I know that the formula for determining the weights of the Tangency portfolio is given as $w_{tan}$ = $\frac{\Sigma \mu}{\iota^{\prime}\Sigma\mu }$, but I was wondering how to derive the weights in case we add the constraints that the weights should be larger than or equal to -1, and smaller than or equal to 1.

I was wondering whether there is a closed form solution available, and/or what the derivation looks like?

I guess the optimisation problem would look something like this: $$ \frac{w^{\prime}\mu}{\sqrt{w^{\prime}\Sigma w}} $$ s.t. $$ w^{\prime}\iota = 1 $$ $$ w_{i} \geq -1, \forall i = 1, \dots, N $$ $$ w_{i} \leq 1, \forall i = 1, \dots, N $$

Please correct me if this is the wrong representation of the problem.


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