Impara Calculating Returns and Log Returns | Financial Data Manipulation with Python

Understanding how to measure the performance and risk of investments is a cornerstone of financial analysis. Two fundamental metrics used for this purpose are returns and log returns. Returns allow you to quantify how much an investment has gained or lost over a specific period, while log returns provide a way to analyze compounded growth and aggregate returns over time more effectively. Both metrics are widely used to compare asset performance, assess volatility, and inform investment decisions.


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import pandas as pd
import numpy as np

# Example: closing prices for a single stock
prices = pd.Series([100, 102, 101, 105, 107])

# Calculate daily simple returns
simple_returns = prices.pct_change()

# Calculate daily log returns
log_returns = np.log(prices / prices.shift(1))

print("Simple Returns:")
print(simple_returns)
print("\nLog Returns:")
print(log_returns)

To understand the calculations above, it's important to know the mathematical formulas behind each type of return. The simple return for day t is calculated as:

(P_t - P_{t-1}) / P_{t-1}

where P_t is the price at the end of day t, and P_{t-1} is the price on the previous day. This gives the percentage change from one day to the next.

The log return (also called continuously compounded return) is calculated as:

ln(P_t / P_{t-1})

where ln denotes the natural logarithm. Log returns are particularly useful because they are time-additive: the sum of daily log returns over a period equals the log return over the entire period.

In the code above, pct_change() computes the simple returns, while taking the natural log of the price ratio gives the log returns. These results help you see how much a stock's price fluctuates each day, and provide a foundation for more advanced risk and performance analysis.


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# Example: DataFrame with multiple stocks
data = {
    'AAPL': [150, 153, 151, 156, 158],
    'MSFT': [250, 252, 249, 255, 257]
}
df = pd.DataFrame(data)

# Add columns for simple returns
df['AAPL_simple_return'] = df['AAPL'].pct_change()
df['MSFT_simple_return'] = df['MSFT'].pct_change()

# Add columns for log returns
df['AAPL_log_return'] = np.log(df['AAPL'] / df['AAPL'].shift(1))
df['MSFT_log_return'] = np.log(df['MSFT'] / df['MSFT'].shift(1))

print(df)

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              12345678910111213141516
            
import pandas as pd
import numpy as np

# Example: closing prices for a single stock
prices = pd.Series([100, 102, 101, 105, 107])

# Calculate daily simple returns
simple_returns = prices.pct_change()

# Calculate daily log returns
log_returns = np.log(prices / prices.shift(1))

print("Simple Returns:")
print(simple_returns)
print("\nLog Returns:")
print(log_returns)