3-Factor Model

# Define function to read in factors from csv and return cleaned dataframe: def get_factors(factors):

factor_file = factors + ".csv"

factor_df = pd.read_csv(factor_file)

# Clean factor dataframe:

factor_df = factor_df.rename(columns={

'Unnamed: 0': 'Date',

})

factor_df['Date'] = factor_df['Date'].apply(lambda x: pd.to_datetime(str(x), format='%Y%m%d'))

# Set "Date" as Index:

factor_df = factor_df.set_index('Date')

return factor_df

The Python code defines a function named get_factors, which takes a string input likely indicating a factor's name and uses this to locate a .csv file containing relevant factor data related to the Fama-French models. The function reads this CSV file into a pandas DataFrame and executes a series of data cleaning steps. The first cleaning step involves renaming a column that is presumably the date column but is unnamed in the original file to 'Date'.

Next, it converts the values in the Date column to Python datetime objects, ensuring they are formatted in the YYYYMMDD style, essential for time-series analysis. After formatting the dates, the code sets the Date column as the index of the DataFrame, a common practice when working with time-series data to facilitate time-based indexing and analysis. Finally, the cleaned DataFrame is returned.

This function is beneficial within the broader context of an Algorithmic Trading project that investigates the Fama-French 3-Factor Model and the Fama-French 5-Factor Model as it prepares the necessary data for further analysis and prediction of portfolio returns.

# Confirm Fama-French dataframe: factors = get_factors("french_fama") factors.head()

This Python code snippet is part of an Algorithmic Trading project focusing on analyzing financial models, specifically the Fama-French 3-Factor and 5-Factor models. These models aim to explain stock returns through various market factors.

The code performs two primary functions: 1. It retrieves a dataset containing Fama-French factors using the get_factors function with the argument "french_fama," indicating the specific set of factors or the data source. 2. It previews the first few rows of the dataset using factors.head(), a common method in data analysis for a quick examination of the dataset's structure and initial data for verification and understanding.

# Do same thing as above, but for the individual stock CSV: def choose_stock(ticker):

ticker_file = ticker + ".csv"

stock = pd.read_csv(ticker_file, index_col='Date', parse_dates=True, infer_datetime_format=True)

stock["Returns"] = stock["Close"].dropna().pct_change() * 100

stock.index = pd.Series(stock.index).dt.date

return stock

The code defines a Python function named choose_stock, which takes a ticker symbol as an argument. The purpose of this function is to load historical stock data from a CSV file corresponding to the provided ticker symbol, compute daily percentage returns of the stock, and return the processed stock data.

When invoked, the function constructs the filename of the CSV by appending .csv to the ticker symbol, reads this file into a pandas DataFrame while ensuring the Date column is used as the index, and that the dates are correctly parsed. After loading the data, it calculates the daily percentage change in the stock's closing price, expressing it as a percentage, and adds these returns as a new column in the DataFrame.

Finally, the function converts the DataFrame index to a Python date object for easier handling and returns the modified DataFrame. This function acts as a utility within a more extensive algorithmic trading project that examines various Fama-French models to predict portfolio returns. By isolating the process of loading and preparing individual stock data, the function assists in analyzing single stocks against these models.

# Read in ATT dataframe using above function: ticker = "T" stock = choose_stock(ticker) stock.head()

This Python code snippet retrieves and displays the first few rows of a stock data frame, specifically for the stock with the ticker symbol T, typically representing AT&T Inc. This is part of an Algorithmic Trading project that investigates the predictive capabilities of the Fama-French 3-Factor and 5-Factor models on portfolio returns.

In this snippet, the choose_stock function is called with the argument set to the string "T." This function presumably defined elsewhere in the project is responsible for obtaining the stock information from a data source. After calling the choose_stock function, an object named stock is created, containing the data frame with AT&T stock information. By invoking the head method on this data frame, the code displays the first five rows.

These rows usually include essential information such as the date, opening price, closing price, volume, and potentially other relevant analytical metrics. The purpose of this snippet is to briefly preview the AT&T stock data, ensuring that the information has been correctly loaded into the data frame for further analysis within the context of evaluating the Fama-French models. These models are used in financial economics to explain stock returns by considering market risk factors.

# Concatenate Fama-French dataframe with Stock dataframe: combined_df = pd.concat([factors, stock], axis='columns', join='inner')

# Drop nulls: combined_df = combined_df.dropna() combined_df = combined_df.drop('RF', axis=1)

# Preview dataframe: combined_df.head()

This Python code snippet merges two dataframes: one containing Fama-French factors and the other containing stock data. This is achieved using the pandas library's concat function, which combines the two dataframes column-wise and only includes rows with matching index values in both dataframes, an inner join. After concatenation, the code ensures data integrity by removing any rows with missing values using the dropna method.

This step is vital for preparing the data for accurate and meaningful analysis in algorithmic trading, especially when assessing financial models like the Fama-French 3-Factor and 5-Factor Models. The code subsequently removes the column labeled RF, representing the risk-free rate, a component typically considered in the Fama-French models but possibly unnecessary for the specific analysis intended here.

Lastly, the code previews the resulting combined dataframe by calling the head method, which displays the first five rows, serving as a quick verification check to ensure the preceding operations were executed correctly, and the dataframe is ready for further analysis in the trading algorithm. This code focuses on data preparation, a critical step in developing an algorithmic trading strategy.

# Define X and y variables: X = combined_df.drop('Returns', axis=1) X = X.drop('Close', axis=1) y = combined_df.loc[:, 'Returns']

This Python code snippet is focused on preparing the data for regression analyses, part of examining the Fama-French 3-Factor and 5-Factor Models for predicting portfolio returns. The code preprocesses data by defining independent variables X and the dependent variable y using data from a presumably existing DataFrame named combined_df.

The independent variables are created by removing the column labeled 'Returns' and the column labeled 'Close' from combined_df to form the X variable. The 'Returns' column serves as the dependent variable, representing portfolio returns that the Fama-French models aim to predict. The 'Close' column likely contains the closing prices of stocks or assets and is not needed for the model inputs.

Subsequently, the dependent variable y is generated by selecting only the 'Returns' column from combined_df. In summary, this code structures the data into a format suitable for input into a statistical model or machine learning algorithm to explore the relationship between the factors outlined by the Fama-French models and portfolio returns.

# Split into Training/Testing Data: split = int(0.8 * len(X)) X_train = X[:split] X_test = X[split:] y_train = y[:split] y_test = y[split:] close_test = combined_df["Close"][split:]

The provided Python code snippet is designed to divide datasets into training and testing subsets for validating the performance of the Fama-French 3-Factor and 5-Factor models in an algorithmic trading context. These models aim to explain and predict portfolio returns based on various financial factors.

The snippet first determines the index for splitting the dataset, calculated as 80% of the total length of the dataset denoted by X. This index is then employed to divide X (the set of independent variables or features) and y (the dependent variable or target, which in this context would be the portfolio returns) into training and test sets. The training sets X_train and y_train will be used to fit the models, while test sets X_test and y_test will assess the models' predictive performance.

Additionally, the code selects the closing prices from the combined_df DataFrame that correspond to the test set period, likely for further analysis or comparisons with the model predictions. This closing data can be utilized to juxtapose the actual closing prices of assets against predicted values derived from the model applied to X_test.

# Import Linear Regression Model from SKLearn: from sklearn.linear_model import LinearRegression

# Create, train, and predict model: lin_reg_model = LinearRegression(fit_intercept=True) lin_reg_model = lin_reg_model.fit(X_train, y_train) predictions = lin_reg_model.predict(X_test)

The provided code snippet discusses implementing a linear regression model using scikit-learn, a Python machine learning library. This approach is common in financial analyses, particularly in the context of the Fama-French factor models, which describe stock returns. The code commences by importing the LinearRegression class from the scikit-learn library.

Following that, it establishes an instance of this class with fit_intercept=True, indicating that the model will calculate the intercept term in the regression equation. Next, it trains the model by feeding the training data X_train and y_train, where X_train contains the independent variables believed to influence portfolio returns, and y_train encompasses the dependent variable, or the actual portfolio returns.

After fitting the model to the training data, the code utilizes the trained model to predict values on a separate dataset, X_test, which likely contains similar factors but from different time frames or assets, enabling the user to assess the model's performance. The predictions can be compared with actual returns to evaluate how well the Fama-French model explains or predicts stock returns in the realm of algorithmic trading.

# Convert y_test to a dataframe: y_test = y_test.to_frame()

The code snippet converts the y_test variable, which represents test data, into a pandas DataFrame. This is a common practice in data analysis and machine learning tasks in Python, as pandas DataFrames are a preferred structure for managing tabular data due to their versatility and extensive functionality. In the context of an Algorithmic Trading project, the y_test data likely contains actual portfolio returns that are used to assess the model's predictions.

The model, based on the Fama-French 3-Factor or 5-Factor Model, aims to explain stock returns through various economic factors. By converting y_test into a DataFrame, it can be more easily compared to the predicted returns generated by these models, facilitating further analysis such as calculating performance evaluation metrics.

signals_df = y_test.copy()

# Add "predictions" to dataframe: y_test['Predictions'] = predictions y_test["Close"] = close_test

# Add "Buy Signal" column based on whether day's predictions exceeded the day's actual returns: y_test['Buy Signal'] = np.where(y_test['Predictions'] > y_test['Returns'], 1.0, 0.0)

# Drop nulls: y_test = y_test.dropna()

y_test.head()

The provided Python code is part of an algorithmic trading project that manages financial data to generate trading signals. It utilizes a testing dataset y_test, which likely includes the actual returns of a portfolio.

The code executes the following tasks: 1. Copies the y_test DataFrame to another DataFrame called signals_df, presumably to preserve the original testing data. 2. The predictions variable, which seems to contain predicted returns from a Fama-French model, is appended to the y_test DataFrame. 3. The actual closing prices of the assets, close_test, are also integrated into the y_test DataFrame. 4. It computes a Buy Signal by comparing the predicted returns with the actual returns. If the prediction is higher, it marks 1.0, signaling a buy; otherwise, it notes 0.0, indicating no buy signal. 5. The DataFrame is cleaned by removing any rows with null values. 6. Finally, it displays the first few rows of the modified y_test DataFrame, now containing additional columns for predictions and buy signals, using the .head() method for quick inspection.

Overall, this code enriches the dataset with predictive insights and trade signals to inform trading decisions within an algorithmic trading strategy.

# Define function to generate signals dataframe for algorithm: def generate_signals(input_df, start_capital=100000, share_count=2000):

# Set initial capital:

initial_capital = float(start_capital)

signals_df = input_df.copy()

# Set the share size:

share_size = share_count

# Take a 500 share position where the Buy Signal is 1:

signals_df['Position'] = share_size * signals_df['Buy Signal']

# Create Entry / Exit Column:

signals_df['Entry/Exit'] = signals_df["Buy Signal"].diff()

# Identify points in time for buying or selling:

signals_df['Entry/Exit Position'] = signals_df['Position'].diff()

# Multiply share price by entry/exit positions and compute cumulative sum:

signals_df['Portfolio Holdings'] = signals_df['Close'] * signals_df['Entry/Exit Position'].cumsum()

# Subtract initial capital from portfolio holdings to calculate liquid cash:

signals_df['Portfolio Cash'] = initial_capital - (signals_df['Close'] * signals_df['Entry/Exit Position']).cumsum()

# Determine total portfolio value by adding cash and portfolio holdings:

signals_df['Portfolio Total'] = signals_df['Portfolio Cash'] + signals_df['Portfolio Holdings']

# Calculate portfolio daily returns:

signals_df['Portfolio Daily Returns'] = signals_df['Portfolio Total'].pct_change()

# Calculate cumulative returns:

signals_df['Portfolio Cumulative Returns'] = (1 + signals_df['Portfolio Daily Returns']).cumprod() - 1

signals_df = signals_df.dropna()

return signals_df

The provided Python code is part of an algorithmic trading project designed to facilitate trading of financial securities based on the Fama-French 3-Factor and 5-Factor models. The function generate_signals takes an input DataFrame, input_df, containing financial data, alongside two optional parameters for setting the initial capital and the number of shares per position.

It begins by copying the input DataFrame to avoid altering the original data and establishes the initial capital and share size. Within this DataFrame, based on a column named 'Buy Signal', the function calculates and records when to enter buy or exit sell positions, defined as purchasing or selling a fixed number (e.g., 500) of shares.

The code computes various financial metrics such as the number of shares, cash in the portfolio, value of owned shares, total portfolio value, and daily and cumulative portfolio returns. By tracking these metrics, the code provides insights into the trading strategy's effectiveness, evaluating how the portfolio's value fluctuates over time in response to the computed buy or sell signals. This is crucial for assessing the performance of the trading strategy based on historical data and optimizing it for future applications in live trading scenarios.

# Generate and view signals dataframe using generate signals function signals_df = generate_signals(y_test) signals_df.head(10)

This Python code snippet generates trading signals based on predictive models, particularly in the context of algorithmic trading influenced by the Fama-French 3-Factor and 5-Factor models. These models are widely recognized in finance for explaining stock returns concerning three or five different risk factors.

The code invokes the generate_signals function, which takes y_test as input. Although the details are not shown, y_test might contain historical data, test data, or anticipated returns predicted by either the 3-Factor or 5-Factor model, or a variation thereof. The generate_signals function processes this input and returns a DataFrame with trading signals.

After generating the signals DataFrame, the code displays the first ten rows of this DataFrame using the head method, a common function in the pandas library for previewing the top rows. The intention of displaying these rows is likely to conduct a quick visual check to ensure that the signal generation is functioning as intended before utilizing these signals for live trading decisions or further analysis.

def algo_evaluation(signals_df):

# Prepare dataframe for metrics

metrics = [

'Annual Return',

'Cumulative Returns',

'Annual Volatility',

'Sharpe Ratio',

'Sortino Ratio']

columns = ['Backtest']

# Initialize the DataFrame with index set to evaluation metrics and column as Backtest

portfolio_evaluation_df = pd.DataFrame(index=metrics, columns=columns)

# Calculate cumulative returns:

portfolio_evaluation_df.loc['Cumulative Returns'] = signals_df['Portfolio Cumulative Returns'][-1]

# Calculate annualized returns:

portfolio_evaluation_df.loc['Annual Return'] = (signals_df['Portfolio Daily Returns'].mean() * 252)

# Calculate annual volatility:

portfolio_evaluation_df.loc['Annual Volatility'] = (signals_df['Portfolio Daily Returns'].std() * np.sqrt(252))

# Calculate Sharpe Ratio:

portfolio_evaluation_df.loc['Sharpe Ratio'] = (signals_df['Portfolio Daily Returns'].mean() * 252) / (signals_df['Portfolio Daily Returns'].std() * np.sqrt(252))

# Calculate Sortino Ratio:

sortino_ratio_df = signals_df[['Portfolio Daily Returns']].copy()

sortino_ratio_df.loc[:, 'Downside Returns'] = 0

target = 0

mask = sortino_ratio_df['Portfolio Daily Returns'] < target

sortino_ratio_df.loc[mask, 'Downside Returns'] = sortino_ratio_df['Portfolio Daily Returns'] ** 2

down_stdev = np.sqrt(sortino_ratio_df['Downside Returns'].mean()) * np.sqrt(252)

expected_return = sortino_ratio_df['Portfolio Daily Returns'].mean() * 252

sortino_ratio = expected_return / down_stdev

portfolio_evaluation_df.loc['Sortino Ratio'] = sortino_ratio

return portfolio_evaluation_df

The code defines a function named algo_evaluation that takes a DataFrame signals_df as input, which contains the daily returns of a trading portfolio. This code evaluates the performance of an algorithmic trading strategy by calculating various performance metrics commonly utilized in finance.

The code initializes a new DataFrame with performance metrics as index rows, including Annual Return, Cumulative Returns, Annual Volatility, Sharpe Ratio, and Sortino Ratio. These metrics indicate the portfolio's overall performance and risk-adjusted returns. The function calculates cumulative returns, annualized returns, and annual volatility by performing operations on the daily returns data contained within the input DataFrame.

Additionally, the code computes the Sharpe Ratio, which is used to assess the return of an investment relative to its risk. It measures the average return earned in excess of the risk-free rate per unit of volatility or total risk. Lastly, the code calculates the Sortino Ratio, similar to the Sharpe Ratio but only considers downside volatility, making it more relevant for investors concerned about downside risks.

Finally, the function algo_evaluation returns a DataFrame summarizing all these calculated performance metrics, providing a quick overview of the trading strategy's performance based on historical data. This output can be utilized to compare different trading strategies or evaluate the effectiveness of a single strategy over time.

# Generate Metrics for Algorithm: algo_evaluation(signals_df)

The Python function algo_evaluation(signals_df) is part of a larger algorithmic trading code focused on evaluating the performance of a trading algorithm that applies the Fama-French 3-Factor and 5-Factor Models. These models are recognized in financial economics for explaining how stock returns are influenced by three or five different types of economic risks, respectively.

The function accepts a DataFrame signals_df, which likely contains the signals or trading decisions generated by the investment algorithm based on those models. These signals could indicate when to buy or sell a specific asset and may include associated data like expected returns, factor exposures, or other relevant metrics. The purpose of algo_evaluation is to assess these algorithm-generated signals and compute various performance metrics.

These metrics may include the algorithm's profitability, risk-adjusted returns, accuracy of predictions, and adherence to the Fama-French model premises.

Overall, the function serves as a tool for backtesting, a method for understanding how well a trading strategy would have performed historically. By using this function, one can critically evaluate the algorithm's effectiveness and decide its utility for future trading.

# Define function to evaluate the underlying asset: def underlying_evaluation(signals_df):

underlying = pd.DataFrame()

underlying["Close"] = signals_df["Close"]

underlying["Portfolio Daily Returns"] = underlying["Close"].pct_change()

underlying["Portfolio Daily Returns"].fillna(0, inplace=True)

underlying['Portfolio Cumulative Returns'] = (1 + underlying['Portfolio Daily Returns']).cumprod() - 1

underlying_evaluation = algo_evaluation(underlying)

return underlying_evaluation

This Python code defines a function called underlying_evaluation, which analyzes the performance of a financial asset based on its closing prices over time. The code uses a pandas DataFrame to manipulate and analyze the data. The function takes a DataFrame signals_df as input.

This DataFrame includes the historical closing prices of the asset under the 'Close' column. The code first creates a new DataFrame called underlying and copies the closing prices into it. Then it calculates the daily returns by comparing each closing price with the previous day's closing price percentage change. Any missing values in the daily returns are filled with zero, ensuring no gaps in the data.

Additionally, the code computes the cumulative returns of the portfolio. This calculation is done by progressively applying the daily returns to understand the asset's performance over the entire period. The cumulative return is critical for investors to evaluate the total return on investment from the starting date to the current or specified date. Finally, the code calls another function, algo_evaluation, with the newly created underlying DataFrame as an argument.

This suggests that another part of the code will further evaluate the asset's performance. The outcome of the algo_evaluation function is returned as the output of the underlying_evaluation function. In the context of an Algorithmic Trading project, this function helps assess how well an investment strategy or model, such as the Fama-French 3-Factor or 5-Factor Model, has performed by analyzing the actual historical returns of a portfolio. This step is crucial in back-testing trading strategies to ensure their effectiveness before deploying them with real capital.

# Define function to return algo evaluation relative to underlying asset: def algo_vs_underlying(signals_df):

metrics = [

'Annual Return',

'Cumulative Returns',

'Annual Volatility',

'Sharpe Ratio',

'Sortino Ratio']

columns = ['Algo', 'Underlying']

algo = algo_evaluation(signals_df)

underlying = underlying_evaluation(signals_df)

comparison_df = pd.DataFrame(index=metrics, columns=columns)

comparison_df['Algo'] = algo['Backtest']

comparison_df['Underlying'] = underlying['Backtest']

return comparison_df

# Generate Metrics for Function vs. Buy-and-Hold Strategy: algo_vs_underlying(signals_df)

The provided Python code defines a function designed to assess the performance of an algorithmic trading strategy relative to a benchmark underlying asset. This function is utilized in a project that examines the effectiveness of the Fama-French 3-Factor and 5-Factor Models in predicting portfolio returns.

The function algo_vs_underlying takes one argument, signals_df, which is likely a DataFrame containing trading signals and data necessary for evaluation. It establishes a list of performance metrics such as Annual Return, Cumulative Returns, Annual Volatility, Sharpe Ratio, and Sortino Ratio that are pertinent for assessing the trading strategy.

The function then creates a new DataFrame with rows corresponding to these performance metrics and two columns labeled for the algorithmic strategy "Algo" and the underlying benchmark asset "Underlying." The evaluation results for both the algorithmic strategy and the underlying asset are calculated using the algo_evaluation and underlying_evaluation functions, respectively. The results from these evaluations for the respective Backtest data are populated into the new comparison DataFrame.

Finally, the comparison DataFrame is returned from the function, providing a side-by-side performance comparison that can be analyzed to determine how well the algorithmic strategy performs in relation to merely holding the underlying asset—a method typically referred to as a Buy-and-Hold Strategy. This code is part of a larger algorithmic trading project that employs complex financial models for predictive purposes. In this context, the function enriches the analysis by offering a straightforward way to compare the trading strategy against a passive investment benchmark.

# Define function to evaluate individual trades: def trade_evaluation(signals_df):

# Initialize DataFrame:

trade_evaluation_df = pd.DataFrame(

columns=[

'Entry Date',

'Exit Date',

'Shares',

'Entry Share Price',

'Exit Share Price',

'Entry Portfolio Holding',

'Exit Portfolio Holding',

'Profit/Loss']

)

entry_date = ''

exit_date = ''

entry_portfolio_holding = 0

exit_portfolio_holding = 0

share_size = 0

entry_share_price = 0

exit_share_price = 0

# Loop through signal DataFrame

# If Entry/Exit is 1, set entry trade metrics

# Else if Entry/Exit is -1, set exit trade metrics and calculate profit,

# Then append the record to the trade evaluation DataFrame

for index, row in signals_df.iterrows():

if row['Entry/Exit'] == 1:

entry_date = index

entry_portfolio_holding = row['Portfolio Total']

share_size = row['Entry/Exit Position']

entry_share_price = row['Close']

elif row['Entry/Exit'] == -1:

exit_date = index

exit_portfolio_holding = abs(row['Portfolio Total'])

exit_share_price = row['Close']

profit_loss = exit_portfolio_holding - entry_portfolio_holding

trade_evaluation_df = trade_evaluation_df.append(

{

'Entry Date': entry_date,

'Exit Date': exit_date,

'Shares': share_size,

'Entry Share Price': entry_share_price,

'Exit Share Price': exit_share_price,

'Entry Portfolio Holding': entry_portfolio_holding,

'Exit Portfolio Holding': exit_portfolio_holding,

'Profit/Loss': profit_loss

},

ignore_index=True

)

# Print the DataFrame

return trade_evaluation_df

The provided Python code defines a function called trade_evaluation, which is part of an Algorithmic Trading project. This function analyzes trading signals within a given DataFrame that contains daily trading information, calculating a detailed performance evaluation for individual trades. The code starts by initializing a DataFrame to store trade evaluations with specific columns including entry and exit dates, shares involved, share prices, and the portfolio holdings' value at entry and exit, along with the profit or loss from the trade.

Within a loop, the function processes the signals DataFrame row by row. When a signal indicates an entry into a position (denoted by Entry/Exit being 1), it records the date, portfolio value, number of shares traded, and entry share price. Conversely, when a signal indicates an exit from a position (denoted by Entry/Exit being -1), the exit date, portfolio value, and share price are recorded. It then calculates the profit or loss for that trade by comparing the entry and exit portfolio holdings.

After evaluating each trade, the function appends this information to the initialized DataFrame. Once all rows have been processed and individual trades evaluated, the function returns the DataFrame, providing a report on the trade performance according to the daily signals. Overall, this code offers insights into the profitability of trades by pairing entry and exit points as per the strategy defined in the trading signals. It enables traders to assess each trade's contribution to overall portfolio returns, which is useful for refining trading strategies based on models like the Fama-French 3-Factor or 5-Factor Model.

# Generate Evaluation table: trade_evaluation_df = trade_evaluation(signals_df) trade_evaluation_df

The Python code snippet executes a function called trade_evaluation, which likely takes a DataFrame named signals_df as input. This DataFrame contains trading signals generated based on the Fama-French 3-Factor and 5-Factor models, which are utilized in finance to describe stock returns.

The function processes the trading signals and outputs a new DataFrame assigned to the variable trade_evaluation_df. This resulting DataFrame systematically assesses the performance of the trading signals, including metrics like return on investment, accuracy of signals, and other statistical measures that help gauge the effectiveness of the trading signals produced by the Fama-French models.

The purpose of this code is to enable a rigorous evaluation of how well the trading strategy performs when applying the Fama-French factors to actual or hypothetical trades. Traders or portfolio managers can use the results to refine their models, enhance their strategies, and ultimately make more informed investment decisions.

# Set X and y variables: y = combined_df.loc[:, 'Returns'] X = combined_df.drop('Returns', axis=1) X = X.drop('Close', axis=1)

# Add "Constant" column of "1s" to DataFrame to act as an intercept, using StatsModels: X = sm.add_constant(X)

# Split into Training/Testing data: split = int(0.8 * len(X)) X_train = X[:split] X_test = X[split:] y_train = y[:split] y_test = y[split:]

# Run Ordinary Least Squares (OLS) Model: model = sm.OLS(y_test, X_test) model_results = model.fit() print(model_results.summary())

The provided Python code is part of an algorithmic trading project that employs the Fama-French 3-Factor and 5-Factor models to predict portfolio returns. The code aims to prepare the data for regression analysis, conduct the analysis, and present the results.

Initially, the code defines the dependent variable y as the 'Returns' column from a DataFrame named combined_df. Next, it creates the independent variables X by excluding the 'Returns' and 'Close' columns from the same DataFrame. The code then adds a column of ones to the independent variables DataFrame X to represent the intercept term for the regression model.

This is necessary for performing statistical tests and accurately interpreting the model. Afterward, the code divides the data into training and testing subsets. This split aims to train the model on a portion of the data (80% in this case) and assess its predictive capability on the remaining unseen data. An Ordinary Least Squares (OLS) regression model is subsequently fitted using the independent variables of the testing set X_test and the dependent variable of the testing set y_test.

Although typically an OLS model is fitted on the training set and evaluated on the test set, here it is applied directly to the test set. Upon fitting the model, the script generates a summary of the model's results. This summary includes statistical measures that help evaluate the performance and significance of the individual factors involved in the model. The output of the model summary will guide the user on how well the factors explain the portfolio's returns.

# Plot Partial Regression Plot: fig = sm.graphics.plot_partregress_grid(model_results, fig=plt.figure(figsize=(12, 8))) plt.show()

This Python code snippet generates a partial regression plot for a statistical model, likely from the results of an econometric analysis examining the Fama-French 3-Factor or 5-Factor Model. The Fama-French models aim to explain stock returns, and this plot is useful in an Algorithmic Trading project for visualizing the relationship between portfolio returns and the factors included in the model, after accounting for the impact of other variables.

The function plot_partregress_grid from the statsmodels library takes the results of a regression model stored in the variable model_results and plots the relationship between the dependent variable and each predictor variable individually, controlling for other predictors. The fig parameter receives a new figure object plt.figure with a specified size, creating space for the plots.

Once the function generates the partial regression plot on the figure, the plt.show() command is called to display the plot. This visual representation helps in understanding how much of the variation in portfolio returns can be attributed to each individual factor—such as market risk, size, value, profitability, or investment—while holding other factors constant, which is crucial for making informed trading decisions based on the Fama-French model analysis.

# Plot P&L Histogram: trade_evaluation_df["Profit/Loss"].hist(bins=20)

This Python code snippet generates a histogram plot of the Profit/Loss values from a DataFrame named trade_evaluation_df. A histogram graphically represents the distribution of the Profit/Loss data, dividing the range of Profit/Loss values into 20 intervals and counting how many values fall into each interval.

The goal of this code is to visualize the performance of a trading algorithm as part of an Algorithmic Trading project. By plotting the profits and losses of trades, the histogram allows traders and analysts to quickly perceive the frequency and distribution of trading outcomes, which can be essential for assessing the effectiveness of the trading strategies being evaluated.

The context of this code suggests it is used to examine the Fama-French 3-Factor and 5-Factor Models, which describe stock returns in terms of various risk factors. Histograms can be particularly useful in this analysis as they illustrate whether the models effectively predict portfolio returns by showing the distribution and range of profits and losses resulting from applying the algorithm based on these factors.

# Define function that plots Algo Cumulative Returns vs. Underlying Cumulative Returns: def underlying_returns(signals_df):

underlying = pd.DataFrame()

underlying["Close"] = signals_df["Close"]

underlying["Underlying Daily Returns"] = underlying["Close"].pct_change()

underlying["Underlying Daily Returns"].fillna(0, inplace=True)

underlying['Underlying Cumulative Returns'] = (1 + underlying['Underlying Daily Returns']).cumprod() - 1

underlying['Algo Cumulative Returns'] = signals_df["Portfolio Cumulative Returns"]

graph_df = underlying[["Underlying Cumulative Returns", "Algo Cumulative Returns"]]

return graph_df

The provided Python code defines a function intended to facilitate the comparison between the cumulative returns of an algorithm-driven trading strategy and the underlying asset it is based on. The code performs calculations on a DataFrame presumably containing historical price data and trading signals.

The function first creates a new DataFrame to store the underlying asset's prices and calculates the daily returns by comparing price changes from one day to the next. It replaces any missing values in the daily returns with zero to maintain continuity. From these daily returns, the function computes the cumulative returns, representing the total return over time while accounting for the compounding effect. Simultaneously, the function retrieves the cumulative returns of the trading algorithm, likely pre-calculated within the signals DataFrame.

This enables a direct comparison. Finally, the function prepares a new DataFrame containing only the cumulative returns of both the underlying asset and the trading algorithm. This resultant DataFrame is structured for easy visualization, such as plotting the returns over time to compare the performance of the algorithm against the underlying asset.

The purpose of this code is to assess the Fama-French models in predicting portfolio returns within an algorithmic trading project. The visual comparison facilitated by this function can be critical in understanding the algorithm's efficacy in capturing various risk factors and delivering excess returns over the asset it trades on.

# Generate Cumulative Return plot using above defined function: underlying_returns(signals_df).plot(figsize=(20, 10))

The given Python code snippet is part of a larger project that applies algorithmic trading concepts, particularly dealing with the Fama-French 3-Factor and 5-Factor Models used to explain stock returns. These models are well-known in financial economics for describing the impact of various risk factors on portfolio returns. Specifically, the code generates a plot of the cumulative returns of a trading strategy or portfolio.

This is accomplished by calling the underlying_returns function with signals_df as its parameter, which presumably calculates the returns based on trading signals or investment decisions contained within the signals_df DataFrame. The function's output results in a series of cumulative returns over time. After calculating these returns, the code plots them using the plot function, part of the pandas or matplotlib libraries in Python.

The plot is configured to have a figure size of 20x10 inches, specifying the width and height for visualization. By analyzing such a plot, investors and analysts can visually assess the performance of their trading strategies over time, helping to make informed decisions regarding the efficacy of applying the Fama-French models in predicting portfolio returns.

This is not the complete code; find the entire code here: