Covariance: Measuring How Asset Returns Move Together
Summary
The document introduces covariance as a measure of how two variables vary together, defining it through the expected product of each variable’s deviation from its mean. Positive covariance indicates a tendency to move in the same direction, while negative covariance indicates a tendency to move in opposite directions. It connects these patterns to portfolio risk: assets with negative covariance may offset one another, while positive covariance can concentrate portfolio fluctuations.
A simulated example contrasts positive and negative relationships between two assets’ daily returns using scatter plots and sample covariance calculations. The discussion describes uses in portfolio risk assessment, asset allocation, and comparison with a market benchmark. Covariance’s magnitude depends on the units of the variables, so it can be hard to interpret directly; correlation standardizes the relationship for easier comparison. The examples are illustrative rather than evidence of persistent real-world relationships, and zero covariance should not be taken to rule out every kind of dependence.
Key ideas
- Covariance summarizes the direction in which two variables tend to move together.
- Positive covariance suggests that the variables tend to rise or fall together, while negative covariance suggests opposing movement.
- Negative covariance can help diversify a portfolio by allowing asset returns to offset one another.
- Covariance supports portfolio risk analysis and asset allocation, but its magnitude depends on measurement units.
- Correlation standardizes covariance, making relationships easier to compare across variables.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.