Individual Data Lab 2
- Portfolio Construction (portfolio optimization)
Note 1: Review what you have learned in DataCamp assignments (e.g., Introduction to Portfolio Analysis in Python).¶ Note 2: To deep dive into what each function does, use the help function, e.g., run "help(npf.npv)."
1. Craft an all-weather portfolio. Pick your own portfolio of stocks following an investment theme that has stood and will stand the test of time. Extract the data from Yahoo Finance/Refinitiv/any other platforms and explore the statistical distribution of each stock's past 5-year returns.
# Install yahoo finance API package
!pip install yfinance
# Import
import yfinance as yf
import pandas as pd
import numpy as np
import datetime as dt
import matplotlib.pyplot as plt
# Define a list of stock tickers for your portfolio
# 10 companies: Apple, Microsoft, Google, Amazon, NVIDIA, Tesla, Meta, UnitedHealth, Walmart, JPMorgan Chase
stock_tickers = ["AAPL", "MSFT", "GOOGL", "AMZN", "NVDA", "TSLA", "META", "UNH", "WMT", "JPM"]
# start and end dates for past 5-year
start_date = dt.datetime(2018,9,8)
end_date = dt.datetime(2023,9,8)
# Download historical stock price data from Yahoo Finance
stocks_price = yf.download(stock_tickers, start=start_date, end=end_date)
# Extract adjusted closing prices
adj_prices = stocks_price["Adj Close"]
# Calculate the daily returns for each stock [.dropna()removes missing values)]
daily_returns = adj_prices.pct_change().dropna()
# Explore:
# print(stocks_price)
# stocks_price.info()
# stocks_price.describe()
# stocks_price.head()
# Explore the statistical distribution of each stock's past 5-year returns.
for ticker in stock_tickers:
stock_returns = daily_returns[ticker]
print(f"Stock Name: {ticker}")
print(f"Mean: {stock_returns.mean()}")
print(f"Std. dev / Volatility: {stock_returns.std()}")
print(f"Skewness: {stock_returns.skew()}")
print(f"Kurtosis: {stock_returns.kurtosis()}")
print()
[*********************100%%**********************] 10 of 10 completed
Stock Name: AAPL
Mean: 0.0011953447742575152
Std. dev / Volatility: 0.0210352256977011
Skewness: -0.05669532989639144
Kurtosis: 4.523925065305724
Stock Name: MSFT
Mean: 0.0011170886067587758
Std. dev / Volatility: 0.019737199708404384
Skewness: 0.019894449281605393
Kurtosis: 6.398696441468854
Stock Name: GOOGL
Mean: 0.0008689011377693623
Std. dev / Volatility: 0.020243704276955043
Skewness: 0.011079078396462229
Kurtosis: 3.4468055344332864
Stock Name: AMZN
Mean: 0.0005473404809143355
Std. dev / Volatility: 0.023126288082679712
Skewness: 0.10459944195167964
Kurtosis: 3.839429938406828
Stock Name: NVDA
Mean: 0.0021045929372477297
Std. dev / Volatility: 0.03404218270152162
Skewness: 0.14045176587413188
Kurtosis: 4.51870062310065
Stock Name: TSLA
Mean: 0.0029205307377940704
Std. dev / Volatility: 0.041589625835712594
Skewness: 0.11119927815139374
Kurtosis: 3.291813379495686
Stock Name: META
Mean: 0.0008706146040383815
Std. dev / Volatility: 0.02784679837270109
Skewness: -0.5181917052521029
Kurtosis: 17.367463393750537
Stock Name: UNH
Mean: 0.0007323608478360226
Std. dev / Volatility: 0.018910245971289295
Skewness: -0.02625573371074217
Kurtosis: 12.186160253282068
Stock Name: WMT
Mean: 0.0005817262317861116
Std. dev / Volatility: 0.013986103902166596
Skewness: 0.1517081062954399
Kurtosis: 13.97443612884718
Stock Name: JPM
Mean: 0.0005124183057082227
Std. dev / Volatility: 0.020308988331634067
Skewness: 0.41239849111542054
Kurtosis: 12.65612942779793
daily_returns.head()
2018-09-11 00:00:00
0.02528301468
0.02482707844
2018-09-12 00:00:00
-0.01241906063
0.001434233286
2018-09-13 00:00:00
0.02415534452
-0.00006532908684
2018-09-14 00:00:00
-0.01135110833
-0.009890105003
2018-09-17 00:00:00
-0.02662626205
-0.03155027437
5 rows, showing
per page
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2. Build an equally-weighted all-weather portfolio of your stock picks. Then, deep dive into the return characteristics of the portfolio (i.e., annualized portfolio return and volatility, portfolio's Sharpe ratio, portfolio's daily return profile - mean, volatility, skewness, kurtosis). Finally, draw the cumulative return of your all-weather portfolio for the past five years.
# ---------- Function : portChar. --------------
# portChar function outputs the return characteristics of the portfolio
# 1. annualized portfolio return and volatility
# 2. portfolio's Sharpe ratio
# 3. portfolio's daily return profile - mean, volatility, skewness, kurtosis
# 4. portfolio's cumulative return
def portChar(daily_returns, weights):
# 1. annualized portfolio return and volatility,
# Calculate average return for each stock
meanDailyReturns = daily_returns.mean()
# Calculate average portfolio return
portReturn = np.sum(meanDailyReturns * weights)
# annualized portfolio return --- 252 trading days in one calendar year
annualized_portReturn = portReturn * 252
print("Portfolio's Annualized Return: ", str(np.round(annualized_portReturn, 4) * 100) + '%')
# Construct a covariance matrix for the daily returns data
cov_matrix = (daily_returns.cov()) * 252
# Calculate the variance with the formula
port_variance = np.dot(weights.T, np.dot(cov_matrix, weights))
# Calculate the standard deviation of portfolio
port_stddev = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
# annualized portfolio volatility --- 252 trading days in one calendar year
annual_portStdDev = port_stddev * np.sqrt(252)
print("Portfolio's Annualized Volatility/Std. Dev: ", np.round(annual_portStdDev, 3))
# 2. portfolio's Sharpe ratio
# 10 Year Treasury Rate (I:10YTCMR)
# Risk-Free-Rate 4.26% for Sep 08 2023
risk_free = 0.042
port_SharpeRatio = (annualized_portReturn - risk_free) / annual_portStdDev
print("Portfolio's Sharpe Ratio: ", str(np.round(port_SharpeRatio, 4) * 100), '%')
# 3. portfolio's daily return profile - mean, volatility, skewness, kurtosis
# portfolio's daily returns
port_daily_Return = daily_returns.dot(weights)
print("Portfolio daily return - Mean : ", str(np.round(port_daily_Return.mean(), 4) * 100) + '%')
print("Portfolio daily return - Standard Deviation : ", str(np.round(port_daily_Return.std(), 4) * 100) + '%')
print("Portfolio daily return - skewness : ", np.round(port_daily_Return.skew(), 4))
print("Portfolio daily return - Kurtosis : ", np.round(port_daily_Return.kurtosis(), 4))
# 4. portfolio's cumulative return
# # Create portfolio returns column
# daily_returns['Portfolio']= daily_returns.dot(weights)
# # Compound the [daily] portfolio percentage returns over time
# port_daily_Cum_Return = (1 + daily_returns).cumprod()
port_daily_Cum_Return = (1 + port_daily_Return).cumprod()
# RETURN -----------
return daily_returns.index, port_daily_Cum_Return
# --------------------- Excute the portChar function ------------------
# Weights - an equally-weighted all-weather portfolio
weights = np.repeat(1 / len(stock_tickers), len(stock_tickers))
index, port_Cum_Return = portChar(daily_returns, weights)
# draw the cumulative return of your all-weather portfolio for the past five years.
fig, ax = plt.subplots()
ax.plot(index, port_Cum_Return, color='blue', label="portfolio")
plt.title('Cumulative Return of the All-Weather Portfolio for the past 5 years')
plt.xlabel('Date')
plt.ylabel('Cumulative Return')
# ax.xaxis.set_major_locator(plt.dates.YearLocator())
plt.grid(True)
plt.legend()
plt.show()
Portfolio's Annualized Return: 28.860000000000003%
Portfolio's Annualized Volatility/Std. Dev: 4.408
Portfolio's Sharpe Ratio: 5.59 %
Portfolio daily return - Mean : 0.11%
Portfolio daily return - Standard Deviation : 1.7500000000000002%
Portfolio daily return - skewness : -0.3752
Portfolio daily return - Kurtosis : 5.9488
3. Repeat (2) but with the maximum Sharpe portfolio and minimum volatility portfolio.
!pip install PyPortfolioOpt
3.1 With maximum Sharpe portfolio
from pypfopt.efficient_frontier import EfficientFrontier
from pypfopt import risk_models
from pypfopt import expected_returns
# ------------- IMPORTANT. ----------------
# need daily price data as the input. - SO can not use [daily_returns], use [adj_prices]
# available data：
# [daily_returns] - the daily returns for each stock
# [adj_prices] - extract adjusted closing prices for stocks
# ---------------- ---------------- ---------------- ---------------- ----------------
# ------------- ef ----------------
# Calculate expected annualized returns and sample covariance / risk
mu = expected_returns.mean_historical_return(adj_prices)
Sigma = risk_models.sample_cov(adj_prices)
# Calculate the Efficient Frontier with mu and S
ef = EfficientFrontier(mu, Sigma)
# ------------ the Maximum Sharpe ratio portfolio -------------------
raw_weights_MaxSharpe = ef.max_sharpe()
cleaned_weights_MaxSharpe = ef.clean_weights()
portfolio_returns_MaxSharpe = ef.portfolio_performance(verbose=True)
# ---------- Function : convert_ef_weight_2arrayweight --------------
# Output of ef weights is a dictionary, extract the weight in Array type.
def convert_ef_weight_2arrayweight (ef_weight, stock_tickers):
list_weight = []
for ticker in stock_tickers:
weight = ef_weight[ticker]
list_weight.append(weight)
array_weight = np.array(list_weight)
return array_weight
# ----------- Plot -------------
# ---get array weight for MaxSharpe
array_weight_MaxSharpe = convert_ef_weight_2arrayweight(cleaned_weights_MaxSharpe, stock_tickers)
print(array_weight_MaxSharpe)
MaxSharpe_index, MaxSharpe_port_Cum_Return = portChar(daily_returns, array_weight_MaxSharpe)
# draw the cumulative return of your all-weather portfolio for the past five years.
fig, ax = plt.subplots()
ax.plot(MaxSharpe_index, MaxSharpe_port_Cum_Return, color='red', label="MaxSharpe portfolio")
plt.title('Cumulative Return of the [MaxSharpe Portfolio] for the past 5 years')
plt.xlabel('Date')
plt.ylabel('Cumulative Return')
# ax.xaxis.set_major_locator(plt.dates.YearLocator())
plt.grid(True)
plt.legend()
plt.show()
Expected annual return: 40.6%
Annual volatility: 34.9%
Sharpe Ratio: 1.11
[0.06899 0.04814 0. 0. 0.18588 0.35872 0. 0.00963 0.32865
0. ]
Portfolio's Annualized Return: 23.69%
Portfolio's Annualized Volatility/Std. Dev: 4.3
Portfolio's Sharpe Ratio: 4.53 %
Portfolio daily return - Mean : 0.09%
Portfolio daily return - Standard Deviation : 1.71%
Portfolio daily return - skewness : -0.2973
Portfolio daily return - Kurtosis : 9.2244
3.2 With minimum volatility portfolio.
# ------------- ef ----------------
# Calculate expected annualized returns and sample covariance / risk
mu = expected_returns.mean_historical_return(adj_prices)
Sigma = risk_models.sample_cov(adj_prices)
# Calculate the Efficient Frontier with mu and S
ef = EfficientFrontier(mu, Sigma)
# ------------ the Minimum Volatility portfolio -------------------
raw_weights_MinVol = ef.min_volatility()
cleaned_weights_MinVol = ef.clean_weights()
portfolio_returns_MinVol = ef.portfolio_performance(verbose=True)
# ----------- Plot -------------
# ---get array weight for MinVol
array_weight_MinVol = convert_ef_weight_2arrayweight(cleaned_weights_MinVol, stock_tickers)
print(array_weight_MinVol)
MinVol_index, MinVol_port_Cum_Return = portChar(daily_returns, array_weight_MinVol)
# draw the cumulative return of your all-weather portfolio for the past five years.
fig, ax = plt.subplots()
ax.plot(MinVol_index, MinVol_port_Cum_Return, color='green', label="MinVol portfolio")
plt.title('Cumulative Return of the [MinVol Portfolio] for the past 5 years')
plt.xlabel('Date')
plt.ylabel('Cumulative Return')
# ax.xaxis.set_major_locator(plt.dates.YearLocator())
plt.grid(True)
plt.legend()
plt.show()
Expected annual return: 12.7%
Annual volatility: 19.6%
Sharpe Ratio: 0.54
[0. 0. 0.0723 0.05106 0. 0. 0.0009 0.15028 0.58998
0.13548]
Portfolio's Annualized Return: 26.22%
Portfolio's Annualized Volatility/Std. Dev: 4.076
Portfolio's Sharpe Ratio: 5.4 %
Portfolio daily return - Mean : 0.1%
Portfolio daily return - Standard Deviation : 1.6199999999999999%
Portfolio daily return - skewness : -0.4878
Portfolio daily return - Kurtosis : 12.3724
# Plot comparison
# Compare the Cumulative Return between the [MaxSharpe Portfolio] & [MinVol Portfolio] for the past 5 years
# draw the cumulative return of your all-weather portfolio for the past five years.
fig, ax = plt.subplots()
ax.plot(MaxSharpe_index, MaxSharpe_port_Cum_Return, color='red', label="MaxSharpe portfolio")
ax.plot(MinVol_index, MinVol_port_Cum_Return, color='green', label="MinVol portfolio")
plt.title('Cumulative Return of the [MaxSharpe Portfolio] & [MinVol Portfolio] for the past 5 years')
plt.xlabel('Date')
plt.ylabel('Cumulative Return')
# ax.xaxis.set_major_locator(plt.dates.YearLocator())
plt.grid(True)
plt.legend()
plt.show()
4. [Optional Bonus] With PyPortfolioOpt, how can you further improve your all-weather portfolio construction?
Hint: The Black-Litterman model (https://pyportfolioopt.readthedocs.io/en/latest/BlackLitterman.html) to express subjective views and L2 regularisation to alleviate extreme portfolio allocation (i.e., weights).
# ------------- IMPORTANT. ----------------
# need daily price data as the input. - SO can not use [daily_returns], use [adj_prices]
# available data：
# [daily_returns] - the daily returns for each stock
# [adj_prices] - extract adjusted closing prices for stocks
# [risk_free]. Risk Free Rate. 4.26% for Sep 08 2023
# ---------------- ---------------- ---------------- ---------------- ----------------
# Import Black-Litterman model
from pypfopt import BlackLittermanModel
from pypfopt import CLA
from pypfopt import objective_functions
from pypfopt import BlackLittermanModel, CLA, objective_functions
from pypfopt import expected_returns, risk_models
from pypfopt.efficient_frontier import EfficientFrontier
# Calculate expected returns and covariance matrix
mu = expected_returns.mean_historical_return(adj_prices)
Sigma = risk_models.sample_cov(adj_prices)
# print(type(mu))
# print(type(Sigma))
# Create the Black-Litterman model
viewdict = {"AAPL": 0.20, "MSFT": 0, "NVDA": -0.2, "TSLA": 0.131321}
bl = BlackLittermanModel(Sigma, pi="equal", absolute_views=viewdict, omega="default")
# bl = BlackLittermanModel(Sigma, pi="equal", absolute_views=viewdict, omega="default")
# Set the risk aversion coefficient
delta = 0.5
# bl.market_implied_risk_aversion(delta)
# Set the views
P = [[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, -1, 0, 0], [0, 0, 0, 0, 0.5]]
Q = [[0.20], [-0.30], [0], [-0.2]]
# bl.bl_weights(P, Q)
# Get the adjusted expected returns and covariance matrix
adjusted_mu = bl.bl_returns()
adjusted_cov_matrix = bl.bl_cov()
# the Efficient Frontier
ef = EfficientFrontier(adjusted_mu, adjusted_cov_matrix)
# Apply L2 regularization to alleviate extreme portfolio allocation
ef.add_objective(objective_functions.L2_reg, gamma=0.1)
# Set the risk aversion coefficient -eg: if you believe stock with ticker "AAPL" will outperform the market by 5%
# delta = 0.5
# BL.market_implied_risk_aversion(delta)
# Set your subjective views
# BL.bl_weights(delta=0.5, P=[[0, 0, 0, 0, 0]], Q=[[0.05]])
# ------------ the Black-Litterman modeled portfolio -------------------
# Get the optimized all-weather portfolio
raw_weights_BlackLitterman = ef.max_sharpe()
# Clean the weights for better interpretation
cleaned_weights_BlackLitterman = ef.clean_weights()
portfolio_returns_BlackLitterman = ef.portfolio_performance(verbose=True)
# ----------- Plot -------------
# ---get array weight for MinVol
array_weight_BlackLitterman = convert_ef_weight_2arrayweight(cleaned_weights_BlackLitterman, stock_tickers)
BlackLitterman_index, BlackLitterman_port_Cum_Return = portChar(daily_returns, array_weight_BlackLitterman)
# draw the cumulative return of your all-weather portfolio for the past five years.
fig, ax = plt.subplots()
ax.plot(BlackLitterman_index, BlackLitterman_port_Cum_Return, color='black', label="BlackLitterman portfolio")
plt.title('Cumulative Return of the [Black-Litterman Modeled Portfolio] for the past 5 years')
plt.xlabel('Date')
plt.ylabel('Cumulative Return')
# ax.xaxis.set_major_locator(plt.dates.YearLocator())
plt.grid(True)
plt.legend()
plt.show()
/root/venv/lib/python3.9/site-packages/pypfopt/efficient_frontier/efficient_frontier.py:259: UserWarning: max_sharpe transforms the optimization problem so additional objectives may not work as expected.
warnings.warn(
Expected annual return: 9.0%
Annual volatility: 21.4%
Sharpe Ratio: 0.33
Portfolio's Annualized Return: 31.330000000000002%
Portfolio's Annualized Volatility/Std. Dev: 4.21
Portfolio's Sharpe Ratio: 6.4399999999999995 %
Portfolio daily return - Mean : 0.12%
Portfolio daily return - Standard Deviation : 1.67%
Portfolio daily return - skewness : -0.4669
Portfolio daily return - Kurtosis : 8.8655