Portfolio Optimization

You're rebalancing a portfolio with two risky assets. Asset 1 has expected return ${\mu }_1=8\%$ and volatility ${\sigma }_1=15\%$; Asset 2 has ${\mu }_2=12\%$ and ${\sigma }_2=20\%$. Their correlation is $\rho =0.3$. A risk-free asset pays $r_f=3\%$.

Part A

Derive the weights of the global minimum-variance portfolio (GMV) of the two risky assets.

Part B

Derive the weights of the tangency portfolio (maximum Sharpe ratio) that combines the two risky assets with the risk-free asset.

Part C

Report the Sharpe ratio of the tangency portfolio.