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I want to compute: $$ \mathbb{V}_t \left[ \sum_{i=1}^N \sigma_i \cdot \frac{X_{it}}{Y_t} \cdot Z_{i,t+1} \right] $$ Where $X_{it}$ is correlated with $Y_t$, and $Z_{it} \sim N(0,1)$ uncorrelated random variables. $\sigma_i$ is the standard deviation of $X_{it}$.

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