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Exam 2 Review

Exam 2 Review. Net Interest Margin (NIM). Given the following information: Assets $$ Rate Liabilities $$ Rate Rate sensitive 3000 10% Rate sensitive 2000 8% Non sensitive 1500 9% Non sensitive 2000 7% Non earning 500 Equity 1000

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Exam 2 Review

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  1. Exam 2Review

  2. Net Interest Margin (NIM) Given the following information: Assets$$RateLiabilities$$ Rate Rate sensitive300010%Rate sensitive20008% Non sensitive1500 9%Non sensitive 20007% Non earning500 Equity 1000 Total Assets 5000 Total Liabilities5000

  3. Net Interest Margin (NIM) Calculate the expected net interest income at current interest rates and assuming no change in the composition of the portfolio. What is the net interest margin? Assuming that all interest rates rise by 1%, calculate the new expected net interest income and net interest margin.

  4. Net Interest Margin (NIM) a. Net interest income = $3,000*.10+$1,500*.09-$2,000*.08 - $2,000*.07 = $435 - $300 = $135 Net interest margin = $135/$5000 = 0.027 = 2.7% b. Net interest income = $3,000*.11+$1,500*.09-$2,000*.09 - $2,000*.07 = $145 Net interest margin = $145/$5000 = 0.028 = 2.8%

  5. Duration The balance sheet of Capital Bank appears as follows: AssetsAmtDurationLiabilitiesAmt Duration ST Sec + ST and floating AdjRtlns 2206 mofunds560 6 mo Fxdratelns7008 yrsfxd rate funds27030 mo Non earn80 n/aEquity 170n/a TA 1000TL & Eq 1000

  6. Duration Calculate the duration of this balance sheet. Assuming that the required rate of return is 8 percent, what would be the effect on the bank’s net worth if interest rates increased by 1 percent? Suppose that the expected change in net worth is unacceptable to management. What outcome could management take to reduce this change?

  7. Duration The duration of assets is as follows: $220*.5years+$700*8years/$920=110+5600/920=6.2 years The duration of liabilities is as follows: $560*.5years+$270*2.5years/830=280+675/830=1.15 years The duration gap is: 6.2 years-(1.15yrs)*(830/920)=6.2-1.035 = 5.165 years The change in net worthE = -[ DA - DL (L/A)] * [R/(1+R)] * A

  8. Duration The change in net worth = E = -[ DA - DL (L/A)] * [R/(1+R)] * A E = -(5.165)*(.01/1.08) * 920 = -4.78% * 920 E = -4.78% * 920 E = -43.976 The bank could alter the duration of its assets and liabilities. Specifically, it could shorten the duration of assets and lengthen the duration of liabilities.

  9. Maturity Gap • Repricing of Book Values of Assets vs. Liabilities in common time periods • Pg. 5 of any output • Rate Sensitive Assets (RSAs) and Rate Sensitive Liabilities (RSLs) • 3, 6, 9 mo., 1 yr., 1-3 yrs., Over 3 yrs. • Idea is: (Gap = RSA – RSL) NII = Gap *  R

  10. Maturity Gap • Rates Go Up • Positive Gap  Increase NII • Negative Gap  Decrease NII • Rates Go Down • Positive Gap  Decrease NII • Negative Gap  Increase NII • Problems: • Ignores Market Value Changes • Ignores variation in intra-bucket value changes • Concentrates on single-period CF, not MV

  11. Duration Gap • Duration Weighted Assets and Liabilities • Managing the Change in Equity (Value) from a change in interest rates and their effect on Assets and Liabilities • Remember: Price = - D * r / (1 + YTM) * Price • Applied to Assets and Liabilities: A = - DA * R / (1 + R) * A L = - DL * R / (1 + R) * L

  12. Duration Gap • Then: E = A - L • E = -[ DA - DL (L/A)] * [R/(1+R)] * A Change in Equity is negative of difference in durations multiplied by interest rate change multiplied by asset base

  13. Duration Gap Your bank is exhibiting the following separations of rate sensitive assets and liabilities: Rate Sensitive Assets 1-90 91-180 181-270 271-1yrs 1yr-3yrs Over 3yrs Total Securities 787.62 787.62 Fed Funds Sold0 0 0 0 0 0 0 Loans2748.36 174.32124.29 115.35724.6803887.00 Total RSAs 3535.98174.32 124.29115.35 724.680 4674.62 Rate Sensitive Liabilities Demand Deposits117.450 0 0 171.32 984.25 1273.02 Time Deposits2753.54208116178 0 0 3255.54 Fed Funds Purchased 10.480 0 0 0 0 10.48 Capital Notes0.620.62 0.62 0.62 6.24 28.4637.18 Total RSLs 2882.09 208.62 116.62 178.62177.56 1012.714576.22

  14. Duration Gap and the duration values per time bucket are: 1-90 91-180 181-270 271-1yrs 1yr-3yrs Over 3yrs Duration RSAs0.25 0.35 0.420.6551.75 0 Duration RSLs0.12 0.32 0.46 0.7501.8 5.3 What is the expected change in Net Income if all rates jump 0.4%? Assume a tax rate of 30% What is the expected change in Equity Value if all rates drop 1.5%? Assume the market yield is 8%

  15. Duration Gap Total Maturity Gap = Total RSA - Total RSL= 4674.62 - 4576.22 =98.4 Change NII = Gap*interest rate change = 98.4 * +.004 =0.3936or +$393,600 Change NI=Change NII*(1-Tax Rate)=$393,600*(1-.30) =$275,520 if #'s in millions Duration of Assets (Liabilities) is duration-weighted bucket values divided by Total RSA D(A)=(.25*3535.98+.35*174.32+.42*124.29+.655*115.35 +1.75*724.68)/4674.62=0.50 D(L)=(.12*2882.09+.32*208.62+.46*116.62+.75*178.62 +1.8*177.56+5.3*1012.71)=1.374 Chg Eq = -[D(A) - D(L)*L/A]* Chg int rate / (1+YTM) *A= -[0.50 - 1.374*(4576.22/4674.62)] * -.015/1.08 * 4674.62=-54.8669or -$54.87 million (if #'s in millions)

  16. Duration Gap • Rates Go Up • Positive Duration Gap  Decrease Value • Negative Duration Gap  Increase Value • Rates Go Down • Positive Duration Gap  Increase Value • Negative Duration Gap  Decrease Value

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