Exercise $6$:

a$.$ Calculate the rate of return and standard deviation for the portfolio composed of $20\%$ of the stocks A and $80\%$ of the stocks $B$ with the following characteristics: $R_A=10\%,R_B=20\%,$ Sigma $A=15\%,$ Sigma B $=30\%,$ Correlation Coefficient $=0\mathrm{.}5.$

b$.$ Assuming the short sale is possible, find the share of the stocks A and B in a portfolio D having an expected rate of return of $5\%.$