A portfolio risk calculation needs the covariances between its asset returns. This lesson derives covariance, correlation and the variance of a sum. It proves that independence implies zero covariance, then shows why the converse fails. A dependent-indicator example develops the same accounting used in joint portfolio-return calculations.
Learning objectives. By the end of this note you should be able to:
- compute covariance from its definition and from the shortcut formula ;
- prove independence implies zero covariance, and produce a counterexample to the converse;
- state and apply the general variance-of-a-sum formula, including for a sum of dependent indicator variables;
- compute and interpret the correlation coefficient, including the perfect-correlation () case.
In this lesson
- Covariance
- Variance of a sum — the general (dependent) case
- Correlation
Before you start
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