I have seen the following formula for the tangency portfolio in Markowitz portfolio theory but couldn't find a reference for derivation, and failed to derive myself. If expected excess returns of $N$ securities is the vector $\mu$ and the covariance of returns is $\Sigma$, then the tangent portfolio (maximum Sharpe Tatio portfolio) is:

\begin{equation} w^* = (\iota \Sigma^{-1} \mu)^{-1} \Sigma^{-1} \mu \end{equation}

Where $\iota$ is a vector of ones. Anyone know a source of the derivation?

I have seen the following formula for the tangency portfolio in Markowitz portfolio theory but couldn't find a reference for derivation, and failed to derive myself. If expected excess returns of $N$ securities is the vector $\mu$ and the covariance of returns is $\Sigma$, then the tangent portfolio (maximum Sharpe Ratio portfolio) is:

\begin{equation} w^* = (\iota \Sigma^{-1} \mu)^{-1} \Sigma^{-1} \mu \end{equation}

Where $\iota$ is a vector of ones. Anyone know a source of the derivation?