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