Two Basic Components in the Stock Returns (Alpha and Beta).. w. ChatGPT generated python example codes
Alpha and beta are two main components of stock returns that are often used in financial/quantitative analysis.
Definitions
Alpha: Alpha is a measure of an investment’s performance relative to a benchmark index, such as the S&P 500. It is the excess return earned by the investment above and beyond what would be expected given its level of systematic risk, as measured by its beta. A positive alpha indicates that the investment has outperformed its benchmark, while a negative alpha indicates underperformance.
Beta: Beta is a measure of an investment’s sensitivity to market movements. It represents the degree to which the investment’s returns move in tandem with the overall market. A beta of 1.0 means that the investment moves in lockstep with the market, while a beta greater than 1.0 means the investment is more volatile than the market, and a beta less than 1.0 means it is less volatile.
In general, investors seek to achieve positive alpha by selecting investments that outperform their benchmark index, while also taking into account their level of systematic risk, as represented by beta. A well-diversified portfolio that achieves a positive alpha relative to its benchmark index is often seen as evidence of skilled investment management.
Python — Code Example
Here is an example (from ChatGPT) how to calculate the alpha and beta return components for Apple (AAPL) during 2010–2022 period, compared to the Nasdaq 100 ETF (QQQ), which is used as the underlying market index for technology companies.
%reset -f
import yfinance as yf
import pandas as pd
import numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as plt
# Define the start and end dates for the data
start_date = '2009-12-31'
end_date = '2022-12-31'
# Retrieve AAPL stock data from Yahoo Finance
aapl = yf.download('AAPL', start_date, end_date)
# Calculate the daily returns for AAPL
aapl['daily_return'] = aapl['Adj Close'].pct_change()
# Retrieve QQQ stock data from Yahoo Finance (as a proxy for the market)
qqq = yf.download('QQQ', start_date, end_date)
# Calculate the daily returns for QQQ
qqq['daily_return'] = qqq['Adj Close'].pct_change()
# Combine the AAPL and QQQ daily returns into a single DataFrame
df = pd.concat([aapl['daily_return'], qqq['daily_return']], axis=1)
df.columns = ['AAPL', 'QQQ']
df = df.dropna()
# Calculate the beta and alpha for AAPL
X = df['QQQ']
y = df['AAPL']
X = sm.add_constant(X)
model = sm.OLS(y, X).fit()
beta = model.params[1]
alpha = model.params[0]
# Calculate the cumulative returns for QQQ and AAPL
cumulative_qqq = (1 + qqq['daily_return']).cumprod() - 1
cumulative_aapl = (1 + aapl['daily_return']).cumprod() - 1
# Calculate the cumulative alpha
cumulative_alpha = cumulative_aapl - (beta * cumulative_qqq)
# Plot the cumulative returns for QQQ, AAPL, and the alpha
plt.plot(cumulative_qqq, label='QQQ')
plt.plot(cumulative_aapl, label='AAPL')
plt.plot(cumulative_alpha, label='Alpha')
plt.legend()
plt.title('Cumulative Returns for AAPL, QQQ, and Alpha')
plt.xlabel('Date')
plt.ylabel('Cumulative Return')
plt.show()Importance of Alpha under the Systematic Investing Framework
The ability to capture alpha measures how good a security selection signal or the investing framework is.
In general as quantitative researchers, we simply measure the ability from two angles below.
- Absolute Level of Alpha
In general given all else equal, higher absolute alpha level suggests a stronger signal.
- Consistency Level of Alpha
Consistency is another key metrics to determine if the alpha captured by the signal is due to pure luck or the skill.
The more consistent alpha pattern the signal can populate, the higher confidence we can have on the signal (as its hit ratio is higher, which measures the percentage of trades that are profitable out of the total number of trades based on a particular trading signal or strategy).
Source: ChatGPT
