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Adjust CML model for VIX factor

I’m trying to incorporate the VIX index into my efficient frontier model. One way of doing this that I thought about was to extend the model to include investor utility indifference curves. I would then add a simple if/then condition to determine the coefficient in the utility indifference equation based on the position of the VIX index. But I think that this is too rudimentary. I also think that there has to be a more practical way to guide my portfolio strategy than utility curves.

Is there a better, more systematic way of incorporating the VIX index into my CML model?

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    $\begingroup$ Wouldn’t you want to add an instrument that makes the VIX tradeable and use its return mean and covariance wrt your other assets as input to your portfolio selection? $\endgroup$ – Kermittfrog May 8 at 9:33

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