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What would be the difference between the following. Both techniques will result is an ex-ante risk of $\sigma$. However, that would be achieved via two different values of h. I want to understand which might be superior or better.

  1. Doing a mean variance optimization :

$h = \frac{V^{-1} \alpha}{2 \lambda} $ choosing

$\lambda = \sqrt{\frac{\alpha^T V ^{-1} \alpha}{4 \sigma^2}}$

which is just risk targeting to $\sigma$.

  1. Scaling your weights (signal) to risk target.

$h = \frac{\sigma}{\sqrt{\alpha^T V \alpha}} \alpha$

Notations:

$h$ : Final weights

$V$ : Covariance matrix

$\alpha$: Signal ( assume it to be normal in the cross section)

If we calculate the ex-ante risk we will get $\sigma$ from both ex-Ante risk: $h^TVh$

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  • $\begingroup$ Both techniques target an ex-ante volatility of $\sigma$. $\lambda$ is the Lagrangian multiplier and for a specific solution, one would have to specify the value of $\lambda$ $\endgroup$ – whisperer Aug 29 '19 at 20:54
  • $\begingroup$ Ok, I see. Sort of. I'll think about it. $\endgroup$ – Alex C Aug 29 '19 at 21:16

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