BANK CAPITAL AND SOLVENCY RISKS

Bank capital and solvency risks:given balance sheet,Retail deposits rateBonds and other long term loans rateShort term wholesale loans rate.1. What is the probability that the bank is insolvent a year ahead?2. What is the expected or average return on the equity over the year? (remember the shareholders have limited liability so this calculation is not straightforward and you definitely cannot do it with a pocket calculator!).3. Devise a fair scheme to pay the holders of all the debt of the bank if the bank is insolvent. (Take note of the fact that there are three types of debt and each has been promised a different interest rate and each has provided a different amount of debt).4. Assuming that there was no change in the return promised on all types of funding or in the returns on assets, how much of the deposits of the bank would need to switched to equity funding for the chances of insolvency to be halved?5. Could the situation described in question 4 be an equilibrium? If it is not an equilibrium what might change?
Bank capital and solvency risks:Here is a simplified balance sheet for a large bank: (£ billions)Assets: Liabilities:Loans: £1050 Equity £60Financial assets £425 retail deposits £950Physical assets £15 bonds and other long term debt £290Reserves at the central bank £25 short term wholesale borrowing £215
The annual interest rates the bank offers on its liabilities are:Retail deposits: 3%?Bonds and other long term loans: 5%?Short term wholesale loans: 4%These are the promised interest rates if there is a chance of insolvency the expected rates of return on these forms of debt finance will be lower. Shareholders have limited liability (their equity can be worth no less than zero).The expected value of the return on the assets is 6%. Suppose that the total value of the assets a year ahead is normally distributed around its expected value and has a standard deviation of £60 billion.1. What is the probability that the bank is insolvent a year ahead? ?2. What is the expected or average return on the equity over the year? (remember the shareholders have limited liability so this calculation is not straightforward and you definitely cannot do it with a pocket calculator!). ?3. Devise a fair scheme to pay the holders of all the debt of the bank if the bank is insolvent. (Take note of the fact that there are three types of debt and each has been promised a different interest rate and each has provided a different amount of debt). ?4. Assuming that there was no change in the return promised on all types of funding or in the returns on assets, how much of the deposits of the bank would need to switched to equity funding for the chances of insolvency to be halved? ?5. Could the situation described in question 4 be an equilibrium? If it is not an equilibrium what might change? ?

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