consider five tradable assets with the following expected values and standard deviations of the rates of return of the assets ;

u_1=0.08, u_2=0.1 u_3=0.13 u₄=0.15 u_5=0.2

standards dev ; 0.14, 0.18, 0.23, 0.25, 0.35

correlation matrix of the rates of the return is 5x5 matrix with components; 1, -0.3, 0.4,0.25, -0.2, -0.3, 1, -0.1, -0.2, 0.15, 0.4, -0.1, 1, 0.35, 0.25, 0.25, -0.2, 0.35, 1, -0.15, -0.2, 0.15, 0.25, -0.15, 1.

Assume that it is possible to take both long and short positions of arbitrary size in these assets.

1. find the assets allocation for a minimal variance portfolio with 15% expected rate of return and the corresponding minimal standard deviation of the rate of the portfolio,

2. , find the assets allocation for a maximum expected return portfolio with 25% expected rate of return and the corresponding maximal expected rate of return of the portfolio