23*. The balance sheet for Gotbucks Bank, Inc. (GBI), is presented below ($ millions): Assets Liabilities and equity Cash $30 Core deposits $20 Interbank $20 Interbank borrowing $50 lending Loans (floating) $105 Euro CDs $130 Loans (fixed) $65 Equity $20 Total assets $220 Total liabilities and $220 equity Notes to the balance sheet: The interbank cash rate is 8.5 per cent, the floating loan rate is (BBR+4 per cent), and currently BBR is 11 per cent. Fixed rate loans have five-year maturities, are priced at par, and pay 12 per cent annual interest. The principal is repaid at maturity. Core deposits are fixed rate for two years at 8 per cent paid annually. The principal is repaid at maturity. Euro CDs currently yield 9 per cent. (a) What is the duration of the fixed-rate loan portfolio of Gotbucks Bank? (b) If the duration of the floating-rate loans and interbank lending is 0.36 year, what is the duration of GBI's assets? ) What is the duration of the core deposits if they are priced at par? (d) If the duration of the Euro CDs and Interbank borrowings is 0.401 year, what is the duration of GBI's liabilities? (e) What is GBI's duration gap? What is its interest rate risk exposure? (f) What is the impact on the market value of equity if the relative change in all interest rates is an increase of 1 per cent (100 basis points)? Note that the relative change in interest rates is AR/(1+R)=0.01. What is the impact on the market value of equity if the relative change in all interest rates is a decrease of 0.5 per cent (-50 basis points)? (h) What variables are available to GBI to immunise the bank? How much would each variable need to change to get DGAP equal to zero? Problem 7 Consider Chapter 6, Q23 of your textbook (which was discussed in Tutorial Questions). Consider using a repricing gap model for the bank in this question. (i) Create a similar table to the one below (which is from the lecture notes example): Assets Liabilities Gaps CGap 1 day $10 $40 -$30 -$30 1 day to 3 months 25 50 -25 -55 3 to 6 months 50 60 -10 -65 6 to 12 months 30 35 -5 -70 1 to 5 years 70 5 +65 -5 Over 5 years 10 5 +5 0 $195 $195 0 (ii) Calculate the change in net interest income for each bucket assuming a 1% increase in interest rates for all assets and liabilities (when they are repriced). (iii) Calculate the change in net interest income if all assets and liabilities that can be repriced within the next year are subject to a 1% increase in interest rates. (iv) Explain carefully whether the problem of runoffs is relevant for this bank. 23*. The balance sheet for Gotbucks Bank, Inc. (GBI), is presented below ($ millions): Assets Liabilities and equity Cash $30 Core deposits $20 Interbank $20 Interbank borrowing $50 lending Loans (floating) $105 Euro CDs $130 Loans (fixed) $65 Equity $20 Total assets $220 Total liabilities and $220 equity Notes to the balance sheet: The interbank cash rate is 8.5 per cent, the floating loan rate is (BBR+4 per cent), and currently BBR is 11 per cent. Fixed rate loans have five-year maturities, are priced at par, and pay 12 per cent annual interest. The principal is repaid at maturity. Core deposits are fixed rate for two years at 8 per cent paid annually. The principal is repaid at maturity. Euro CDs currently yield 9 per cent. (a) What is the duration of the fixed-rate loan portfolio of Gotbucks Bank? (b) If the duration of the floating-rate loans and interbank lending is 0.36 year, what is the duration of GBI's assets? ) What is the duration of the core deposits if they are priced at par? (d) If the duration of the Euro CDs and Interbank borrowings is 0.401 year, what is the duration of GBI's liabilities? (e) What is GBI's duration gap? What is its interest rate risk exposure? (f) What is the impact on the market value of equity if the relative change in all interest rates is an increase of 1 per cent (100 basis points)? Note that the relative change in interest rates is AR/(1+R)=0.01. What is the impact on the market value of equity if the relative change in all interest rates is a decrease of 0.5 per cent (-50 basis points)? (h) What variables are available to GBI to immunise the bank? How much would each variable need to change to get DGAP equal to zero? Problem 7 Consider Chapter 6, Q23 of your textbook (which was discussed in Tutorial Questions). Consider using a repricing gap model for the bank in this question. (i) Create a similar table to the one below (which is from the lecture notes example): Assets Liabilities Gaps CGap 1 day $10 $40 -$30 -$30 1 day to 3 months 25 50 -25 -55 3 to 6 months 50 60 -10 -65 6 to 12 months 30 35 -5 -70 1 to 5 years 70 5 +65 -5 Over 5 years 10 5 +5 0 $195 $195 0 (ii) Calculate the change in net interest income for each bucket assuming a 1% increase in interest rates for all assets and liabilities (when they are repriced). (iii) Calculate the change in net interest income if all assets and liabilities that can be repriced within the next year are subject to a 1% increase in interest rates. (iv) Explain carefully whether the problem of runoffs is relevant for this bank