Attention, please! After moving to the next page, it will be impossible to go back! Logreturns X and Y for shares of two companies A and B follow normal distributions with parameters respectively m_(A)=2,Var(X)=0.86 and m_(B)=11 Var(Y)=0.39 It is known that a correlation coefficient between these logreturns is rho (X,Y)=-0.28 Find the expected value and variance for logreturns of a portfolio consisting of 5 shares of company A and 9 shares of company B. Enter your answers: E(5X+9Y)= Var(5X+9Y)= By moving on to the next question, you

To find the expected value and variance of the logreturns of the portfolio, we can use the following formulas:<br /><br />$E(5X+9Y) = 5E(X) + 9E(Y)$<br />$Var(5X+9Y) = 5^2Var(X) + 9^2Var(Y) + 2(5)(9)\rho(X,Y)Var(X)Var(Y)$<br /><br />Given that $E(X) = m_A = 2$, $Var(X) = 0.86$, $E(Y) = m_B = 11$, $Var(Y) = 0.39$, and $\rho(X,Y) = -0.28$, we can substitute these values into the formulas:<br /><br />$E(5X+9Y) = 5(2) + 9(11) = 10 + 99 = 109$<br /><br />$Var(5X+9Y) = 5^2(0.86) + 9^2(0.39) + 2(5)(9)(-0.28)(0.86)(0.39) = 21.5 + 32.49 - 5.88 = 47.11$<br /><br />Therefore, the expected value of the logreturns of the portfolio is $E(5X+9Y) = 109$, and the variance of the logreturns of the portfolio is $Var(5X+9Y) = 47.11$.