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Exercise 1:

This exercise studies the diversification of default risk for corporate loans. A financial institution has 200,000 AUD for investment. There are 2 corporations available for investment. For each corporation a 100,000 AUD investment leads to a promised repayment repayment of 110,000 AUD. The default probability for each corporation is 10%. a) Calculate the expected repayment and the variance of the total repayment, when the corporation invests 200, 000 AUD in only one firm. b) The default events between the firms are independent. Calculate the expected repayment and the variance of the total repayment, when the corporation invests 100,000 AUD in both firms. c) Assume that the default probabilities of the two firms are positively correlated, how does this change your answer to question b)?

Exercise 2:

This exercise studies the diversification of withdrawal needs a) Consider two households, and each of them deposits 500 AUD with the financial institution. The probability for a household to withdraw its deposit over the next year is 25%. The household withdrawal needs are independent. Calculate the probability for the financial institution to have deposits of 0 AUD, 500 AUD, or 1000 AUD at the end of the year. b) Consider 4 households, and each of them deposits 250 AUD with the financial institution. The probability for a household to withdraw the deposit over the next year is 25%. Calculate the probability for the financial institution to have deposits of 0 AUD, 250 AUD, 500 AUD, 750 AUD or 1000 AUD at the end of the year. c) Compare the distribution of deposits in part a) and b). What do you notice?

Exercise 4:

a) Consider a financial institution which has assets of 100 million AUD with a maturity of 2 years and liabilities of 100 million AUD with a maturity of 5 years. Does this financial institution face refinancing risk or reinvestment risk? Which direction of interest rate changes leads to a reduction in the profitability of the financial institution? b) Consider a financial institution which has liabilities of 100 million AUD with a maturity of 2 years and assets of 100 million AUD with a maturity of 5 years. Does this financial institution face refinancing risk or reinvestment risk? Which direction of interest rate changes leads to a reduction in the profitability of the financial institution?

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