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Index implied volatility is a easy quant interview question on option theory.
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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.