Principal Component Analysis (PCA): Reduces the dimensionality of the data and finds the optimal number of components that captures the max amount of explained variance
PCA Risk-Factor Model:
Using Principal Component Analysis (PCA) as a Risk-Factor Model to reduces the dimensionality of these data and finds a representation of them that explains a maximum amount of their variance
├── src
│ ├── main.py # Use Principal Component Analysis as a Risk Factor Model
│ ├── data.py # Clean data and get daily returns for all 10 SPDR ETF Sector ETFs
│ ├── config.py # Define path as global variable
│ ├── ETF_main.py # Calculated n-components needed to retain a given amount of variance and percentage of dimensionality reduction
│ ├── ETF_webscrape.py # Webscrape the SP500 WikiTable using BeautifulSoup and append all assets into a list
│ ├── ETF_data.py # Extract Adjusted-Closing price of all SP500 Equities from the webscrape.py list
├── plots
│ ├── Factor Returns.png # Factor Returns time-series
│ └── TotalPCA.png # Total Percent Variance Explained
├── inputs
│ ├── train.csv # Adj-Closing Price for SPDR Sector ETF
│ ├── sp_train.py # SPDR Sector ETF Adj-Closing Price
│ └── train.csv # Adj-Closing Price data
├── requierments.txt # Packages used for project
└── README.md
Principal Component 0 for 0.6286258454061395
Principal Component 1 for 0.18822793060925014
Principal Component 2 for 0.06392275282080973
Principal Component 3 for 0.04026355667943605Sum of all Variance Retained: 0.928%
Number of Principal Components Needed: 4
Reduced the Dimenionality of the timeseries by: 70.0%
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Factor Exposure (B): Number of ETFs X Number of Factors (matrix) -
Factor Returns (f): Number of Factors X Number of Timestamps (matrix)
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Idiosyncratic Risk (s): Number of ETFs X Number of Timestamps (matrix)
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Idiosyncratic Risk of the Residuals (S):
Calculated the covar matrix of the residuals and set off-diagonal elements to 0
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Returns (r): Number of ETFs X Number of Timestamps (matrix)
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Factor Covariance Matrix (F):
