Consider a CDO with a total notional of $500 million, consisting of three tranches: Senior (75%), Mezzanine (15%), and Equity (10%). The underlying portfolio has a total expected loss of 6%. a. Calculate the expected losses for each tranche, assuming they follow the standard tranche subordination rules. b. If the actual realized losses are 30%, determine the losses allocated to each tranche. c. Plot a graph that shows how the payoff of the holders to the Mezzanine tranche owners varies with the value of the assets in the mortgage pool at the time of maturity. d. Represent this payoff as a combination of payoffs of options and risk-free debt for Mezzanine tranche. e. Suppose the CDO manager decides to create a fourth tranche, called the Super- Senior tranche, which has the highest priority in the cash flow waterfall. If the Super-Senior tranche is sized at 50% of the total notional, recalculate the expected losses for all tranches. (hint: Super- Senior tranche is created out of Senior tranche). f. Explain how the inclusion of the Super-Senior tranche impacts the risk profile of the other tranches, particularly the Senior tranche.