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There are some subtleties / difficulties. Implied volatiliy, which depends on the strike of a vanilla option, is only a forward looking measure in the sense that it can be regarded as the risk-neutral expectation of break-even delta-hedging profit and loss of a vanilla option of strike $K$ which is delta hedged to expiration using a constant volatility. If ...

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Please let me be sure I have this right. Your strategy is positively correlated with market; but the beta is non-zero. IS the beta positive or negative? if negative, your previous statement cannot be true; you have to mis-measuring something somewhere (happy to help)! If your beta is the right sign but <>1, then that just reflects the imperfect ability ...

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...this technique works only when returns are generated from normal distributions? Yes and no. Multiplying them by $C$ will produce the correlation that you wanted, but it won't preserve the distribution in general. Remember that when we apply $C$ to a vector of i.i.d. random variables $\boldsymbol{x}$ that the resultant vector element is $\sum_j C_{ij}x_j$,...

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