12. Correct. The answer is false.

 

You can deduce the formula of X + Y as follows:

 

Var [X+Y] = E [ (X+Y) - E(X+Y) ]2

 

Squarin the binomial, you get:

 

Var [X+Y] = E{[X - E(X)2} + E{[Y - E(Y)2} + 2 E {[X - E(X)] [Y - E(Y)] }

 

Applying the definitions of variance and covariance to the right-hand side, the variance of the sum becomes:

 

Var [X+Y] = Var (X) + Var (Y) + 2Cov(X,Y).

 

Using the numbers with this formula, you have:

 

Var [X+Y] = 50 + 20 + 2*(-27) = 16

 

The standard deviation of the portfolio is: {Var[X+Y]}0.5 = US$ 4.