Investment bankers use linear regression to predict the market or value a company.
Linear regression may sound technical, but at its core, it’s just about drawing the best straight line through data to see patterns and make predictions.
In finance, this means it can help you:
- Estimate risks
- Forecast returns
- Value investments more accurately.
It’s also an important topic for the CFA exam, particularly in Level 2, where concepts such as multiple regression and correlation are thoroughly tested.
By mastering linear regression, you’ll be able to price assets better, measure risk, and build stronger portfolios for clients.
Let’s break down what linear regression is and how it’s applied in the investment banking world.
What is Linear Regression?
Linear regression is a way to find the relationship between two variables by fitting a straight line through data points.
This line can then be used to make predictions.
The equation looks like this: Y = α + βX + ε
Where:
- Y is the dependent variable (what you’re trying to predict)
- X would serve as the independent variable (the predictor)
- α / alpha: intercept (value of Y when X = 0)
- β / beta: slope (How much Y changes when X changes by 1 unit)
- ε / error : (this represents the part of the data that the model cannot predict)
In investment banking, linear regression helps forecast revenues, value companies, and assess risk.
A Quick tip for CFA aspirants: Focus on understanding the core formula (y = mx + c).
And these key components like:
- Residual Sum of Squares (RSS)
- Sum of Squared Errors (SSE)
- Total Sum of Squares (SST).
These are foundational concepts that come up in exams in a straightforward manner and also help further in your career journey.
Before diving deeper, let’s look at three key concepts behind regression: correlation, variance, and covariance.
3 Key Statistical Concepts Behind Linear Regression
Before we can fully understand linear regression, we need to know 3 basic ideas from statistics:
- Correlation
- Variance
- Covariance.
These are the building blocks that regression relies on.
1. Correlation: Measuring Relationships:
Correlation shows how two things move together. The value of correlation (r) ranges from –1 to +1:
+1 → perfect positive relationship (both move up or down together).
–1 → perfect negative relationship (one goes up while the other goes down).
0 → no clear relationship.
Important notes:
- Correlation does not mean one thing causes the other.
- A single unusual data point (outlier) can change the result a lot.
In regression, correlation is the starting point for finding relationships.
2. Variance: Measuring risk:
Variance tells you how spread out the values of one variable are around the average.
- High variance = values jump around a lot (more risk/volatility).
- Low variance = values stay close to the average (more stability).
Formula: Variance = (1 / N) * Σ (Ri – R̄)²
Where:
- Ri = each return
- Rˉ = average return
- N = number of data points
In finance, variance shows how risky an investment is.
Bankers use it when valuing companies or building portfolios.
3. Covariance: Measuring movement together:
Covariance shows how two variables move together or in opposite directions, giving insight into their relationshipIt shows if they move in the same direction or opposite directions:
Positive covariance → both move together.
Negative covariance → one goes up while the other goes down.
Formula: Cov(X, Y) = (1 / N – 1) * Σ [(Xi – X̄) * (Yi – Ȳ)]
However, the problem with covariance is that it depends on the units of measurement, so the number itself is hard to compare.
That’s why correlation (a standardized version) is often used instead.
Now that you have understood these 3 metrics, it’s time for you to learn how bankers use these in practice.
Bankers combine these 3 key metrics to calculate beta, which tells you how risky a stock is compared to the market.
Let’s learn how to calculate it.
How to Calculate Beta?
Beta (β) tells you how much a stock moves compared to the overall market.
The formula is: β = Cov(Rasset, Rmarket) / Var(Rmarket)
What this means:
- Rasset = returns of the stock (the thing we’re studying)
- Rmarket = returns of the market index (e.g., S&P 500)
- Covariance = how the stock and market move together
- Variance of market = how much the market itself moves around
In simple terms, Beta = How closely the stock’s moves are tied to the market’s moves, compared to how much the market moves on its own.
How to read Beta:
- β = 1 → stock moves in line with the market.
- β > 1 → stock is more volatile (riskier) than the market.
- β < 1 → stock is less volatile (safer) than the market.
- β < 0 → stock moves in the opposite direction of the market.
Example:
- Imagine the market goes up by 10%
- A stock goes up by 15% in the same time.
- This means the stock is moving 1.5 times as much as the market.
So, Beta = 1.5.
If instead the stock only went up 5%, Beta would be 0.5 (less sensitive than the market).
Why it matters in banking:
- Used in the CAPM model to estimate the cost of equity.
- Helps value companies (IPOs, M&A deals).
- Useful in risk management and hedging strategies.
Applications of Linear Regression in Investment Banking:
Linear regression is a tool that helps investment bankers understand the relationship between different financial factors.
It’s like a way to predict how things will behave based on past data.
Let’s break down how it’s used in 4 key areas of investment banking.
1. M&A Valuation and deal structuring:
In Mergers and Acquisitions (M&A), bankers need to value a company accurately before a deal.
They use linear regression to predict a company’s future revenue based on economic trends.
It also helps test how the deal’s returns (IRR) might change with different economic conditions, like rising interest rates.
2. Equity Research and price forecasting:
For equity research, which is analyzing stocks, regression helps predict how things like oil prices or interest rates will affect a stock’s price.
After making predictions, bankers backtest the model with past data to make sure it’s reliable for future forecasts.
3. Trading strategy development:
In trading, linear regression is used for strategies like pair trading, where two related stocks are traded based on their price movements.
It helps identify when one stock is moving differently from the other, suggesting a trading opportunity.
It also helps traders understand and manage risk by showing how much their trades are exposed to changes in the market.
4. Risk management and stress testing:
Linear regression helps estimate how a portfolio reacts to market changes.
It’s also used to assess regulatory capital needs through scenario analysis.
By using linear regression in tools like Excel or Python, investment bankers improve analysis accuracy and add more value for clients.
These are a few ways linear regression is used by investment bankers.
Best Practices and Common Pitfalls
When working with linear regression, it’s important to follow best practices to get accurate results and avoid mistakes.
Here’s our best-kept ones:
1. Use scatter plots to spot any non-linear patterns or outliers.
2. Always check the key assumptions: linearity, constant variance, and normality of errors.
3. Be careful of multicollinearity if you’re using many predictors in your model.
4. Update your models regularly to keep up with market changes.
5. Pair regression results with qualitative analysis for a full picture.
For advanced Excel tips on regression analysis, check out our Excel Functions for Finance tutorial.
Conclusion
And that’s a wrap on our dive into linear regression in investment banking!
We’ve seen how linear regression helps bankers make:
- Better predictions
- Assess risks
- Value investments more accurately.
It’s a powerful tool that connects theory with real-world financial decisions.
For anyone preparing for the CFA exam, don’t overlook this concept.
It’s not only key to passing the exam but will also become invaluable in your finance career.
We hope this explanation made things clearer and more manageable.
Keep practicing, and remember, linear regression is a skill that gets easier the more you work with it.
Good luck, you’ve got this!
Further Resources
- Investment Banking Program: Immersive course covering financial modeling, valuation, and M&A tactics
- Free Videos: Quick lessons on regression diagnostics, portfolio theory, and risk measures
- Case Studies: Real‐world examples of regression in deal execution and equity research
- Blog Archive: Over 100 posts on finance, analytics, and career development
Are you eager to sharpen your regression skills?
Explore our Financial Modeling flagship program or join our live sessions on linear regression fundamentals.
