Covariance Calculator
Measure of joint variability.
Formula first
Overview
Covariance measures the joint variability of two random variables, indicating the direction of their linear relationship. A positive value signifies that variables move in the same direction, while a negative value indicates an inverse relationship.
Symbols
Variables
Cov(X,Y) = Covariance, E[XY] = Mean Product, \mu_x = Mean X, \mu_y = Mean Y
Apply it well
When To Use
When to use: Apply this formula when you need to assess the linear dependency between two sets of data or as a step toward calculating correlation. It is used in probability distributions to determine how much variables change together.
Why it matters: It is crucial in finance for risk management and portfolio optimization, helping investors identify assets that do not move in tandem. It also underpins dimensionality reduction techniques like Principal Component Analysis (PCA) in data science.
Avoid these traps
Common Mistakes
- Mixing up means for X and Y.
- Interpreting covariance as correlation.
One free problem
Practice Problem
A financial analyst determines that the expected value of the product of two stocks (X and Y) is 45. If the average return of stock X is 5 and the average return of stock Y is 8, find the covariance.
Solve for:
Hint: Subtract the product of the means from the expected product.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Covariance
- A First Course in Probability by Sheldon Ross
- Probability and Statistics for Engineers and Scientists, 9th Edition, by Walpole, Myers, Ye, and Shafer
- Sheldon M. Ross, A First Course in Probability
- IUPAC Gold Book: Covariance (C01373)
- AQA A-Level Mathematics — Statistics (Bivariate Data)