1 Public Affairs 974-001 Menzie D. Chinn Fall 2010 Social Sciences 7418 University of Wisconsin-Madison Problem Set 3 Answers Due in lecture on Wednesday, December 8th. 1. Suppose the bank you own has the following balance sheet, in millions: Assets Liabilities Reserves $1600 Deposits $10000 Loans $10400 Bank Capital $2000 If the bank suffers a deposit outflow of $1 billion with a required reserve ratio on deposits of 10%, what actions must you take to keep you bank from failing? Answer: Required reserves: 10% of $10000 = $1000 Excess reserve: $1600-$1000 = $600 Deposit outflow of $1 billion. Balance sheet becomes: Required reserves: 10% of $9000 = $900 Excess reserve: $600-$900= -$300 Insufficient reserves. To eliminate shortfall the bank has 4 basic options to acquire reserves to meet deposit outflow: 1. borrowing them from other banks in the Fed funds market or corporations (cost: interest rates on the loans) 2. sell some of its securities (cost: transaction costs) 3. borrowing from the Fed (cost: 1.interest rate on loan; 2. non-explicit cost of increased scrutiny and Fed’s discouragement of too much borrowing) 4. reducing loans by this amount (cost: lose customers, very costly) Option 1: Assets Liabilities Reserves $900 Deposits $9000Loans $10400 Borrowing from other banks or corporations$300 Bank Capital $2000 Option 2: no securities owned Assets Liabilities Reserves $600 Deposits $9000Loans $10400 Bank Capital $20002 Option 3: Assets Liabilities Reserves $900 Deposits $9000Loans $10400 Discount loans from Fed $300 Bank Capital $2000 Option 4: Assets Liabilities Reserves $900 Deposits $9000Loans $10100 Bank Capital $2000 2. Consider these two banks, which are the same size in terms of assets. Suppose further that the return on assets (ROA) is 2%. High Capital Bank Low Capital Bank Assets Liabilities Assets Liabilities Reserves $10 Deposits $90 Reserves $10 Deposits $96 Loans $90 Bank Capital $10 Loans $90 Bank Capital $4 2.1 Calculate the ROE for each bank. Answer: For high capital bank: ROE = (net profit after taxes)/(equity capital) = ROA*EM EM = (assets)/(equity capital) = $100/$10 = 10 ROE = 2%*10=20% For low capital bank: ROE = (net profit after taxes)/(equity capital) = ROA*EM EM = (assets)/(equity capital) = $100/$4 = 25 ROE = 2%*25=50% 2.2 What is the advantage of being a high capital bank? Answer: The likelihood of having a shock to assets that makes the bank go insolvent is reduced.3 2.3 Is either of the banks more susceptible to liquidity problems? Answer: Not clear. 3. Consider the case of a manager of a bank that is attempting to reduce the risk associated with interest rate changes. The bank has $30 million of fixed-rate assets, $20 million of rate-sensitive assets, $10 million of fixed-rate liabilities, and $40 million of rate-sensitive liabilities. If the bank manager conducts a gap analysis for the bank, show what would happen to bank profits if interest rates rise by 2 percentage points. What actions could the bank manager take to reduce the bank’s interest rate risk, if he/she so decided? Answer: The sensitivity of bank profits to changes in interest rates is given by (rate-sensitive assets – rate-sensitive liabilities)* (change in interest rates) ($20-$30)*(2%) = -$10*2%=-$10*0.02=-$0.2 If interest rates rise by 2% the bank’s profits falls by $0.2 million. Actions to reduce bank’s interest rate risk: 1. shorten the duration of the bank’s assets to increase their rate sensitivity 2. lengthen the duration of the bank’s liabilities to reduce their rate sensitivity 4. Consider the balance sheet of the Fed. 4.1 If the return on loans and Treasury securities rise, what will happen to the money supply, holding all else constant. Explain the mechanism for this effect. Answer: Banks will then tend to lend out more of their reserves; this will increase deposits, and hence money supply. 4.2 What could the Fed do in order to control the money supply? Answer: The Fed could either reduce reserves, or increase the interest rate paid on reserves. The former entails reducing the asset side as well (selling T-bills, bonds, or MBS), while the latter would entail higher payments by the Fed. 5. The Taylor rule. Collect monthly data on the Fed funds rate, inflation, real GDP and potential GDP, and unemployment, over the 1987Q1-2010Q2 period. Potential GDP can be retrieved from here: http://www.cbo.gov/ftpdocs/117xx/doc11705/KeyAssumptionsPotentialGDP.xls . 5.1 Estimate the Taylor rule, using the output gap. Define interest rate as Fed Funds rate, inflation as annualized quarter-on-quarter core PCE inflation (calculated using logs), output gap is log ratio of real output to CBO potential, Gaps, interest and inflation rates expressed in decimal terms. 󰇛󰇜 󰇛󰇜 󰇛1󰇜󰇛󰇜 Dependent Variable: FEDFUNDS1 Method: Least Squares Date: 12/03/10 Time: 22:024 Sample: 1986Q1 2010Q3 Included observations: 99 Variable Coefficient Std. Error t-Statistic Prob. C 0.016706 0.003670 4.551575 0.0000 GAP 0.531157 0.059948 8.860334 0.0000 INFLPCE_CORE 1.320172 0.136032 9.704896 0.0000 R-squared 0.669425 Mean dependent var 0.045001 Adjusted R-squared 0.662538 S.D. dependent var 0.024207 S.E. of regression 0.014062 Akaike info criterion -5.660830 Sum squared resid 0.018983 Schwarz criterion -5.582190 Log likelihood 283.2111 Hannan-Quinn criter. -5.629012 F-statistic 97.20158 Durbin-Watson stat 0.425421 Prob(F-statistic) 0.000000 Using the second equation, one can see that δ = 0.32, β = 0.53. The regression estimates imply that 0.017  . With the target inflation rate at 2% (0.02), 0.017   0.32  0.02 Or, the natural rate of interest equals 0.023, or 2.3%. 5.2 Estimate the Taylor rule, using the unemployment gap. Use this equation: 󰇛1󰇜󰇛󰇜 Where γ < 0, u is the unemployment rate in decimal form. In order to estimate this, one has to get the unemployment gap. I estimate the natural rate