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If the value of $V(S,t)$ and of $U(S,t)$ is identical at $t=T$, then the value/price at $t=0$ should be the same too. Otherwise there is arbitrage. Imagine $V(S,T) = U(S,T) = X_T$ for some unknown $X_T$ but $V(S,0) > U(S,0)$ then we apply sell high and buy low. We sell $V(S,0)$ and buy $U(S,0)$ and we have a gain of $x :=V(S,0)-U(S,0)$. We can put this ...

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Conceptually, I think of this as the volatility of a portfolio with a -100% position in the benchmark. Then you can just add a row and column to the portfolio's co-variance matrix. $Tracking Variance = \sum \sum w_i w_j \sigma_i \sigma_j \rho_{i,j} + \sigma^2_{bench} + 2\sum w_i (w_{bench} = -1)\sigma_i \sigma_{bench}\rho_{i,bench}$ Taking the first ...

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I don't know that there is a "standard-solution crystalized in the community," but there are alternatives. The ones that I prefer are Omega, Sortino, and Kappa. All three of these ratios, unlike Sharpe, do not assume normally distributed returns. Omega Ratio: This is the probability-weighted ratio of gains versus losses for a given minimum acceptable ...

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