About this question
Medium · Probability & Statistics · Quant Trader interview question · probability, variance, conditional-expectation
You are analyzing the volatility of a stock. Let $Y$ be the daily return of the stock, and let $X$ be a signal derived from a machine learning model predicting market regime. You want to understand how much of the total variance of the stock's return $Y$ can be explained by the variance within each regime $X$, and the variance between the expected returns of each regime. Express $\text{Var}(Y)$ in terms of $E\text{Var}(Y|X)$ and $\text{Var}(EY|X)$.