In finance, assets do not exist in a vacuum. Understanding how the returns of two different stocks, or a stock and the market as a whole, move together is critical for building a diversified portfolio.

2.1. The Correlation Coefficient: How Two Assets Move Together

The correlation coefficient is a statistic that measures the strength and direction of the linear relationship between two variables. It is always a number between -1 and +1.

• +1: Perfect positive correlation. The two variables move perfectly in the same direction.
• 0: No linear correlation. The movement of one variable tells you nothing about the linear movement of the other.
• -1: Perfect negative correlation. The two variables move perfectly in opposite directions.

For example, an analysis of monthly returns found that the correlation coefficient between the S&P 500 index and General Electric (GE) stock was 0.7125. This value indicates a “fairly strong correlation in the same direction,” meaning that when the overall market goes up, GE’s stock tends to go up as well. It is important to note, as the source text highlights, that this statistic is dependent on the frequency of the data; the correlation was slightly higher using weekly (0.7616) or daily (0.7660) returns from the same period. This underscores a key lesson in econometrics: our results are always a function of the data we choose to observe.

2.2. A Critical Warning: Spurious Regression

A common pitfall in regression analysis is spurious regression, which occurs when two variables appear to be correlated, but the relationship is purely accidental and not genuine. This can happen due to accidental comovements in the data that have no underlying economic connection. The core lesson here is one of the most important in all of statistics: correlation does not imply causation. Just because two variables move together does not mean that one is causing the other to move.

Understanding these relationships in past data is useful, but finance is ultimately about the future, which requires us to model the uncertainty of future outcomes.