Regression Analysis for Financial Relationships › Regression Analysis for Financial Relationships

Financial markets are built on relationships. The return of a stock depends on broad market movements. Bond yields respond to changes in interest rate expectations. Currency pairs move with economic fundamentals. Understanding these relationships, including quantifying their strength, testing their significance, and using them for prediction, requires a powerful statistical framework: regression analysis.

Regression analysis sets up many core concepts in quantitative finance. When you hear that a stock has a "beta of 1.2," that number comes from a regression. When you claim to generate "alpha" as a portfolio manager, you're making a statement about regression intercepts. When we test whether momentum or value factors explain returns, we're running regressions. The Capital Asset Pricing Model, which we'll explore in depth in Part IV, is fundamentally a regression model relating expected returns to market exposure.

Building on the statistical inference techniques from Part I and the time-series models from the previous chapters, this chapter develops regression analysis with a focus on financial applications. We'll start with the ordinary least squares framework, then apply it to estimate factor exposures, conduct hypothesis tests, and diagnose the problems that arise when regression meets financial time series data. By the end, you'll be able to estimate a stock's market beta, test whether it generates statistically significant alpha, and correct for the autocorrelation and heteroskedasticity that plague financial data.