Index implied volatility

What this index implied volatility question tests

This is an easy option-theory question that asks you to compute the implied volatility of a portfolio given the individual components' volatilities and their correlations. It is a foundational skill for traders and structurers who price index derivatives.

The core idea is that portfolio volatility is not simply a weighted average of component volatilities—correlation structure matters. When stocks move together, the portfolio is riskier; when they diversify, it is safer. To solve this, you need to set up the variance of a weighted sum, account for all pairwise covariances, and then extract the volatility. This tests whether you can apply basic linear-algebra reasoning to a practical derivatives problem.

• Portfolio variance formula with correlation
• Relationship between correlation, covariance, and individual volatilities
• Implicit assumption that index IV equals portfolio volatility