opportunities for an investor to simplify their investment strategy without sacrificing (and potentially enhancing) the risk-adjusted return.

Methodology

Let K be the total number of available stocks to choose from (here $K = 253$ $K = 253$ ), that is the size of the stock pool. We want to choose a subset of $K^\prime$ $K^{'}$ ( $K^\prime < K$ $K^{'} < K$ ) stocks such that the portfolio risk is minimized, while the portfolio expected return is maximized, that is

\min_{\{x_{i}\}_{i \in \{1, 2,..., K\}}} [-E(R)^2 + \xi VAR(R)]

min_{{x_{i}}_{i \in {1, 2, ..., K}}} [- E (R)^{2} + ξ V A R (R)]

where $R$ $R$ is the daily returns of the portfolio over some period of time, $VAR(R)$ $V A R (R)$ and $E(R)$ $E (R)$ are the variance and expectation of daily returns, $\xi$ $ξ$ is a hyper-parameter, and $\{x_{i}\}$ ${x_{i}}$ are binary variables representing inclusion or exclusion of a stock. A large value means the focus of optimization is to increase return, whereas a small value indicates the reduction of risk is more important. As we can take both long and short positions on stocks, we assume that $x_1, x_2, ..., x_K$ $x_{1}, x_{2}, ..., x_{K}$ corresponds to long positions on stocks 1 to $K$ $K$ .

As we are choosing a subset of $K^\prime$ $K^{'}$ stocks, we also need the following constraint,

\sum_{i=1}^{K} x_i = K^\prime

\sum_{i = 1}^{K} x_{i} = K^{'}

Assuming that the same amount is invested on each of the K' selected stocks, the portfolio daily return at time t over a time period denoted by m can be expanded as follows,

R^{(m)}(t) =\frac{1}{K^\prime} \sum_{i=1}^{K} x_i r^{(m)}_i(t)

R^{(m)} (t) = \frac{1}{K ^{'}} \sum_{i = 1}^{K} x_{i} r_{i}^{(m)} (t)

where $r^{(m)}_i(t)$ $r_{i}^{(m)} (t)$ is the daily return of stock i at time $t$ $t$ in time period $m$ $m$ . The expectation of portfolio daily return over time period $m$ $m$ can thus be expanded as,

E(R^{(m)}) = \frac{1}{K^\prime} \sum_{i=1}^{K} x_i E(r^{(m)}_i)

E (R^{(m)}) = \frac{1}{K ^{'}} \sum_{i = 1}^{K} x_{i} E (r_{i}^{(m)})

and the variance portfolio daily return over time period m is expanded as,

VAR(R^{(m)}) = \frac{1}{K^{\prime 2}} \sum_{i=1}^{K} \sum_{j=1}^{K} x_i x_j COV(r^{(m)}_i, r^{(m)}_j)

V A R (R^{(m)}) = \frac{1}{K ^{'2}} \sum_{i = 1}^{K} \sum_{j = 1}^{K} x_{i} x_{j} CO V (r_{i}^{(m)}, r_{j}^{(m)})

where $COV$ $CO V$ is the covariant function.

The problem then reduces to

\min_{\{x_i\}} {\bf{x}^T} \frac{1}{K^{\prime 2}} [ Q^{(m)} - \xi P^{(m)}] {\bf{x}}

min_{{x_{i}}} x^{T} \frac{1}{K ^{'2}} [Q^{(m)} - ξ P^{(m)}] x

where

Q^{(m)}_{ij} = COV(r^{(m)}_{i}, r^{(m)}_{j})

Q_{ij}^{(m)} = CO V (r_{i}^{(m)}, r_{j}^{(m)})

P^{(m)}_{ij}= E(r_i^{(m)}) \delta_{ij}

P_{ij}^{(m)} = E (r_{i}^{(m)}) δ_{ij}

To avoid an over-fit on the portfolio data, we can minimize the average of the cost function over $M$ $M$ overlapping time periods, that is $m=1,2,...,M$ $m = 1, 2, ..., M$ . The problem becomes,

\min_{\{x_i\}} {\bf{x}^T} \frac{1}{MK^{\prime 2}} \sum_{m=1}^{M}[ Q^{(m)} - \xi P^{(m)}] {\bf{x}}

min_{{x_{i}}} x^{T} \frac{1}{M K ^{'2}} \sum_{m = 1}^{M} [Q^{(m)} - ξ P^{(m)}] x

subject to,

\sum_{i=1}^{K} x_i = K^\prime

\sum_{i = 1}^{K} x_{i} = K^{'}

Implementation

The above-mentioned approach was used to construct an optimal portfolio based on the constituents of the Nasdaq-100 index. The following constituents were used,

In [2]:

import pandas as pd
from IPython.display import display, HTML
df = pd.read_csv("nasdaq100_stocks.csv")
display(HTML(df[["Company", "Symbol"]].to_html()))

Out [ ]:

	Company	Symbol
0	Microsoft Corp	MSFT
1	Apple Inc	AAPL
2	Amazon.com Inc	AMZN
3	Alphabet Inc	GOOG
4	Alphabet Inc	GOOGL
5	NVIDIA Corp	NVDA
6	Tesla Inc	TSLA
7	Meta Platforms Inc	META
8	PepsiCo Inc	PEP
9	Broadcom Inc	AVGO
10	Costco Wholesale Corp	COST
11	Cisco Systems Inc	CSCO
12	T-Mobile US Inc	TMUS
13	Adobe Inc	ADBE
14	Texas Instruments Inc	TXN
15	Comcast Corp	CMCSA
16	Honeywell International Inc	HON
17	Amgen Inc	AMGN
18	Netflix Inc	NFLX
19	QUALCOMM Inc	QCOM
20	Starbucks Corp	SBUX
21	Intel Corp	INTC
22	Intuit Inc	INTU
23	Gilead Sciences Inc	GILD
24	Advanced Micro Devices Inc	AMD
25	Automatic Data Processing Inc	ADP
26	Intuitive Surgical Inc	ISRG
27	Mondelez International Inc	MDLZ
28	Applied Materials Inc	AMAT
29	Analog Devices Inc	ADI
30	Regeneron Pharmaceuticals Inc	REGN
31	PayPal Holdings Inc	PYPL
32	Moderna Inc	MRNA
33	Booking Holdings Inc	BKNG
34	Vertex Pharmaceuticals Inc	VRTX
35	CSX Corp	CSX
36	Fiserv Inc	FISV
37	Lam Research Corp	LRCX
38	Activision Blizzard Inc	ATVI
39	Micron Technology Inc	MU
40	KLA Corp	KLAC
41	Monster Beverage Corp	MNST
42	O'Reilly Automotive Inc	ORLY
43	Keurig Dr Pepper Inc	KDP
44	ASML Holding NV	ASML
45	Synopsys Inc	SNPS
46	Kraft Heinz Co/The	KHC
47	Charter Communications Inc	CHTR
48	American Electric Power Co Inc	AEP
49	Marriott International Inc/MD	MAR
50	Palo Alto Networks Inc	PANW
51	Cintas Corp	CTAS
52	Cadence Design Systems Inc	CDNS
53	MercadoLibre Inc	MELI
54	Dexcom Inc	DXCM
55	Exelon Corp	EXC
56	Biogen Inc	BIIB
57	AstraZeneca PLC ADR	AZN
58	NXP Semiconductors NV	NXPI
59	Paychex Inc	PAYX
60	Enphase Energy Inc	ENPH
61	Autodesk Inc	ADSK
62	Pinduoduo Inc ADR	PDD
63	Ross Stores Inc	ROST
64	Fortinet Inc	FTNT
65	Microchip Technology Inc	MCHP
66	Xcel Energy Inc	XEL
67	Lululemon Athletica Inc	LULU
68	Airbnb Inc	ABNB
69	Workday Inc	WDAY
70	PACCAR Inc	PCAR
71	Walgreens Boots Alliance Inc	WBA
72	IDEXX Laboratories Inc	IDXX
73	Electronic Arts Inc	EA
74	Marvell Technology Inc	MRVL
75	Old Dominion Freight Line Inc	ODFL
76	GLOBALFOUNDRIES Inc	GFS
77	CoStar Group Inc	CSGP
78	Dollar Tree Inc	DLTR
79	Illumina Inc	ILMN
80	Baker Hughes Co	BKR
81	Copart Inc	CPRT
82	Constellation Energy Corp	CEG
83	Cognizant Technology Solutions Corp	CTSH
84	JD.com Inc ADR	JD
85	Fastenal Co	FAST
86	Verisk Analytics Inc	VRSK
87	Seagen Inc	SGEN
88	Crowdstrike Holdings Inc	CRWD
89	Diamondback Energy Inc	FANG
90	Sirius XM Holdings Inc	SIRI
91	eBay Inc	EBAY
92	Datadog Inc	DDOG
93	Warner Bros Discovery Inc	WBD
94	ANSYS Inc	ANSS
95	Atlassian Corp	TEAM
96	Rivian Automotive Inc	RIVN
97	Zoom Video Communications Inc	ZM
98	Zscaler Inc	ZS
99	Align Technology Inc	ALGN
100	Lucid Group Inc	LCID

We got the historical prices of the constituent stocks, as well as those of Nasdaq-100 (NDX) and equal-weighted Nasdaq-100 (QQQE) using the Yahoo Finance Python library,

In [4]:

# Import libs                                                                                 
import os
import pandas as pd
import yfinance as yf
# Define some parameters                                                                                            
OUT_DIR = "data"
DROP_STOCKS = []
# Get the list of all existing stocks                                                         
stocks = list(df["Symbol"].unique()) + ["NDX", "QQQE"] 
for stock in stocks:
try:
tmp_df = yf.Ticker(stock).history(
period="max", interval="1d",
)[["Close"]].rename(
columns={
"Close": stock,
}
)
tmp_df["Date"] = tmp_df.index
tmp_df.to_csv(
os.path.join(OUT_DIR, "%s.csv" % stock),
index=False,
)
except Exception as exc:
print("Could not get price for %s" % stock)
print(exc)
DROP_STOCKS.append(stock)
if tmp_df.shape[0] == 0:
DROP_STOCKS.append(stock)

Out [ ]:

- FISV: No data found, symbol may be delisted
- ATVI: No data found, symbol may be delisted
- SGEN: No data found, symbol may be delisted

Let us import some libraries and set some parameters,

In [5]:

# Import libs                                                                                
import os
import sys
import time
import datetime
import json
import warnings
from functools import wraps
import numpy as np
import pandas as pd
from qci_client import QciClient
warnings.filterwarnings("ignore")
ALPHA = 1.0 # The coefficient for penalty term (for linear constraint)
N_SAMPLES = 20 # Number of solution samples
XI = 5.0 # The xi variable as defined in Methodology
K_PRIME = 30 # Number of selected stocks
WINDOW_DAYS = 30 # Size of each sliding window in days
WINDOW_OVERLAP_DAYS = 15 # Overlap between sliding windows in days
IN_SAMPLE_DAYS = 180 # Size of the lookback period in days
OUT_OF_SAMPLE_DAYS = 30 # Size of the horizon window in days

We now define a function that calculates daily returns of all constituent stocks,

In [6]:

def get_stock_returns(stocks, min_date, max_date):
min_date = pd.to_datetime(min_date)
max_date = pd.to_datetime(max_date)
return_df = None
for stock in stocks:
stock_df = pd.read_csv("data/%s.csv" % stock)
stock_df["Date"] = stock_df["Date"].astype("datetime64[ns]")
stock_df = stock_df.fillna(method="ffill").fillna(method="bfill")
stock_df[stock] = stock_df[stock].pct_change()
stock_df = stock_df.dropna()
stock_df = stock_df[
(stock_df["Date"] >= min_date) & (stock_df["Date"] <= max_date)
]
if return_df is None:
return_df = stock_df
else:
return_df = return_df.merge(stock_df, how="outer", on="Date",)
return_df = return_df.fillna(method="ffill").fillna(method="bfill")
return return_df

And a function that calculates the hamiltonian matrix,

In [7]:

def get_hamiltonian(
return_df, stocks, min_date, max_date,
):
K = len(stocks)
# Calculate P and Q                                                                       
Q = np.zeros(shape=(K, K), dtype="d")
P = np.zeros(shape=(K, K), dtype="d")
m = 0
min_date = pd.to_datetime(min_date)
max_date = pd.to_datetime(max_date)
tmp_date = min_date
while tmp_date <= max_date:
tmp_min_date = tmp_date
tmp_max_date = tmp_date + datetime.timedelta(days=WINDOW_DAYS)
tmp_df = return_df[
(return_df["Date"] >= tmp_min_date)
& (return_df["Date"] <= tmp_max_date)
]
r_list = []
for i in range(K):
r_list.append(np.array(tmp_df[stocks[i]]))
Q += np.cov(r_list)
for i in range(K):
for j in range(K):
P[i][j] += np.mean(r_list[i]) * np.mean(r_list[j])
tmp_date += datetime.timedelta(
days=WINDOW_DAYS - WINDOW_OVERLAP_DAYS,
)
m += 1
fct = m
if fct > 0:
fct = 1.0 / fct
P = fct * P
Q = fct * Q
# Calculate the Hamiltonian                                                              
H = -P + XI * Q
# make sure H is symmetric up to machine precision                                       
H = 0.5 * (H + H.transpose())
return H

And, we define a function that yields an optimal portfolio given a hamiltonian $H$ $H$ ,

In [8]:

def optimize_portfolio(H, stocks, curr_date):
beg_time = time.time()
K = len(stocks)
assert H.shape[0] == K
assert H.shape[1] == K
# Generate the constraint                                                                
cons_lhs = np.ones(shape=(K), dtype=np.float32)
cons_rhs = np.array([-K_PRIME])
constraints = np.hstack([cons_lhs, cons_rhs])
# Create json objects   
objective_json = {
"file_name": "objective_tutorial_eq_wt_port_opt.json",
"file_config": {
"objective": {"data": H, "num_variables": K},
}  
}
constraint_json = {
"file_name": "constraints_tutorial_eq_wt_port_opt.json",
"file_config": {
"constraints": {
"data": constraints, 
"num_variables": K,
"num_constraints": 1,
}
}
}
job_json = {
"job_name": "moodys_eqc1_equal_weights",
"job_tags": ["moody_nasda100_eqc1_equal_weights",],
"params": {
"sampler_type": "csample", #"eqc1",                                               
"n_samples": N_SAMPLES,
"alpha": ALPHA,
},
}
# Solve the optimization problem                                                          
qci = QciClient()
response_json = qci.upload_file(objective_json)
objective_file_id = response_json["file_id"]
response_json = qci.upload_file(constraint_json)
constraint_file_id = response_json["file_id"]
job_params = {
"sampler_type": "dirac-1", 
"alpha": ALPHA, 
"nsamples": N_SAMPLES,
}
job_json = qci.build_job_body(
job_type="sample-constraint", 
job_params=job_params,
constraints_file_id=constraint_file_id, 
objective_file_id=objective_file_id,
job_name=f"tutorial_eqc1",
job_tags=["tutorial_eqc1"],
)
print(job_json)
job_response_json = qci.process_job(
job_body=job_json, job_type="sample-constraint",
)
print(job_response_json)
results = list(job_response_json["results"]["file_config"].values())[0]
energies = results["energies"]
samples = results["solutions"]
is_feasibles = results["feasibilities"]
# The sample solutions are sorted by energy                                               
sol = None
for i, item in enumerate(samples):
sol = item
is_feasible = is_feasibles[i]
if is_feasible:
break
if not is_feasible:
print("Solution is not feasible!")
assert len(sol) == K, "Inconsistent solution size!"
if sum(sol) != K_PRIME:
print(
"Expected to select %d stocks, but selected %d!"
% (K_PRIME, sum(sol))
)
sel_stocks = []
for i in range(K):
if sol[i] > 0:
sel_stocks.append(stocks[i])
print(
"In optimize_portfolio; done with checking constraints; %0.2f seconds!"
% (time.time() - beg_time)
)
return sol, sel_stocks

Results

We can now test the approach over a period of time, for example, between 2020-01-15 to 2023-12-30. We define,

In [9]:

def run(curr_date):
print("Processing curr date:", curr_date)
curr_date = pd.to_datetime(curr_date)
min_ins_date = curr_date - datetime.timedelta(days=IN_SAMPLE_DAYS)
max_ins_date = curr_date - datetime.timedelta(days=1)
min_oos_date = curr_date
max_oos_date = curr_date + datetime.timedelta(days=OUT_OF_SAMPLE_DAYS)
df = pd.read_csv("nasdaq100_stocks.csv", low_memory=False)
stocks = list(set(df["Symbol"]) - set(DROP_STOCKS))
ins_return_df = get_stock_returns(stocks, min_ins_date, max_ins_date)
oos_return_df = get_stock_returns(stocks, min_oos_date, max_oos_date)
ins_return_df = ins_return_df.sort_values("Date")
ins_return_df = ins_return_df.fillna(method="ffill").fillna(0)
oos_return_df = oos_return_df.sort_values("Date")
oos_return_df = oos_return_df.fillna(method="ffill").fillna(0)
H = get_hamiltonian(ins_return_df, stocks, min_ins_date, max_ins_date)
sol, sel_stocks = optimize_portfolio(H, stocks, curr_date)
sel_stock_df = pd.DataFrame()
sel_stock_df["Date"] = [curr_date] * len(sel_stocks)
sel_stock_df["Stock"] = sel_stocks
return sel_stock_df

We can then run a backtest,

In [20]:

min_date = pd.to_datetime("2022-01-13")                                    
max_date = pd.to_datetime("2022-12-30")
SEL_STOCK_OUT_FILE = "selected_stocks.csv"
curr_date = min_date
while curr_date < max_date:
tmp_sel_stock_df = run(curr_date)
if os.path.exists(SEL_STOCK_OUT_FILE):
tmp_sel_stock_df.to_csv(
SEL_STOCK_OUT_FILE, index=False, mode="a", header=False,
)
else:
tmp_sel_stock_df.to_csv(
SEL_STOCK_OUT_FILE, index=False,
)
curr_date += datetime.timedelta(days=OUT_OF_SAMPLE_DAYS + 1)

Out [ ]:

Processing curr date: 2022-02-13 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4c84e38d25ec78cae76a6', 'objective_file_id': '65f4c84d38d25ec78cae76a4', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4c84ea657b4e45963cc79'-: 2024/03/15 15:14:38
QUEUED: 2024/03/15 15:14:40
RUNNING: 2024/03/15 15:30:19
COMPLETED: 2024/03/15 15:35:04
Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '65f4c84ea657b4e45963cc79', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4c84e38d25ec78cae76a6', 'objective_file_id': '65f4c84d38d25ec78cae76a4', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-03-15T22:14:38.756Z', 'queued_at_rfc3339nano': '2024-03-15T22:14:38.757Z', 'running_at_rfc3339nano': '2024-03-15T22:30:19.102Z', 'completed_at_rfc3339nano': '2024-03-15T22:35:03.957Z'}, 'job_result': {'file_id': '65f4cd1738d25ec78cae76aa', 'device_usage_s': 40}, 'details': {'status': 'COMPLETED'}}, 'results': {'file_id': '65f4cd1738d25ec78cae76aa', 'num_parts': 1, 'num_bytes': 12488, 'file_name': 'tutorial_eqc1', 'file_config': {'quadratic_linearly_constrained_binary_optimization_results': {'counts': [2, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1], 'energies': [-899.7963256835938, -899.7960815429688, -899.7958374023438, -899.7955932617188, -899.7955932617188, -899.7955932617188, -899.7954711914062, -899.7954711914062, -899.7949829101562, -899.7948608398438, -899.7948608398438, -899.7944946289062, -899.7944946289062, -899.7943725585938, -899.7940063476562], 'feasibilities': [True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], 'objective_values': [0.20369557323033616, 0.20388814901805405, 0.20418966300356534, 0.20438077700310434, 0.20443863101159693, 0.2044567209569369, 0.2045380135356829, 0.20454698282745962, 0.20500405446625788, 0.20508160200564368, 0.20518514483182357, 0.20552384253214112, 0.20553403280592786, 0.20564387422012306, 0.20594401748556387], 'solutions': [[1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 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In optimize_portfolio; done with checking constraints; 1228.37 seconds!
Processing curr date: 2022-03-16 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4cd1b38d25ec78cae76ae', 'objective_file_id': '65f4cd1b38d25ec78cae76ac', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4cd1ca657b4e45963cc7a'-: 2024/03/15 15:35:08
RUNNING: 2024/03/15 15:35:09
COMPLETED: 2024/03/15 15:39:50
Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '65f4cd1ca657b4e45963cc7a', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4cd1b38d25ec78cae76ae', 'objective_file_id': '65f4cd1b38d25ec78cae76ac', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-03-15T22:35:08.493Z', 'queued_at_rfc3339nano': '2024-03-15T22:35:08.493Z', 'running_at_rfc3339nano': '2024-03-15T22:35:09.037Z', 'completed_at_rfc3339nano': '2024-03-15T22:39:49.625Z'}, 'job_result': {'file_id': '65f4ce3538d25ec78cae76b0', 'device_usage_s': 39}, 'details': {'status': 'COMPLETED'}}, 'results': {'file_id': '65f4ce3538d25ec78cae76b0', 'num_parts': 1, 'num_bytes': 6758, 'file_name': 'tutorial_eqc1', 'file_config': {'quadratic_linearly_constrained_binary_optimization_results': {'counts': [10, 3, 2, 1, 1, 1, 1, 1], 'energies': [-899.7587890625, -899.7586669921875, -899.758544921875, -899.7584228515625, -899.75830078125, -899.75830078125, -899.75830078125, -899.7578125], 'feasibilities': [True, True, True, True, True, True, True, True], 'objective_values': [0.24119182679735562, 0.24131389219151933, 0.24150392804416737, 0.24155724141091345, 0.24168889093742402, 0.24172747089956806, 0.24172983780904703, 0.2422582565204664], 'solutions': [[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]]}}}}
In optimize_portfolio; done with checking constraints; 284.62 seconds!
Processing curr date: 2022-04-16 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4ce3938d25ec78cae76b4', 'objective_file_id': '65f4ce3938d25ec78cae76b2', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4ce3aa657b4e45963cc7b'-: 2024/03/15 15:39:54
QUEUED: 2024/03/15 15:39:55
RUNNING: 2024/03/15 17:00:15
COMPLETED: 2024/03/15 17:05:29
Dirac allocation balance = 0 s (unmetered)
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In optimize_portfolio; done with checking constraints; 5137.52 seconds!
Processing curr date: 2022-05-17 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e24c38d25ec78cae76c0', 'objective_file_id': '65f4e24c38d25ec78cae76be', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4e24da657b4e45963cc7d'-: 2024/03/15 17:05:33
RUNNING: 2024/03/15 17:05:34
COMPLETED: 2024/03/15 17:10:14
Dirac allocation balance = 0 s (unmetered)
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In optimize_portfolio; done with checking constraints; 283.34 seconds!
Processing curr date: 2022-06-17 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e36938d25ec78cae76cc', 'objective_file_id': '65f4e36838d25ec78cae76ca', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4e36aa657b4e45963cc80'-: 2024/03/15 17:10:18
RUNNING: 2024/03/15 17:10:19
COMPLETED: 2024/03/15 17:15:00
Dirac allocation balance = 0 s (unmetered)
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In optimize_portfolio; done with checking constraints; 284.86 seconds!
Processing curr date: 2022-07-18 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e48738d25ec78cae76da', 'objective_file_id': '65f4e48738d25ec78cae76d8', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4e488a657b4e45963cc83'-: 2024/03/15 17:15:04
RUNNING: 2024/03/15 17:15:05
COMPLETED: 2024/03/15 17:19:45
Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '65f4e488a657b4e45963cc83', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e48738d25ec78cae76da', 'objective_file_id': '65f4e48738d25ec78cae76d8', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-03-16T00:15:04.367Z', 'queued_at_rfc3339nano': '2024-03-16T00:15:04.368Z', 'running_at_rfc3339nano': '2024-03-16T00:15:04.674Z', 'completed_at_rfc3339nano': '2024-03-16T00:19:45.142Z'}, 'job_result': {'file_id': '65f4e5a138d25ec78cae76e0', 'device_usage_s': 39}, 'details': {'status': 'COMPLETED'}}, 'results': {'file_id': '65f4e5a138d25ec78cae76e0', 'num_parts': 1, 'num_bytes': 5943, 'file_name': 'tutorial_eqc1', 'file_config': {'quadratic_linearly_constrained_binary_optimization_results': {'counts': [13, 1, 2, 1, 1, 1, 1], 'energies': [-899.478515625, -899.4781494140625, -899.47802734375, -899.4766845703125, -899.476318359375, -899.475830078125, -899.47314453125], 'feasibilities': [True, True, True, True, True, True, True], 'objective_values': [0.5214603078128224, 0.5218969949789258, 0.5220147467374703, 0.5233189543750865, 0.5237230268958093, 0.5241313185100483, 0.5268431633545608], 'solutions': [[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]]}}}}
In optimize_portfolio; done with checking constraints; 283.57 seconds!
Processing curr date: 2022-08-18 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e5a438d25ec78cae76e4', 'objective_file_id': '65f4e5a438d25ec78cae76e2', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4e5a5a657b4e45963cc85'-: 2024/03/15 17:19:49
RUNNING: 2024/03/15 17:19:50
COMPLETED: 2024/03/15 17:24:30
Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '65f4e5a5a657b4e45963cc85', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e5a438d25ec78cae76e4', 'objective_file_id': '65f4e5a438d25ec78cae76e2', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-03-16T00:19:49.344Z', 'queued_at_rfc3339nano': '2024-03-16T00:19:49.345Z', 'running_at_rfc3339nano': '2024-03-16T00:19:50.223Z', 'completed_at_rfc3339nano': '2024-03-16T00:24:30.648Z'}, 'job_result': {'file_id': '65f4e6be38d25ec78cae76ee', 'device_usage_s': 39}, 'details': {'status': 'COMPLETED'}}, 'results': {'file_id': '65f4e6be38d25ec78cae76ee', 'num_parts': 1, 'num_bytes': 5128, 'file_name': 'tutorial_eqc1', 'file_config': {'quadratic_linearly_constrained_binary_optimization_results': {'counts': [11, 4, 2, 1, 1, 1], 'energies': [-899.4928588867188, -899.4913940429688, -899.4911499023438, -899.4895629882812, -899.4894409179688, -899.4894409179688], 'feasibilities': [True, True, True, True, True, True], 'objective_values': [0.5070904192884772, 0.5085829941485729, 0.5087828367595719, 0.5104381912056234, 0.5105143985622359, 0.5105987515954077], 'solutions': [[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]]}}}}
In optimize_portfolio; done with checking constraints; 283.87 seconds!
Processing curr date: 2022-09-18 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e6c238d25ec78cae76f2', 'objective_file_id': '65f4e6c138d25ec78cae76f0', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4e6c2a657b4e45963cc88'-: 2024/03/15 17:24:34
RUNNING: 2024/03/15 17:24:35
COMPLETED: 2024/03/15 17:29:15
Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '65f4e6c2a657b4e45963cc88', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e6c238d25ec78cae76f2', 'objective_file_id': '65f4e6c138d25ec78cae76f0', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-03-16T00:24:34.656Z', 'queued_at_rfc3339nano': '2024-03-16T00:24:34.656Z', 'running_at_rfc3339nano': '2024-03-16T00:24:34.719Z', 'completed_at_rfc3339nano': '2024-03-16T00:29:15.645Z'}, 'job_result': {'file_id': '65f4e7db38d25ec78cae76fc', 'device_usage_s': 39}, 'details': {'status': 'COMPLETED'}}, 'results': {'file_id': '65f4e7db38d25ec78cae76fc', 'num_parts': 1, 'num_bytes': 2683, 'file_name': 'tutorial_eqc1', 'file_config': {'quadratic_linearly_constrained_binary_optimization_results': {'counts': [15, 4, 1], 'energies': [-899.3742065429688, -899.3726196289062, -899.3721313476562], 'feasibilities': [True, True, True], 'objective_values': [0.6258614048985105, 0.6274494985815712, 0.6278980056721158], 'solutions': [[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]]}}}}
In optimize_portfolio; done with checking constraints; 283.45 seconds!
Processing curr date: 2022-10-19 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e7de38d25ec78cae7700', 'objective_file_id': '65f4e7de38d25ec78cae76fe', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4e7dfa657b4e45963cc8b'-: 2024/03/15 17:29:19
RUNNING: 2024/03/15 17:29:20
COMPLETED: 2024/03/15 17:34:00
Dirac allocation balance = 0 s (unmetered)
{'job_info': {'job_id': '65f4e7dfa657b4e45963cc8b', 'job_submission': {'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1'], 'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e7de38d25ec78cae7700', 'objective_file_id': '65f4e7de38d25ec78cae76fe', 'alpha': 1, 'atol': 1e-10}}, 'device_config': {'dirac-1': {'num_samples': 20}}}, 'job_status': {'submitted_at_rfc3339nano': '2024-03-16T00:29:19.354Z', 'queued_at_rfc3339nano': '2024-03-16T00:29:19.355Z', 'running_at_rfc3339nano': '2024-03-16T00:29:19.713Z', 'completed_at_rfc3339nano': '2024-03-16T00:34:00.185Z'}, 'job_result': {'file_id': '65f4e8f838d25ec78cae7706', 'device_usage_s': 39}, 'details': {'status': 'COMPLETED'}}, 'results': {'file_id': '65f4e8f838d25ec78cae7706', 'num_parts': 1, 'num_bytes': 6758, 'file_name': 'tutorial_eqc1', 'file_config': {'quadratic_linearly_constrained_binary_optimization_results': {'counts': [8, 5, 2, 1, 1, 1, 1, 1], 'energies': [-899.2722778320312, -899.2716674804688, -899.2713012695312, -899.2708129882812, -899.2705688476562, -899.2702026367188, -899.2700805664062, -899.2695922851562], 'feasibilities': [True, True, True, True, True, True, True, True], 'objective_values': [0.7276977466475752, 0.7282881097574255, 0.7286484491149878, 0.7291494472133333, 0.7294209926816911, 0.7297909625630262, 0.729837303374378, 0.7304178814938523], 'solutions': [[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]]}}}}
In optimize_portfolio; done with checking constraints; 283.65 seconds!
Processing curr date: 2022-11-19 00:00:00
{'job_submission': {'problem_config': {'quadratic_linearly_constrained_binary_optimization': {'constraints_file_id': '65f4e8fb38d25ec78cae770a', 'objective_file_id': '65f4e8fb38d25ec78cae7708', 'alpha': 1.0}}, 'device_config': {'dirac-1': {'num_samples': 20}}, 'job_name': 'tutorial_eqc1', 'job_tags': ['tutorial_eqc1']}}
Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4e8fca657b4e45963cc8d'-: 2024/03/15 17:34:04
RUNNING: 2024/03/15 17:34:05
COMPLETED: 2024/03/15 17:38:46
Dirac allocation balance = 0 s (unmetered)
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In optimize_portfolio; done with checking constraints; 284.78 seconds!
Processing curr date: 2022-12-20 00:00:00
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Dirac allocation balance = 0 s (unmetered)
Job submitted job_id='65f4ea1aa657b4e45963cc8f'-: 2024/03/15 17:38:50
RUNNING: 2024/03/15 17:38:51
COMPLETED: 2024/03/15 17:43:32
Dirac allocation balance = 0 s (unmetered)
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In optimize_portfolio; done with checking constraints; 283.94 seconds!

We can now calculate the optimal portfolio values over the period of time it was tested.

In [22]:

# Import libs                                                                                 
import sys
import datetime
import warnings
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
warnings.filterwarnings("ignore")
# Set params                                                                                  
INIT_PORT_VAL = 1000000.0
OUT_OF_SAMPLE_DAYS = 30
K_PRIME = 30
XI = 5.0
IND_SYMBOL_1 = "QQQE"
IND_SYMBOL_2 = "NDX"
SEL_STOCK_FILE = "selected_stocks.csv"
INDEX_FILE_1 = "data/%s.csv" % IND_SYMBOL_1
INDEX_FILE_2 = "data/%s.csv" % IND_SYMBOL_2
MIN_DATE = pd.to_datetime("2022-01-01")
MAX_DATE = pd.to_datetime("2022-12-31")
# Read allocation file                                                                        
df = pd.read_csv(SEL_STOCK_FILE)
df["Date"] = df["Date"].astype("datetime64[ns]")
df = df[(df["Date"] >= MIN_DATE) & (df["Date"] <= MAX_DATE)]
# Loop through dates and calculate port value                                                 
beg_port_val = INIT_PORT_VAL
df = df.sort_values("Date")
adj_dates = sorted(df["Date"].unique())
num_adj_dates = len(adj_dates)
dates = None
port_vals = None
for i in range(num_adj_dates):
print(
"Processing adjustment date %s"
% pd.to_datetime(adj_dates[i]).strftime("%Y-%m-%d")
)
beg_date = pd.to_datetime(adj_dates[i])
if i < num_adj_dates - 1:
end_date = pd.to_datetime(adj_dates[i + 1])
else:
end_date = beg_date + datetime.timedelta(days=OUT_OF_SAMPLE_DAYS)
tmp_df = df[df["Date"] == beg_date]
stocks = tmp_df["Stock"]
stocks = list(set(stocks))
#stocks = list(set(stocks) - {"LCID", "CEG", "ABNB", "GFS", "RIVN"})
if end_date > pd.to_datetime("2023-10-20"):
stocks = list(set(stocks) - {"ATVI"})
all_dates = [beg_date]
date0 = beg_date
while date0 < end_date:
date0 = date0 + datetime.timedelta(days=1)
all_dates.append(date0)
price_df = pd.DataFrame({"Date": all_dates})
for stock in stocks:
stock_df = pd.read_csv("data/%s.csv" % stock)
stock_df["Date"] = stock_df["Date"].astype("datetime64[ns]")
stock_df = stock_df[
(stock_df["Date"] >= beg_date) & (stock_df["Date"] <= end_date)
]
if price_df is None:
price_df = stock_df
else:
price_df = price_df.merge(stock_df, on="Date", how="outer")
price_df = price_df.fillna(method="ffill").fillna(method="bfill")
price_df = price_df.sort_values("Date")
tmp_dates = np.array(price_df["Date"])
tmp_port_vals = np.zeros(shape=(price_df.shape[0]))
assert price_df.shape[0] > 0
for stock in stocks:
prices = np.array(price_df[stock])
beg_price = prices[0]
stock_wt = 1.0 / len(stocks)
if beg_price <= 0:
print(stock)
print(price_df[["Date", stock]])
assert beg_price > 0, "Error in data for %s" % stock
stock_count = stock_wt * beg_port_val / beg_price
tmp_port_vals += stock_count * prices
if dates is None:
dates = tmp_dates
else:
dates = np.concatenate([dates, tmp_dates])
if port_vals is None:
port_vals = tmp_port_vals
else:
port_vals = np.concatenate([port_vals, tmp_port_vals])
beg_port_val = port_vals[-1]

Out [ ]:

Processing adjustment date 2022-01-13
Processing adjustment date 2022-02-13
Processing adjustment date 2022-03-16
Processing adjustment date 2022-04-16
Processing adjustment date 2022-05-17
Processing adjustment date 2022-06-17
Processing adjustment date 2022-07-18
Processing adjustment date 2022-08-18
Processing adjustment date 2022-09-18
Processing adjustment date 2022-10-19
Processing adjustment date 2022-11-19
Processing adjustment date 2022-12-20

We can then plot the optimal portfolio values and compare them with those of Nasdaq-100 and equal-weighted Nasdaq-100 indexes.

In [23]:

# Plot    
out_df = pd.DataFrame({"Date": dates, "Port_Val": port_vals})
out_df["Date"] = out_df["Date"].astype("datetime64[ns]")
ind_df_1 = pd.read_csv(INDEX_FILE_1)
ind_df_1["Date"] = ind_df_1["Date"].astype("datetime64[ns]")
min_date = out_df["Date"].min()
max_date = out_df["Date"].max()
ind_df_1 = ind_df_1[
(ind_df_1["Date"] >= min_date) & (ind_df_1["Date"] <= max_date)
]
ind_vals_1 = np.array(ind_df_1[IND_SYMBOL_1])
fct = INIT_PORT_VAL / ind_vals_1[0]
ind_vals_1 *= fct
ind_df_2 = pd.read_csv(INDEX_FILE_2)
ind_df_2["Date"] = ind_df_2["Date"].astype("datetime64[ns]")
min_date = out_df["Date"].min()
max_date = out_df["Date"].max()
ind_df_2 = ind_df_2[
(ind_df_2["Date"] >= min_date) & (ind_df_2["Date"] <= max_date)
]
ind_vals_2 = np.array(ind_df_2[IND_SYMBOL_2])
fct = INIT_PORT_VAL / ind_vals_2[0]
ind_vals_2 *= fct
plt.plot(
out_df["Date"], out_df["Port_Val"],                                            
ind_df_1["Date"], ind_vals_1,
ind_df_2["Date"], ind_vals_2,
)
plt.xlabel("Date")
plt.ylabel("Portfolio Value")
plt.legend(
[
"Equal weighted optimal portfolio",                  
"Equal weighted Nasdaq 100",
"Nasdaq 100",
]
)                                 
plt.show()

Out [ ]:

<Figure size 640x480 with 1 Axes>