代做Station 3: Model Design代写Python语言

Project Part B due Week 10 | 50%Project Part B due Week 10 (8.4.2024,10pm) | 50%

Final delivery is in a form. of Python code and data design and analysis report. Code sequence is broken down to continuation of Project Part A moving into iii) model design and iv) implementation. Final report provides contextual, tabular and graphical interpretation of the results and final expected product design. Delivery is via Moodle Assessment Section expecting 3x files one in .pdf (written report) and one in .py (scripts covering station 3 and station 4) and one in .figma/.ppt (product design) formats.

Station 3: Model Design (Basic)

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import minimize
import os
df = pd.read_csv(r'stage_2_crypto_data.csv')
df['date'] = pd.to_datetime(df['date'])
df = df.set_index(['date'])
exportpath = r'Week5'
# Function to plot the mean-variance efficient frontier
def Station_3_Model_Design_Basic(returns_data,exportpath, ra = 0.1 ):
num_assets = len(returns_data.iloc[1,])
# Calculate mean returns and covariance matrix
returns_data = returns_data*100
mean_returns = (returns_data).mean()
cov_matrix = returns_data.cov()
# Define function to calculate portfolio performance
def portfolio_performance(weights, mean_returns, cov_matrix):
returns = np.dot(weights, mean_returns)
std = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
return returns, std
# Number of portfolios to simulate
num_portfolios = 25000
results = np.zeros((3, num_portfolios))
weights_record = []
# Run simulations
num_assets = len(mean_returns)
for i in range(num_portfolios):
weights = np.random.random(num_assets)
weights /= np.sum(weights)
returns, std = portfolio_performance(weights, mean_returns, cov_matrix)
results[0, i] = returns
results[1, i] = std
results[2, i] = results[0, i] / results[1, i]
weights_record.append(weights)
# Convert results array to DataFrame
results_frame. = pd.DataFrame(results.T, columns=['Return', 'Standard Deviation', 'Sharpe Ratio'])
# Locate the portfolio with the highest Sharpe ratio
max_sharpe_idx = results_frame['Sharpe Ratio'].idxmax()
max_sharpe_portfolio = results_frame.loc[max_sharpe_idx]
max_sharpe_weights = weights_record[max_sharpe_idx]
# Locate the portfolio with the minimum standard deviation
min_vol_idx = results_frame['Standard Deviation'].idxmin()
min_vol_portfolio = results_frame.loc[min_vol_idx]
min_vol_weights = weights_record[min_vol_idx]
# Ooptim Functions #
def mean_variance(weights):
portfolio_return = np.dot(weights, mean_returns)
portfolio_volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
return -(portfolio_return / portfolio_volatility)
def minimum_variance(weights):
portfolio_volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
return portfolio_volatility
def mean_variance_risk_aversion(weights,ra=ra):
portfolio_return = np.dot(weights, mean_returns)
portfolio_volatility = (np.dot(weights.T, np.dot(cov_matrix, weights)))
return - (portfolio_return - ra/2 * portfolio_volatility)
# Optional ##############
def risk_parity(weights):
portfolio_volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
marginal_risk_contribution = np.dot(cov_matrix, weights) / portfolio_volatility
risk_contributions = weights * marginal_risk_contribution
risk_target = portfolio_volatility / num_assets
return np.sum((risk_contributions - risk_target) ** 2)
def max_diversification(weights):
individual_volatilities = np.sqrt(np.diag(cov_matrix))
weighted_volatility = np.dot(weights, individual_volatilities)
portfolio_volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
diversification_ratio = weighted_volatility / portfolio_volatility
return -diversification_ratio
#########################
# Constraints and bounds
constraints = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1})
bounds = tuple((0, 1) for asset in range(num_assets))
# Initial guess (equal weights)
initial_guess = num_assets * [1. / num_assets,]
# Optimize for MVO
result = minimize(mean_variance, initial_guess, method='SLSQP',
bounds=bounds, constraints=constraints)
mvo_weights = np.round(result.x,3)
rp_mvo, sigma_mvo = portfolio_performance(mvo_weights, mean_returns, cov_matrix)
sr_mvo            =  rp_mvo/sigma_mvo
# Optimize for MV
result = minimize(minimum_variance, initial_guess, method='SLSQP',
bounds=bounds, constraints=constraints)
mv_weights =np.round( result.x , 3)
rp_mv, sigma_mv = portfolio_performance(mv_weights, mean_returns, cov_matrix)
sr_mv           = rp_mv/sigma_mv
# Optimize for MVO
result = minimize(mean_variance_risk_aversion, initial_guess, method='SLSQP',
bounds=bounds, constraints=constraints)
mvrp_weights =np.round( result.x , 3)
rp_mvrp, sigma_mvrp = portfolio_performance(mvrp_weights, mean_returns, cov_matrix)
sr_mvrp             = rp_mvrp/sigma_mvrp
# 1/N portfolio
ew_weights = np.array( [1/num_assets] * num_assets )
rp_ew, sigma_ew     = portfolio_performance(ew_weights, mean_returns, cov_matrix)
sr_ew               = rp_ew/sigma_ew
# Plot the efficient frontier
plt.figure(figsize=(10, 6))
scatter = plt.scatter(results_frame['Standard Deviation'], results_frame['Return'], c=results_frame['Sharpe Ratio'], cmap='viridis')
cbar = plt.colorbar(scatter)
cbar.set_label('Sharpe Ratio', fontsize=14)
cbar.ax.tick_params(labelsize=14)  # Increase the font size of the color bar ticks
plt.scatter(sigma_mvo , rp_mvo  , marker='*', color='#FFA500', s=200, label='Max Sharpe Ratio')
plt.scatter(sigma_mv  , rp_mv   , marker='*', color='b', s=200, label='Min Volatility')
plt.scatter(sigma_mvrp, rp_mvrp , marker='*', color='g', s=200, label='Mean Variance RA = 0.1')
plt.scatter(sigma_ew  , rp_ew   , marker='x', color='r', s=200, label='Equal Weights')
plt.title('Mean-Variance Efficient Frontier', fontsize=14)
plt.xlabel('Standard Deviation', fontsize=14)
plt.ylabel('Return', fontsize=14)
plt.legend(loc='upper left', fontsize=14)
plt.xticks(fontsize=14)
plt.yticks(fontsize=14)
# Save the figure
filename = 'mean_variance_efficient_frontier.png'
plt.savefig(os.path.join(exportpath, filename))
plt.show()
# Output weights for the different portfolios #
weights = pd.DataFrame({
'MSR Weights':  mvo_weights,
'MV Weights':   mv_weights,
'MVRA Weights': mvrp_weights,
'EW Weights'  : ew_weights
}, index = df.columns)
weights.index.rename('Stocks',inplace=True)
weights = weights.reset_index()
# Plot optimal weights #
fig, ax = plt.subplots(figsize=(10, 6))
bar_width = 0.2  # Adjust bar width to fit four bars comfortably
index = range(len(weights['Stocks']))
# Create bars for each set of weights
bar1 = plt.bar(index, weights['MSR Weights'], bar_width, label='MSR Weights')
bar2 = plt.bar([i + bar_width for i in index], weights['MV Weights'], bar_width, label='MV Weights')
bar3 = plt.bar([i + bar_width * 2 for i in index], weights['MVRA Weights'], bar_width, label='MVRA Weights')
bar4 = plt.bar([i + bar_width * 3 for i in index], weights['EW Weights'], bar_width, label='EW Weights')
# Adding titles and labels
plt.xlabel('Stocks', fontsize=14)
plt.ylabel('Weights', fontsize=14)
plt.title('Optimal Portfolio Weights Comparison', fontsize=15)
plt.xticks([i + bar_width * 1.5 for i in index], weights['Stocks'], fontsize=14)
plt.yticks(fontsize=14)
# Adding a legend
plt.legend(loc='upper left', fontsize=14)
# Save the figure
filename = 'optimal_weights.png'
plt.savefig(os.path.join(exportpath, filename))
plt.show()
# Compute optimal portfolio returns #
weights = weights.set_index('Stocks')
portfolio_returns = (returns_data @ weights)/100 # decimal format
# Rename columns to reflect the portfolio strategies
portfolio_returns.columns = ['MSR Portfolio', 'MV Portfolio', 'MVRA Portfolio','EW Portfolio']
# Calculate cumulative returns
cumulative_returns = (1 + portfolio_returns).cumprod() - 1
# Plot cumulative returns over time
plt.figure(figsize=(10, 8))
for column in cumulative_returns.columns:
plt.plot(cumulative_returns.index, cumulative_returns[column], label=column)
# Customize the plot
plt.title('Cumulative Optimal Portfolio Returns Over Time', fontsize=16)
plt.xlabel('Date', fontsize=14)
plt.ylabel('Cumulative Return', fontsize=14)
plt.legend(title='Stock', fontsize=14, title_fontsize=14)
plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)
plt.tight_layout()
# Save the figure
filename = 'cumulative_optimal_portfolio_return.png'
plt.savefig(os.path.join(exportpath, filename))
plt.show()
# Descriptive statistics of the portfolios #
descriptive_stats = (portfolio_returns*100).describe().transpose().round(3)
descriptive_stats['Sharpe'] = (descriptive_stats['mean']/descriptive_stats['std']).round(3)
cols = list(descriptive_stats.columns)
sharpe_col = cols.pop(cols.index('Sharpe'))
cols.insert(3, sharpe_col)
descriptive_stats =  descriptive_stats[cols]
# Export descriptive statistics #
descriptive_stats.to_csv(os.path.join(exportpath, 'optimal_descriptive_statistics.csv'))
# Export Weights #
weights.to_csv(os.path.join(exportpath, 'optimal_weights.csv'))
return list([weights, portfolio_returns, descriptive_stats])
##################### Execute the function #####################
Station3_output = Station_3_Model_Design_Basic(df,exportpath, ra = 0.1 )
###########################################################
########################### END ###########################
###########################################################

Station 3: Model Design (Advanced)

import pandas as pd
import numpy as np
from scipy.optimize import minimize
import matplotlib.pyplot as plt
import os
df = pd.read_csv(r'stage_2_crypto_data.csv')
df['date'] = pd.to_datetime(df['date'])
df = df.set_index(['date'])
exportpath = r'Week5'
class Station3_Model_Design_Advanced:
def __init__(self, equity_data):
self.equity_data = equity_data.copy()
def optimal_portfolio_weights(self, returns, optimization_type='mean-variance', risk_aversion=1.0, risk_free_rate=0.0):
mean_returns = returns.mean()
cov_matrix = returns.cov()
num_assets = len(mean_returns)
def mean_variance(weights):
portfolio_return = np.dot(weights, mean_returns)
portfolio_volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
return -(portfolio_return / portfolio_volatility)
def minimum_variance(weights):
portfolio_volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
return portfolio_volatility
def mean_variance_quadratic(weights):
portfolio_return = np.dot(weights, mean_returns)
portfolio_variance = np.dot(weights.T, np.dot(cov_matrix, weights))
return -(portfolio_return - (risk_aversion / 2) * portfolio_variance)
def risk_parity(weights):
portfolio_volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
marginal_risk_contribution = np.dot(cov_matrix, weights) / portfolio_volatility
risk_contributions = weights * marginal_risk_contribution
risk_target = portfolio_volatility / num_assets
return np.sum((risk_contributions - risk_target) ** 2)
def max_diversification(weights):
individual_volatilities = np.sqrt(np.diag(cov_matrix))
weighted_volatility = np.dot(weights, individual_volatilities)
portfolio_volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
diversification_ratio = weighted_volatility / portfolio_volatility
return -diversification_ratio
def max_sharpe_ratio(weights):
portfolio_return = np.dot(weights, mean_returns) - risk_free_rate
portfolio_volatility = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
return -portfolio_return / portfolio_volatility
constraints = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1})
bounds = tuple((0, 1) for asset in range(num_assets))
initial_guess = num_assets * [1. / num_assets,]
if optimization_type == 'mean-variance':
objective_function = mean_variance
elif optimization_type == 'minimum-variance':
objective_function = minimum_variance
elif optimization_type == 'mean-variance-risk-aversion':
objective_function = mean_variance_quadratic
elif optimization_type == 'risk-parity':
objective_function = risk_parity
elif optimization_type == 'max-diversification':
objective_function = max_diversification
elif optimization_type == 'equal-weighting':
return np.array(initial_guess)  # No optimization needed for equal weighting
elif optimization_type == 'max-sharpe-ratio':
objective_function = max_sharpe_ratio
else:
raise ValueError("Invalid optimization type.")
result = minimize(objective_function, initial_guess, method='SLSQP', bounds=bounds, constraints=constraints)
return result.x
def rolling_optimal_weights(self, returns_data, holding_period='monthly',
optimization_type='mean-variance', risk_aversion=1.0, risk_free_rate=0.0):
dates = returns_data.index
num_assets = returns_data.shape[1]
weight_matrix = []
date_vector   = []
if holding_period == 'monthly':
rebal_dates = pd.DataFrame(dates).set_index(['date']).resample("ME").last().index.tolist()
elif holding_period == 'daily':
rebal_dates = pd.DataFrame(dates).set_index(['date']).resample("D").last().index.tolist()
elif holding_period == 'weekly':
rebal_dates = pd.DataFrame(dates).set_index('date').resample('W-WED').last().index.tolist()

for start in dates:
rolling_window = returns_data.loc[:start]
date_vector.append(rolling_window.index[-1])

if start not in rebal_dates:
weight_matrix.append(np.full(num_assets, np.nan))
continue
else:
optimal_weights = self.optimal_portfolio_weights(rolling_window, optimization_type, risk_aversion, risk_free_rate)
weight_matrix.append(optimal_weights)

weight_df = pd.DataFrame(weight_matrix, index=date_vector, columns=returns_data.columns).round(3)
weight_df = weight_df.ffill()

return weight_df.dropna()

# Initiate the model with our dataframe. #
model = Station3_Model_Design_Advanced(df)
# Function to perform. row-wise matrix multiplication
def row_multiply(row1, row2):
return np.dot(row1, row2)
# Call the rolling_optimal_weights method on the instance
optim_type = ['mean-variance',
'minimum-variance',
'mean-variance-risk-aversion',
'risk-parity',
'max-diversification',
'equal-weighting']

optimal_weights = []
for i,optim in enumerate(optim_type):
print(optim)
weights_df = model.rolling_optimal_weights(df*100,
holding_period='monthly',
optimization_type=optim,
risk_aversion=1)
equity_data_fwd  = df.shift(-1)
equity_data_fwd  = equity_data_fwd[equity_data_fwd.index>=weights_df.index.min()].dropna()
weights_df       = weights_df[weights_df.index<=equity_data_fwd.index.max()].dropna()
optimal_weights.append(weights_df)

if i == 0:
portfolio_returns = pd.DataFrame(index=equity_data_fwd.index)
portfolio_returns[optim] = [row_multiply(equity_data_fwd.iloc[i], weights_df.iloc[i]) for i in range(len(weights_df))]
else:
portfolio_returns[optim] = [row_multiply(equity_data_fwd.iloc[i], weights_df.iloc[i]) for i in range(len(weights_df))]

########################################
############# Cum. Returns #############
########################################
# Plot cumulative returns over time
# Calculate cumulative returns
cumulative_returns = (1 + portfolio_returns).cumprod() - 1
plt.figure(figsize=(10, 8))
for column in cumulative_returns.columns:
plt.plot(cumulative_returns.index, cumulative_returns[column], label=column)
# Customize the plot
plt.title('Cumulative Optimal Portfolio Returns Over Time', fontsize=16)
plt.xlabel('Date', fontsize=14)
plt.ylabel('Cumulative Return', fontsize=14)
plt.legend(title='Stock', fontsize=14, title_fontsize=14)
plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)
plt.tight_layout()
# Save the figure
filename = 'cumulative_optimal_portfolio_return_advanced.png'
plt.savefig(os.path.join(exportpath, filename))
plt.show()
########################################
############# Weights ##################
########################################
weights_mv = optimal_weights[0].resample("W").mean()
plt.figure(figsize=(10, 8))
for column in weights_mv.columns:
plt.plot(weights_mv.index, weights_mv[column], label=column)
# Customize the plot
plt.title('Optimal Portfolio Weights Over Time', fontsize=16)
plt.xlabel('Date', fontsize=14)
plt.ylabel('Optimal portfolio weight', fontsize=14)
plt.legend(title='Stock', fontsize=14, title_fontsize=14)
plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)
plt.tight_layout()
# Save the figure
filename = 'optimal_weights_over_time.png'
plt.savefig(os.path.join(exportpath, filename))
plt.show()

########################################
############# Descriptive Stats. #######
########################################
# Descriptive statistics of the portfolios #
descriptive_stats = (portfolio_returns*100).describe().transpose().round(3)
descriptive_stats['Sharpe'] = (descriptive_stats['mean']/descriptive_stats['std']).round(3)
cols = list(descriptive_stats.columns)
sharpe_col = cols.pop(cols.index('Sharpe'))
cols.insert(3, sharpe_col)
descriptive_stats =  descriptive_stats[cols]
print(descriptive_stats)
# Export descriptive statistics #
descriptive_stats.to_csv(os.path.join(exportpath, 'descriptive_statistics_advanced.csv'))
###########################################################
########################### END ###########################
###########################################################