Reference no: EM133074128

An investor holds a portfolio of 50 zero-coupon bonds, each one with maturity in 3 years and a face value of 100 $. Half of the bonds have an initial rating Add, 10% are rated B and another 40% are rated Gas. The holder of the bond receives 100$ at maturity plus and interest rate of 3%, 4% and 5% of the face value if the bond is initially rated Add, B and Coo respectively, provided the bond does not default. If it does default the investor recovers 70% of its face value without collecting any interest. Refer to the rating one-step transition matrix Mk , posted on D2L.

a) Compute the transition probability matrix in one and three steps and write the probability that a bond rated Asa, B or Coo defaults.

b) The random variables YA", Y3 and Yam are de?ned as the amount received by the investor for each bond rated Add, B and Coo respec- tively. Compute the expected value of each variable.

c) Assume default of bonds in the portfolio are independent events. Compute the expected value of the random variable Z de?ned as the amount received by the investor at maturity from the entire portfolio.