# Tangency portfolio with two additional constraints

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.