How to compute a tangency portfolio and optimal capital allocation with 3 stocks given their monthly returns over 5 years?

These are my homework questions for more info:

1.Optimal capital allocation with the addition of the EEM fund (10 points):Compute tangency portfolio and optimal capital allocation with all three assets. Show the new complete portfolio (combination of risk-free asset and new tangency portfolio) on the new capital allocation line. No need to compute the new efficient frontier with 3 assets (unless you have time to spare to build a macro in excel and want to impress your professor).Has investor utility improved?

Answer:

Weight in SPY:

Weight in EMM:

Weight in LQD:

Weight in optimal risky portfolio SPY/EEM/LQD:

Weight in the risk-free security:

Attained utility:

2.Optimal capital allocation with short-selling constraints (10 points):How does your answer to question 5 change if negative weights are not allowed?

Weight in SPY

Weight in EMM

Weight in LQD

Weight in optimal risky portfolio SPY/EEM/LQD

Weight in the risk-free security

Attained utility