# Chapter 12 Practice Problems

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2 3. Using T-accounts, describe what happens when Jane Doe writes a \$50 check on her account at the First National Bank to pay her friend John Deer who in turn deposits the check in his account at the Second National Bank. First National Bank Required Reserves -5 Deposits -50 Excess Reserves -45 Second National Bank Required Reserves +5 Deposits +50 Excess Reserves +45 (assuming a required reserve ratio of 10%). Notice, this check does not change the total banking systems level of reserves or deposits. 4. What happens to reserves at the First National Bank if one person withdraws \$1,000 of cash and another deposits \$500 of cash? First National Bank Required Reserves -50 Deposits -500 Excess Reserves -450 (assuming a required reserve ratio of 10%). 5. The bank you own has the following balance sheet: Reserves \$75 m. Deposits \$500 m. Loans \$525 m. Bank Capital \$100 m. If the bank suffers a deposit outflow of \$50 m. with a required reserve ratio on deposits of 10%, what actions must you take to keep your bank from failing? Before taking any actions, the bank s balance sheet would be: Reserves \$25 m. Deposits \$450 m. Loans \$525 m. Bank Capital \$100 m. If the required reserve ratio is 10%, then this bank is violating its required reserve level by \$20 m. The bank can take four basic actions: 1. Borrow \$20 m. on the Federal Funds market in which case its balance sheet would be: Reserves \$45 m. Deposits \$450 m. Loans \$525 m. Bank Borrowings \$20 m. Bank Capital \$100 m.

3 2. Borrow \$20 m. from the Federal Reserve Discount Window in which case its balance sheet would be: Reserves \$45 m. Deposits \$450 m. Loans \$525 m. Federal Reserve \$20 m. Borrowings Bank Capital \$100 m. 3. Sell \$20 million of loans (or not renew \$20 million of loans that come due at the same time of the deposit outflow. Reserves \$45 m. Deposits \$450 m. Loans \$505 m. Bank Capital \$100 m. 4. While none exist on this bank s balance sheets, most banks hold other types of assets (e.g. treasury bills) which could be sold instead of loans. Doing so transforms one type of asset (a treasury bill) into another (reserves). All 4 choices involve a cost. Choices #1 and #2 raise the expenses of the bank and choices #3 and #4 reduce the bank s revenues. 6. If a deposit outflow of \$50 m. occurs, which balance sheet would a bank rather have initially, the balance sheet in Problem 5 or the following? Why? Reserves \$100 m. Deposits \$500 m. Loans \$500 m. Bank Capital \$100 m. A \$50 m. outflow in this bank leads immediately to the position of: Reserves \$50 m. Deposits \$450 m. Loans \$500 m. Bank Capital \$100 m. This bank still holds enough reserves to meet the required reserve level and therefore need not adjust its balance sheet any more. While this may appear to be good that it does not have to incur the additional expenses or loss of revenues that the bank in problem #5 did, it must be remembered that this bank also gave up earning interest on its assets prior to this withdrawal (notice, in order to hold a higher amount of reserves the bank in problem #6 held fewer interest bearing loans). Thus, while the surprise withdrawal outflow is painful for the bank of problem #5, it may have earned enough revenue from its increased prior lending that it ends up in a better position than that of bank #6. 7. What is the difference between insolvency and illiquidity? Insolvency occurs when bank assets are less than its liabilities. This is the traditional meaning of being bankrupt; an insolvent bank cannot meet all of its obligations because it does not own enough to do so. An illiquid bank is not insolvent in that an illiquid bank still has a positive net worth (its assets are equal to its liabilities + capital or, in other words, its capital is greater than zero). However, an illiquid bank does not have enough cash on hand to meet immediate depositor withdrawals. An illiquid bank can become liquid through borrowing from other banks

4 (which they are likely to do since the bank has positive net worth and can repay its loans) or through selling its assets. 8. If a bank falls short of its capital requirements, what can it do? It can raise capital through selling new shares of stock, cutting dividend payments (and increasing its retained earnings) or sell assets so the amount of capital relative to assets rises (remember, the capital requirements are stated in terms of a capital-to-asset ratio). In the recent months, the government has been injecting capital into banks by buying preferred stock on those banks (preferred stock are non-voting shares in a company that take precedence over common shares if the company goes bankrupt). 9. Why do banks require firms that it lends to keep compensating balances at the bank? Compensating balances can act as collateral for loans made by banks to those firms. They also help establish long-term customer relationships which make it easier for the bank to collect information about prospective borrowers, thus reducing the adverse selection problem. Compensating balances help the bank monitor the activities of a borrowing firms so that it can prevent the firm from taking on too much risk, thereby not acting in the interest of the bank. 10. Suppose that you are the manager of a bank whose \$100 billion of assets have an average duration of four years and whose \$90 billion of liabilities have an average duration of 2.5 years. Conduct a duration analysis for the bank and show what will happen to the net worth of the bank if interest rates rise by 2 percentage points. What actions could you take to reduce the bank s interest rate risk? The assets fall by \$8 billion (\$ ) and the value of the liabilities rise by \$4.5 billion (\$ ) so the bank s net worth (capital) is expected to decrease by \$3.5 billion. The interest rate risk can be reduced by shortening the maturity of the assets or by lengthening the maturity of the liabilities. Alternatively, you could engage in an interest-rate swap, in which you swap the interest earned on your assets with the interest on another bank s assets that have a duration of 2.5 years. 11. Suppose you are the manager of a bank that has \$15 million of fixed rate assets, \$30 million of rate sensitive assets, \$25 million of fixed rate liabilities and \$20 million of ratesensitive liabilities. Conduct a gap analysis for the bank and show what will happen to bank profits if interest rates rise by 5 percentage points. What action could you take to reduce the bank s interest rate risk? This bank s gap is \$10 million (\$30 rate sensitive assets - \$20 rate sensitive liabilities). An increase in interest rates by 5% will raise profits by \$500,000 (5% of the gap). While banks enjoy the higher profits, a decrease in interest rates would have reversed the profits into losses of equal amounts. To avoid this profit variability, this bank could have tried to increase the amount of interest rate sensitive liabilities it holds, decrease the rate sensitive assets it holds, or engage in an interest rate swap with another company. 12. A bank has issued a one-year certificate of deposit for \$5 million at an interest rate of 2 percent. With the proceeds, the bank has purchased a 2 year discount Treasury note that pays 4 percent. What risk does the bank face in entering into these transactions? At the end of one year, this bank will have to pay the CD holder \$5.1 million.

5 At the time of purchase, the bank would have spent \$5 million on a two year, 4% treasury bill. The face value of such a bill would be \$5 million = (FV)/( ) or \$5.408 million. However, this bank needs the money at the end of the first year. Notice, the bank does not know the current interest rate at the end of this year, so lets call it i. At the end of the year, the present value of the treasury bill would be: PV = \$5.408/(1+i). Since the bank needs \$5.1 million we can solve this to find the interest rate needed to allow the bank to sell the 2 year bill and gain \$5.1 million. (5.1 = 5.408/(1+i)) yields an i of.0603 or 6.03%. If interest rates remain below 6.03% at the end of the first year, then this bank can sell the 2 year bill and make the \$5.1 million payment. If the rate rises to above 6.03% then if the bank sells the 2 year bill it does not produce enough revenue to make the \$5.1 m. payment and must draw down bank capital to do so. The risk the bank faces in this case is interest rate risk; higher rates reduce bank profitability and lower rates increase it. One can see this approximately with duration analysis. The duration of the CD is 1 year and, using Macaulay s formula, the percent change in the value of the CD is equal to the percent change in interest rates times the duration. In this case, a one percentage point increase in the interest rate raises the value of the CD to the bank by 1%. Since the CD s face value is \$5 m. each one percentage point increase in interest rates raises the value of the CD by \$50,000. The duration of the t-note is 2 years so each one percentage point increase in interest rates reduces the value of the t-note by 2%, or \$100,000. Thus, for every one percentage point increase in interest rates, the net worth of the bank falls by \$50,000 (\$50,000 gain in liabilities less \$100,000 loss in assets). A two percent increase in rates (from 4% to 6%) will then decrease bank net worth by \$100,000. Notice, when rates are 4 percent on the two year note, the bank expects to earn about \$200,000 per year on the note. A rise in rates by 6 percent however, reduces the value of the note by \$100,000 per year to the bank and, given the bank also has to pay the CD owner \$100,000 at the end of one year, the increase in rates by 2% over that year eliminates the bank s added net worth it expected to get from the t-note had its interest rate remained unchanged. 13. Consider the balance sheets of Banks A and B. Which bank faces the greatest liquidity risk? Why? Bank A Reserves \$100 m. Deposits \$500 m. Loans \$500 m. Bank Capital \$100 m. Securities \$50 m. Borrowings \$50 m. Bank B Reserves \$60 m. Deposits \$500 m. Loans \$540 m. Bank Capital \$100 m. Securities \$50 m. Borrowings \$50 m. Bank B faces higher liquidity risk because a withdrawal of \$11.11 m. would eliminate all of its excess reserves and leave it with only required reserves. A withdrawal of any further amounts would then cause the bank to either sell its interest bearing securities and loans or pay interest on

6 borrowings from other banks or the Fed. The level of withdrawals required to put Bank B in a similar position is \$55.55 m. 14. Bank Y and Bank Z both have assets of \$1 billion. The return on assets for both banks is the same. Bank Y has liabilities of (not counting capital) of \$800 m. while Bank Z s are \$900 m. In which bank would you prefer to hold an equity stake? Explain. This depends. ROE = ROA EM where EM = /Equity. In the case of Bank Y, the EM is 5 (\$1 billion / \$200 m.). For bank Z, the EM is 10. Thus, the return on equity for Bank Z is twice that for Bank Y. In other words, for each dollar invested by owners in Bank Z, they expect to earn twice a high of rate of return as those who invested in Bank Y. However, because it holds less capital, Bank Z is more prone to insolvency since losses of \$100 m. in its assets would cause this bank to have less assets than liabilities + capital. This answer depends then on my risk-return preferences. If I am less risk averse then Bank Z would be preferable. If I were more risk averse, then Bank Y would look preferable (because it is less likely to fail).

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