Assume a HNWI that is invested $50-50$ in stocks and bonds wants to allocate $30$ percent of his current portfolio to hedge funds. His advisor suggests reallocating a portion of his equity investments to meet this objective. Assume the historical returns from stocks is $12$ percent, bonds is $4$ percent, and hedge funds are $10$ percent, that the volatility of stocks is $12$ percent, of bonds is $5$ percent, and of hedge funds is $6$ percent and that the correlation between stocks and bonds is $\mathrm{.}1,$ between stocks and hedge funds is $\mathrm{.}4,$ and between bonds and hedge funds is $-\mathrm{.}1.$

a$.$ What is the original expected return and standard deviation?

b$.$ What is the new expected return and standard deviation?

c$.$ What is the old Sharpe ratio?

d$.$ What is the new Sharpe ratio?