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The credit-worthiness of debt issued by companies is assessed at the end of each year by a credit rating agency. The ratings are A (the most credit-worthy), B and D (debt defaulted). Historical evidence supports the view that the credit rating of a debt can be modelled as a Markov chain with the following matrix of one-year transition probabilities: 0.92 0.05 0.03 X = 0.05 0.85 0.1 0 (i) Determine the probability that a company rated A will never be rated B in the future. [2] (ii) (a) Calculate the second order transition probabilities of the Markov chain. (b) Hence calculate the expected number of defaults within the next two years from a group of 100 companies, all initially rated A. [2] The manager of a portfolio investing in company debt follows a "downgrade trigger" strategy. Under this strategy, any debt in a company whose rating has fallen to B at the end of a year is sold and replaced with debt in an A-rated company. (iii) Calculate the expected number of defaults for this investment manager over the next two years, given that the portfolio initially consists of 100 A-rated bonds. [2] (iv) Comment on the suggestion that the downgrade trigger strategy will improve the return on the portfolio. [2] [Total 8]