I’m looking for a nice & detailed explanation for how to derive the formula for the weight of asset 1 in the tangency / maximum Sharpe ratio portfolio in Markowitz portfolio theory in a world with two risky assets and one risk-free investment. I tried but failed to derive myself, hence I’m looking for a reference.
The sources which I found only describe the general approach of how to derive the portfolio with the highest Sharpe ratio and only present the final formula (e.g. slide 42 of this presentation: http://www.kellogg.northwestern.edu/faculty/papanikolaou/htm/FINC460/LN/Lecture1.pdf)
Any recommendations?