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# Solution1-2 - FNA3117 Bank Management Semester 2 AY...

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Unformatted text preview: FNA3117, Bank Management Semester 2, AY 2009‐2010 Nan Li NUS Business School Solution to Class Assignment 1 1. (Diversification of Risk through Financial Intermediation) a) E(R) = ((11‐10)/10)*(0.95)+(0‐10)/10*0.05 = 4.5% σ(R) = [E(R‐E(R))2]1/2 = [(1/10‐0.045)2 *0.95 + (‐1 – 0.045)2* 0.05]1/2 = 0.24 b) There are three possible outcomes, States Prob. Total pay Both proj. succeed 0.95*0.95 = 0.9025 22m 11m One proj. succeeds, 2*0.95*0.05 = 0.095 one proj. fails Both proj. fail 0.05*0.05 = 0.0025 0m Since the returns on the projects are independent and identically distributed, the mean return of two projects is the same that of one project and the standard deviation is the standard deviation of a single project times the square root of ½, or can be calculated directly as E(R) = E[1/2*(R1+R2)] = E(R1) = 4.5% σ(R) = σ [1/2*(R1+R2)] = [1/4*σ2(R1)+ 1/4∗σ2(R2)]1/2 = [1/2σ2(R1)] ½ =1/√2 *σ(R1) = 0.17 c) In general if the returns on the projects are independent and identically distributed, the mean return of N projects is the same that of one project and the standard deviation is the standard deviation of a single project times the square root of 1/N E(R) = E[1/N*(R1+R2+…+ RN)] = E(R1) σ (R) = σ [1/N*(R1+R2+…+ RN)] =1/√N *σ (R1) As N goes to infinity, the expected return remains unchanged while the standard devation goes to zeros. That is, the return on the portfolio of the bank is risk free. d) The bank can reduce the risk of the investment by diversifying its investment in projects that are independent of each other, or at least not perfect correlated with each other. The more diversified is the portfolio of the bank, the less risky is the investment. e) The maximum rate of return this bank can offer is same as the risk‐free return on its portfolio, i.e. 4.5%, assuming the operational cost is zero and the bank is competitive. f) Let’s compare the expected utility of the investor of the two strategies: If he invests in one project: E(u) = 0.95*[10*(11) – 0.5*(11^2)]+ 0.05*[10*(0) – 0.5*(0^2)] = 47.025 If he invests in the one‐year CD, he will get a risk‐free payment of \$10.45m at the end of year 1 and this brings him the risk‐free utility of u = 10*(10.45) ‐ 0.5*(10.45)^2 = 49.899 > 47.025 1 FNA3117, Bank Management Semester 2, AY 2009‐2010 Nan Li NUS Business School Hence the investor would prefer the one‐year CD. g) The special role provided by the bank in this economy is to diversify the risk, provide liquidity and reduce price risk, hence improve the welfare of small investors. The risk associated includes: credit risk, liquidity risk, interest rate risk, market risk. 2. (A simple delegated monitor model) a) No, the small investor will not lend directly to the firm. If the small investor choose to invest and monitor the borrow, the expected net gain he would get is (120*0.9+100*0.1)‐120‐100 = ‐\$102 If he chooses to invest but not monitor, then his gain depends on the action of other investors. If any other investor monitors, he expects to get (120*0.9+100*0.1)‐100 = \$18 If no other investor monitors, he expects to get 100 ‐100 = \$0 The payoff the of the action of the small investor can be summarized in the following table others self Monitor Not monitor Monitor (-102 -102) (18 -102) Not monitor (-102, 18) (0, 0) Given the small investor do not know others’ action, it is optimum for him to not monitor. However, if no one monitors, the small investor expects to incur the loss, so no one will invest. b) If the small investors form a credit union and the lend to the borrower, then they can save the monitoring cost by send only one guy to monitor and spend only \$120, the expected return of investment is then [(120000*0.9+100000*0.1)‐120‐100000 ]/100000= 17.88% and this is what the small investor will get on their investment of \$100. 3. The main feature of the Riegle‐Neal Act of 1994 was the removal of barriers to interstate banking. In September 1995 bank holding companies were allowed to acquire banks in other states. In 1997, banks were allowed to convert out‐of‐state subsidiaries into branches of a single interstate bank. As a result, consolidations and acquisitions have allowed for the emergence of very large banks with branches across the country. 4. M1, measure the medium of exchange, the more narrowly defined measure, consists of the most liquid forms of money, namely currency and checkable deposits. M2, reflect the store‐of‐value function of money. Include M1, household holdings of savings deposits, small time deposits, and retail money market mutual funds (MMMF). 2 FNA3117, Bank Management Semester 2, AY 2009‐2010 Nan Li NUS Business School M3: includes close substitute for M2, large‐denomination time deposits, repurchase agreements (RPs), and Eurodollars. (discountinued) Over the past year, M1 increase by 5.9%, M2 increases by 3.1%. 12000 10000 8000 6000 M1 M2 M3 4000 2000 0 1/1/1959 1/1/1961 1/1/1963 1/1/1965 1/1/1967 1/1/1969 1/1/1971 1/1/1973 1/1/1975 1/1/1977 1/1/1979 1/1/1981 1/1/1983 1/1/1985 1/1/1987 1/1/1989 1/1/1991 1/1/1993 1/1/1995 1/1/1997 1/1/1999 1/1/2001 1/1/2003 1/1/2005 1/1/2007 1/1/2009 5. a. Panel A: Initial Balance Sheets Federal Reserve Bank Assets Liabilities Securities \$50m Reserve accounts \$50m ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ National Bank Assets Liabilities Loans \$450m Transaction deposits \$500m Reserve deposits \$50m at Fed 3 FNA3117, Bank Management Semester 2, AY 2009‐2010 Nan Li NUS Business School Panel B: Balance Sheet after All Changes Resulting from Decrease in Reserve Requirement Federal Reserve Bank Assets Liabilities Securities \$40.74m Reserve accounts \$40.74m ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ National Bank Assets Liabilities Loans \$468.52m Transaction deposits \$509.26m (\$509.26m ‐ \$40.74m) (\$500 + \$10*0.5 + \$10*0.5*0.5*0.92+…. = \$500m + \$5m/(1‐0.92*0.5)= \$509.26m or \$450+\$10+\$10*0.5*0.92+….` Reserve deposits at Fed \$40.74m (\$509.26mx .08) = \$40.74m b. Panel A: Initial Balance Sheets Federal Reserve Bank Assets Liabilities Securities \$50m Reserve accounts \$50m ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ National Bank Assets Liabilities Loans \$450m Transaction deposits \$500m Reserve deposits \$50m at Fed Panel B: Balance Sheet after All Changes Resulting from Decrease in Reserve Requirement Federal Reserve Bank 4 FNA3117, Bank Management Semester 2, AY 2009‐2010 Assets Nan Li NUS Business School Liabilities Securities \$44.88m Reserve accounts \$44.88m ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ National Bank Assets Liabilities Loans \$462.80m Transaction deposits \$507.68m (\$507.68m ‐ \$44.88m) or 450+10*0.75+10*0.75*0.6*0.92*0.75+… (\$500m + \$10m x .75*0.6+\$10m x .75*0.6*0.92*0.75*.06+…) =\$500m+\$4.5m/(1‐0.92*0.75*0.6) = \$7.68m = 450 + 7.5/(1‐0.92*0.75*0.6) = \$462.80m Reserve deposits at Fed 44.88m (required \$507.68m*0.08=\$40.61m, excess reserve = \$10m*0.25+\$10m*0.75*0.6*0.92*0.25+… = \$10m*0.25/(1‐0.92*0.75*0.6)=\$4.27m) 6. Bank Performance Evaluation: a) Net Interest Income Net Noninterest Income Pretax net operating income Net Income After Taxes Total Operating Income Total Operating Expenses Undivided Profit 0.85 *Total Interest Income Less Total Interest Expense -0.13 *Total Noninterest Income Less Total Noninterest Expense 0.62 *Net Interest Income Plus Net Noninterest Income less PLL 0.47 *Pretax net operating income less Taxes 3.17 *Interest Income Plus Noninterest Income 2.55 *Interest Expenses Plus Noninterest Expenses Plus PLL 0.36 Net Income After Taxes Less Dividends b) Total Assets Net Loans Investment Securities Depreciation Total Deposits 429 *Total Liabilities Plus Total Equity Capital 285 *Gross Loans Less Allowance for loan losses 33 *This is the only asset missing so subtract all other assets from total assets 5 *Gross Bank Premises and Equipment less net Bank Premises and Equipment 360 *Total Liabilities less Nondeposit Borrowings c) ROA = net income after tax/ total asset = 0.47/429 = 0.11% ROE = net income after tax/ total equity = 0.47/49 = 0.96% 5 FNA3117, Bank Management Semester 2, AY 2009‐2010 Nan Li NUS Business School Equity Multiplier = 429/49 = 8.76 Profit Margin = Net income/Total operating Income = 0.47/3.17 = 14.86% Interest Margin = Net Interest Income / Total Operating Income = 0.85/3.17 = 26.81% Asset Utilization = Total Operating Income/ Total Asset = 3.17/429 = 0.74% d) ROA 0.13% ROE 1.35% Asset Utilization 5.89% Interest Margin 44.15% Profit Margin 2.15% Equity Multiplier 10.66 Compared with the industry average at the end of 2008, we can see that the bank earns lower interest margin, ROA and ROE than the average, and has lower leverage (high Equity Multiplier). The asset utilization ratio is much lower than the industry average, which means that the assets, especially the interest bearing assets were not used efficiently. On the other hand, the profit margin of the bank is higher than the industry average, which implies that the bank did a better job in non‐interest income than the other banks in the industry. The industry on the average incurs huge non‐interest income loss in 2008, which can be implied by comparing interest margin and profit margin. e) 80.00% 60.00% 40.00% 20.00% ROA ROE Asset Utilization Interest Margin Profit Margin 0.00% 19 93 19 90 19 96 19 99 20 02 19 84 19 72 19 63 19 54 19 60 19 66 19 75 19 51 19 42 19 39 -20.00% -40.00% 19 36 19 45 19 48 19 57 19 69 19 81 19 78 19 87 20 05 The commercial banks enjoy a pretty good interest margin in postwar period and in 1990s. However, the profit margin drops during the 1970s 1980s, in particular during the saving and loans debacle and during the latest financial crisis. f) 6 FNA3117, Bank Management Semester 2, AY 2009‐2010 40.0% Nan Li NUS Business School 35.0% 30.0% 25.0% Real Estate Loans C&I Loans Consumer Loans Other Loans 20.0% 15.0% 10.0% 5.0% 0.0% 19 36 19 39 19 42 19 45 19 48 19 51 19 54 19 57 19 60 19 63 19 66 19 69 19 72 19 75 19 78 19 81 19 84 19 87 19 90 19 93 19 96 19 99 20 02 20 05 Increase in real estate loans and decrease in commercial and industry loans are obvious and this is partly due the competition from other financial service industry and securitization in late 90s and early 2000s. 7 ...
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