291 lines
6.9 KiB
Plaintext
291 lines
6.9 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "8bea070e",
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"metadata": {},
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"source": [
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"<div style=\"background-color:#000;\"><img src=\"pqn.png\"></img></div>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "59b6b6e4",
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"metadata": {},
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"source": [
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"This code performs a multifactor analysis on monthly stock returns, applying the Fama-French three-factor model for financial analysis. It fetches historical factor data, calculates active returns of selected stocks, and estimates their sensitivities to the Fama-French factors. The code also performs rolling regression to analyze the stability of factor exposures over time. Lastly, it calculates and prints the marginal contributions to risk from each factor."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "84290a88",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import pandas as pd"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "2ec2de24",
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"metadata": {},
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"outputs": [],
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"source": [
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"import pandas_datareader as pdr\n",
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"import yfinance as yf"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "06d39571",
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"metadata": {},
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"outputs": [],
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"source": [
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"import statsmodels.api as sm\n",
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"from statsmodels import regression\n",
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"from statsmodels.regression.rolling import RollingOLS"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bc2a7be0",
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"metadata": {},
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"source": [
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"Fetch Fama-French factors data starting from 2000-01-01 and select the SMB and HML factors"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "5aff0b52",
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"metadata": {},
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"outputs": [],
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"source": [
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"factors = pdr.get_data_famafrench(\n",
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" 'F-F_Research_Data_Factors',\n",
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" start='2000-01-01'\n",
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")[0][1:]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "65938e3e",
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"metadata": {},
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"outputs": [],
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"source": [
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"SMB = factors.SMB\n",
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"HML = factors.HML"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8528b4ce",
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"metadata": {},
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"source": [
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"Download monthly adjusted close prices for specified stocks starting from 2000-01-01"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8518efcf",
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"metadata": {},
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"outputs": [],
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"source": [
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"data = yf.download(\n",
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" ['SPY', 'MSFT', 'AAPL', 'INTC'], \n",
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" start=\"2000-01-01\", \n",
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" interval=\"1mo\"\n",
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")['Adj Close']"
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]
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},
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{
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"cell_type": "markdown",
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"id": "439951e5",
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"metadata": {},
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"source": [
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"Calculate the monthly returns and convert them to period-based returns"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "9b300366",
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"metadata": {},
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"outputs": [],
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"source": [
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"monthly_returns = data.pct_change().to_period(\"M\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "246d309b",
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"metadata": {},
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"source": [
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"Extract the benchmark returns (SPY) and calculate active returns against the benchmark"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "f71342e4",
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"metadata": {},
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"outputs": [],
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"source": [
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"bench = monthly_returns.pop(\"SPY\")\n",
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"R = monthly_returns.mean(axis=1)\n",
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"active = R - bench"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ff54a6cb",
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"metadata": {},
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"source": [
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"Create a DataFrame with active returns and Fama-French factors SMB and HML"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d8ed7a12",
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"metadata": {},
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"outputs": [],
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"source": [
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"df = pd.DataFrame({\n",
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" 'R': active,\n",
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" 'F1': SMB,\n",
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" 'F2': HML,\n",
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"}).dropna()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3201423a",
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"metadata": {},
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"source": [
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"Perform Ordinary Least Squares (OLS) regression to estimate sensitivities to the factors"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d5e1b15c",
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"metadata": {},
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"outputs": [],
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"source": [
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"b1, b2 = regression.linear_model.OLS(\n",
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" df.R, \n",
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" df[['F1', 'F2']]\n",
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").fit().params"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "f621be1f",
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"metadata": {},
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"outputs": [],
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"source": [
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"print(f'Sensitivities of active returns to factors:\\nSMB: {b1}\\nHML: {b2}')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2eab25c3",
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"metadata": {},
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"source": [
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"Perform rolling OLS regression to estimate how factor sensitivities change over time"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c2489be4",
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"metadata": {},
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"outputs": [],
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"source": [
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"exog_vars = [\"SMB\", \"HML\"]\n",
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"exog = sm.add_constant(factors[exog_vars])\n",
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"rols = RollingOLS(df.R, exog, window=12)\n",
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"rres = rols.fit()\n",
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"fig = rres.plot_recursive_coefficient(variables=exog_vars)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "f4a1b059",
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"metadata": {},
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"source": [
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"Calculate covariance between factors and marginal contributions to active risk (MCAR) for each factor"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ad0355a8",
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"metadata": {},
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"outputs": [],
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"source": [
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"F1 = df.F1\n",
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"F2 = df.F2"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "6b0126e7",
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"metadata": {},
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"outputs": [],
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"source": [
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"cov = np.cov(F1, F2)\n",
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"ar_squared = (active.std())**2\n",
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"mcar1 = (b1 * (b2 * cov[0,1] + b1 * cov[0,0])) / ar_squared\n",
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"mcar2 = (b2 * (b1 * cov[0,1] + b2 * cov[1,1])) / ar_squared\n",
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"print(f'SMB risk contribution: {mcar1}')\n",
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"print(f'HML risk contribution: {mcar2}')\n",
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"print(f'Unexplained risk contribution: {1 - (mcar1 + mcar2)}')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "96df69b9",
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"metadata": {},
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"source": [
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"<a href=\"https://pyquantnews.com/\">PyQuant News</a> is where finance practitioners level up with Python for quant finance, algorithmic trading, and market data analysis. Looking to get started? Check out the fastest growing, top-selling course to <a href=\"https://gettingstartedwithpythonforquantfinance.com/\">get started with Python for quant finance</a>. For educational purposes. Not investment advise. Use at your own risk."
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]
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}
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],
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"metadata": {
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"jupytext": {
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"cell_metadata_filter": "-all",
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"main_language": "python",
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"notebook_metadata_filter": "-all"
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},
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.13"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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