\\\\sigma _(i,j)={(2 if i=j),(-1 if |i^(2)-j^(2)|=5),(0 otherwise. ):}

\ Let

\\\\alpha

be a real number. A portfolio

P

has weight vector

w=(\\\\alpha ,2\\\\alpha ,\\\\alpha ,1-4\\\\alpha )^(T)

, and has the\ lowest risk among all such portfolios.\ (i) Find the value of

\\\\alpha

.\ (ii) Find the mean and variance of the portfolio

P

.

1. A financial market consists of four risky assets whose rates of return r1,r2,r3 and r4 have means 1,21,1, and 2 respectively, and i,j=210ifi=jifi2j2=5otherwise. Let be a real number. A portfolio P has weight vector w=(,2,,14)T, and has the lowest risk among all such portfolios. (i) Find the value of . (ii) Find the mean and variance of the portfolio P