Correlation, Plainly
What correlation measures, why holdings that don't move together make a portfolio steadier, and why the relationship between stocks and bonds has changed over time.
The short version
Correlation measures how closely two investments move together, on a scale from −1 to +1. Combining holdings with low or negative correlation smooths a portfolio, because their bad years don't all arrive at once. Correlations aren't fixed. In US data, stock and bond returns had almost no relationship over the full century, moved in opposite directions from 2000 to 2021, and fell together in 2022.
By the end of this lesson, you'll be able to
- Explain what a correlation of +1, 0, and −1 means
- Show how combining low-correlation holdings reduces swings
- Explain why historical correlations can change
Why this matters
The last lesson said diversification works best when holdings don't all have bad years at once. Correlation is how investors measure that. You won't need to calculate it yourself, but understanding it explains why bonds are in most portfolios, and why that protection sometimes fails.
The scale
Correlation. A measure from −1 to +1 of how closely two investments move together. +1 means in step, 0 means unrelated, −1 means opposite. Glossary describes how two things tend to move relative to each other, on a scale from −1 to +1:
- +1: they move in perfect step. When one is up, the other is up by a proportional amount. Holding both adds no diversification.
- 0: no consistent relationship. Knowing how one did tells you nothing about the other.
- −1: they move in perfectly opposite directions. When one zigs, the other zags.
Real investments sit somewhere in between. Two large US companies in the same industry usually have a high positive correlation. A stock and a short-term government bond usually have a much lower one.
Two hypothetical investments each swing between +20% and −10%, but in opposite years. A portfolio split evenly between them, rebalanced each year, behaves very differently from either one.
| Year | Investment A | Investment B | Half in each |
|---|---|---|---|
| 1 | +20% | −10% | +5% |
| 2 | −10% | +20% | +5% |
| 3 | +20% | −10% | +5% |
| 4 | −10% | +20% | +5% |
A and B have a correlation of −1. Each one is a bumpy ride, but together the bumps cancel, leaving a steady 5% a year. Each alone would also grow, since 1.2 × 0.9 = 1.08 over two years, but only about 3.9% a year compounded. Perfect opposites are rare in real markets. Even partial differences help.
The rest of this lesson is for members
Still to come in this lesson: Stocks and bonds, in real data, Why it changes, the key takeaways, and 2 quiz questions with explanations.
Membership opens every lesson in the curriculum, the capstone projects, the interactive tools, and the members-only channels in the Hyperion Entities Discord. The first lesson of every module stays free.
Go deeper
- Covariance, Correlation, and BetaPortfolio Theory and Risk (depth track)
- Correlation Is Not CausationMath and Statistics for Investors (depth track)
- Modern Portfolio Theory and the Efficient FrontierPortfolio Theory and Risk (depth track)
Notes and sources
- Aswath Damodaran, NYU Stern School of Business. Historical Returns on Stocks, Bonds and Bills, with annual data through 2025 (updated January 2026). Checked 2026-10-12.