Variance and Covariance in Quant Interviews
How to reason about variance and covariance in quant interviews, including portfolio-style examples, dependence, and common mistakes.
Candidates preparing for statistics, research, and risk questions in quant interviews.
Variance is spread
Variance measures how much a variable moves around its mean. In quant interviews, variance often appears when a strategy, bet, or estimate has uncertainty that matters beyond its expected value.
Covariance is joint movement
Covariance describes how two variables move together. Positive covariance means they tend to move in the same direction; negative covariance means they tend to offset. The scale depends on the units, which is why correlation is often used for normalized comparison.
The missing term in sums
For two variables, Var(X + Y) = Var(X) + Var(Y) + 2Cov(X,Y). Candidates often remember the first two terms and forget covariance. That mistake understates or overstates risk when variables are dependent.
Concrete example
If two bets each have variance 4 and covariance -1, the variance of their sum is 4 + 4 + 2(-1) = 6. The negative covariance reduces total variance because the bets partly offset each other.
Interview explanation
When covariance appears, explain the economic or statistical reason for dependence. In a portfolio-style question, two similar signals may have positive covariance; a hedge may have negative covariance. The story matters because it justifies the sign.
Common mistakes
Candidates confuse variance with standard deviation, ignore covariance in sums, or treat zero covariance as proof of independence. Keep the definitions separate and check whether dependence could be nonlinear.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.