(7) Portfolio (a) Prove that if X is a random variable and a, b are constants we have VaraX +b) = 2Var(X). (b) Use the property above to show that the standard deviation Oy of the value V (T) of any portfolio (x,y) at time T is given by ay = 1 os, where os is the standard deviation of the stock value at time T. (7) Portfolio (a) Prove that if X is a random variable and a, b are constants we have VaraX +b) = 2Var(X). (b) Use the property above to show that the standard deviation Oy of the value V (T) of any portfolio (x,y) at time T is given by ay = 1 os, where os is the standard deviation of the stock value at time T