In class we defined the following quantities: -1, eTE-le Omz = WTEW, -le Prove the following: (i) (2pt) em = 1. (This means that the minimum risk portfolio satisfies the budget constraint.) (ii) (2pt) etw, = 0. (This means that w, does not require any initial cost. Such portfolios are often called self-financed or self-financing portfolio.) (iii) (3pt) 0 = M2. (If needed, you can use omz = ww: = 0) without proving it.) (iv) (3pt) w Tw: = w Twm (This justifies the definition of omz. Hints: The transpose of a number is the same number. The transpose of a matrix-vector product is the product of the transposes in reverse order.)