6) George was given a 10,000 bond portfolio all in AAA perpetual bonds at his birth. He is not allowed to change this investment until his 18th birthday. Assume that on his 18th birthday all the perpetual bonds discount factors are the same as when he was born. The perpetual bonds may take one of three credit states; AAA, BBB or default when they are worthless. Bonds in BBB are only worth 95% of their AAA value. Use the following information to calculate the value of the portfolio on George's 18th birthday. The eigenvalues of the transition probability matrix are: AAA BBB Default 1.0 0.8 0.2 The eigenvector matrix (V) of the transition probability matrix is given by: 0.6 -0.3 0.3 0.2 -0.4 0.6 0.6 0.8 0.9 The inverse eigenvector matrix (V-1) of the transition probability matrix is given by: 0.778816 -1.21495 0.560748 0.794393 0.093458 0.560748 0.654206 -1.02804 0.46729 (25 marks)