Exam 2 Review

Net Interest Margin (NIM) Given the following information: Assets $$ Rate Liabilities $$ Rate Rate sensitive % Rate sensitive % Non sensitive % Non sensitive % Non earning 500 Equity 1000 Total Assets 5000 Total Liabilities 5000

Net Interest Margin (NIM) Calculate the expected net interest income at current interest rates and assuming no change in the composition of the portfolio. 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.

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

Duration The balance sheet of Capital Bank appears as follows: Assets Amt Duration Liabilities Amt Duration ST Sec + ST and floating Adj Rt lns mo funds mo Fxdratelns yrs fxd rate funds mo Non earn 80 n/a Equity 170 n/a TA 1000 TL & Eq 1000

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?

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

Duration The change in net worth =  E = -[ D A - D L (L/A)] * [  R/(1+R)] * A  E = -(5.165)*(.01/1.08) * 920 = -4.78% * 920  E = -4.78% * 920  E = 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.

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

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

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

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

Duration Gap Your bank is exhibiting the following separations of rate sensitive assets and liabilities: Rate Sensitive Assets yrs 1yr-3yrs Over 3yrs Total Securities Fed Funds Sold Loans Total RSAs Rate Sensitive Liabilities Demand Deposits Time Deposits Fed Funds Purchased Capital Notes Total RSLs

Duration Gap and the duration values per time bucket are: yrs 1yr-3yrs Over 3yrs yrs 1yr-3yrs Over 3yrs Duration RSAs Duration RSLs 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%

Duration Gap Total Maturity Gap = Total RSA - Total RSL = = 98.4 Change NII = Gap*interest rate change = 98.4 * = or +$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 divided by Total RSAD(A)=(.25* * * * *724.68)/ = *724.68)/ =0.50D(L)=(.12* * * * * * )= * * )= Chg Eq = -[D(A) - D(L)*L/A]* Chg int rate / (1+YTM) *A = -[ *( / )] * -.015/1.08 * = or -$54.87 million (if #'s in millions)

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