Valuing financial firms, specifically banks and insurance companies, poses unique challenges due to their complex financial structures and regulatory environments. Traditional valuation methods like Price to Earnings (PE), Price to Book (PB), and Price to Sales (PS) ratios often fall short. But there’s a game-changing approach: using regression analysis on relative valuation metrics such as Return on Equity (ROE) and Price to Book (P/B) ratios.
Why Traditional Methods Fall Short:
Price to Earnings (PE) Ratio: For financial firms, earnings can be volatile and heavily influenced by accounting provisions, making PE ratios unreliable.
Price to Sales (PS) Ratio: Sales figures are not easily measurable or meaningful for financial services firms, rendering PS ratios impractical.
Enterprise Value (EV) Multiples: Calculating EV for financial firms is complex due to the difficulty in defining and measuring debt.
The Power of Regression Analysis with ROE and P/B Ratios:
By focusing on ROE and P/B ratios, we can create a more reliable valuation model. ROE measures a firm's profitability relative to its equity, while the P/B ratio compares a firm's market value to its book value. These metrics are particularly relevant for banks and insurance companies, where book values closely track market values. And ROE is not impacted that much by accounting provisions (for revenues) and earnings volaltility.
An turns out they are positively correlated, which will make our regression make some sense.
Hands-On Python Code for Regression Analysis (Model Explanation below the code)
Let’s dive into a practical example. Here’s how you can use Python to perform regression analysis with ROE and P/B ratios:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score
# Sample data including hypothetical data
data = {
'Bank': ['WABC', 'VLY', 'BOH', 'CIB', 'WFC', 'UMB', 'FNB', 'CFR', 'BAC', 'STI', 'BPOP'],
'ROE': [0.22, 0.18, 0.21, 0.23, 0.12, 0.14, 0.13, 0.12, 0.10, 0.07, -0.02],
'PB_Ratio': [4.00, 3.00, 3.00, 2.50, 1.50, 2.00, 1.80, 1.80, 0.80, 1.00, 0.60]
}
# Convert to DataFrame
df = pd.DataFrame(data)
# Define the independent variable (ROE) and the dependent variable (PB_Ratio)
X = df[['ROE']]
y = df['PB_Ratio']
# Create a Linear Regression model
model = LinearRegression()
model.fit(X, y)
# Predict PB Ratio
df['Predicted_PB_Ratio'] = model.predict(X)
# Calculate R-squared value
r2 = r2_score(y, df['Predicted_PB_Ratio'])
print(f'R-squared value: {r2}')
print(f'Intercept: {model.intercept_}')
print(f'Coefficient: {model.coef_[0]}')
# Plot the data and the regression line
plt.scatter(X, y, color='blue', label='Actual')
plt.plot(X, df['Predicted_PB_Ratio'], color='red', label='Fitted Line')
plt.xlabel('ROE')
plt.ylabel('PB Ratio')
plt.title('PB Ratio vs ROE')
plt.legend()
plt.show()
# Example: Applying the model to a new company with hypothetical ROE of 0.15
new_company_roe = 0.15
predicted_pb_ratio = model.predict([[new_company_roe]])
print(f'Predicted PB Ratio for new company with ROE of {new_company_roe}: {predicted_pb_ratio[0]}')
Explanation:
In our analysis, we calculated the projected Price to Book Value (P/BV) ratio using regression analysis with Return on Equity (ROE) as the independent variable.
By fitting a linear regression model to historical data of comparable banks, we established the relationship between ROE and P/BV ratios.
This model allowed us to predict the P/BV ratio for our Financial firm based on its ROE.
Predict Returns:
To estimate the expected returns, we compared the predicted P/BV with the actual P/BV observed in the market. The expected return was calculated using the formula
(Predicted P/BV using regression divided by the Actual P/BV − 1)×100%,
which reflects the percentage difference between the predicted and actual P/BV ratios, indicating potential undervaluation or overvaluation.
By applying this method, investors can gauge if the IPO issue or market price offers a favorable entry point based on relative valuation metrics.
Interpretation of Results:
R-Squared Value: Indicates the proportion of the variance in the dependent variable (P/B Ratio) that is predictable from the independent variable (ROE). A higher value suggests a stronger relationship.
Intercept and Coefficient: Represent the regression line, showing how changes in ROE affect P/B ratios.
Predicted P/B Ratio: Helps estimate the market value based on ROE.
Conclusion:
By leveraging regression analysis, we can create a more robust and reliable valuation model for banks and insurance companies. This approach not only accounts for the unique financial structures of these firms but also provides actionable insights that traditional methods miss.
Unlock the potential of your financial analysis with regression and transform how you value financial firms. Dive into the data, apply the code, and see the difference it makes!
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