You are interested in a portfolio of two stocks: A and B$.$ The monthly average return and standard deviation of Stock A are $4\mathrm{.}5\%$ and $16\mathrm{.}7\%,$ respectively. The monthly average return and standard deviation of Stock B are $0\mathrm{.}4\%$ and $7\mathrm{.}9\%,$ respectively. The correlation between the two stocks is $0\mathrm{.}01.$ The monthly risk$-$free rate is $0\mathrm{.}1\%.$

$(1$ point$)$ What is the Sharpe ratio for Stock A$?$

Show your calculation steps briefly and clearly.

$(1$ point$)$ Calculate the minimum$-$variance portfolio $($MVP$).$

You do NOT need to show your calculation steps for this subquestion.

$(1$ point$)$ Calculate the optimal risky portfolio P$*.$

You do NOT need to show your calculation steps for this subquestion.

$(1$ point$)$ Suppose you add a new stock to the portfolio and re$-$calculate the optimal risky portfolio of the three stocks. Determine whether the optimal Sharpe ratio will increase, decrease, or remain the same after adding a new stock. Briefly explain why.