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Tutorial 2 – Interest Rate Risk IPrepared for FINS 3630 students Prepared by Yufeng (Frank) YaoChapter 8 The repricing model This model is essentially a book value accounting cash flow analysis of the repricing gap between the interest income earned on an FI’s assets and the interest expense paid on its liabilities over a particular period of time. Rate-Sensitive Asset (RSA) & Rate- Sensitive Liability (RSL)Rate sensitivity means that assets or liabilities is repriced at or near current market interest rates within a certain time horizon. Reasons of repricing: Result of a rollover of an asset or liability (Short term investment)Asset or liability is a variable-rate instrument (floating rate loan) RSA < RSL: Refinancing risk: the cost of rolling over or reborrowing funds will rise above the returns being earned on asset investment. Expose to the risk of increasing interest rates RSA > RSLReinvestment risk: The returns on funds to be reinvested will fall below the cost of the funds. Expose to the risk of decreasing interest rates ΔNIIi=GAPiΔRi=RSAi-RSLiΔRiΔNIIi=Change in net interest income in maturity bucket i GAPi=RSAi-RSLiΔRi=Change in the level of interest rates Demand deposits and Passbook savings Demand deposits and passbook saving are not considered as rate-insensitive. The explicit interest rate paid on demand deposits is close to zero. DrawbacksIt ignores market value effects of interest rate changes:Repricing model only tell you about the net interest income which is cash flows. It tells you nothing about market value of assets and liabilities. It is over aggregative:It is very hard to define maturity buckets. Liabilities may be repriced toward the end of the bucket’s range. For example: Maturity bucket (3-4 months): Gap = 50 Maturity bucket (5-6 months): Gap = -50 Maturity bucket (6 months): Gap = 50+(-50) = 0The problem of runoffs: We assume that all consumer loans matured in 1 year or all mortgages matured in 30 years. FI continuously originates and retires consumer and mortgage loans as it creates and retires deposits. For example, some loans may be listed as 30-year mortgages, yet they will sometimes be prepaid early as mortgage holders refinance their mortgages and/ or sell their houses. Thus, the resulting proceeds will be reinvested at current market rates within the year. Cash flows from off-balance-sheet activities RSAs and RSLs used in the repricing model generally include only the assets and liabilities listed on the balance sheet. For example, FIs could hedge its interest rate risk with an interest rate futures contract. The futures produce a daily cash flow (marking to market process). The daily cash flow could affect the NII. Chapter 9 Duration Duration is weighted-average time to maturity of a security. Duration measure the interest rate sensitivityA key assumption of duration model is that the yield curve or the term structure of interest rates is flat and that when rates change, the yield curve shifts in a parallel fashion. The duration of zero-coupon bondsDB=MBThe duration of consol bonds (perpetuities)Mc=∞Dc=1+1RFeatures of duration Duration increases with the maturity of a fixed-income security, but at a decreasing rate. Duration decreases as the yield on a security increases. Duration decreases as the coupon or interest payment increases.ECQWhat is the repricing gap? In using this model to evaluate interest rate risk, what is meant by rate sensitivity? On what financial performance variable does the repricing model focus? Explain.The repricing gap is a measure of the difference between the dollar value of assets that will reprice and the dollar value of liabilities that will reprice within a specific time period, where repricing can be the result of a roll-over of an asset or liability (e.g., a loan is paid off at or prior to maturity and the funds are used to issue a new loan at current market rates) or because the asset or liability is a variable rate instrument (e.g., a variable rate mortgage whose interest rate is reset every quarter based on movements in a prime rate). Rate sensitivity represents the time interval where repricing can occur. The model focuses on the potential changes in the net interest income variable. In effect, if interest rates change, interest income and interest expense will change as the various assets and liabilities are repriced, that is, receive new interest rates. What is a maturity bucket in the repricing model? Why is the length of time selected for repricing assets and liabilities important when using the repricing model? Maturity bucket is the time window over which the dollar amounts of assets and liabilities are measured. Excessively short repricing period understates the rate sensitivity of the balance sheet. Excessively long repricing period overstate the rate sensitivity of the balance sheet. It is over aggregativeThe maturity bucket is the time window over which the dollar amounts of assets and liabilities are measured. The length of the repricing period determines which of the securities in a portfolio are rate-sensitive. The longer the repricing period, the more securities either mature or will be repriced, and, therefore, the more the interest rate risk exposure. An excessively short repricing period omits consideration of the interest rate risk exposure of assets and liabilities are that repriced in the period immediately following the end of the repricing period. That is, it understates the rate sensitivity of the balance sheet. An excessively long repricing period includes many securities that are repriced at different times within the repricing period, thereby overstating the rate sensitivity of the balance sheet. What is the CGAP effect? According to the CGAP effect, what is the relation between changes in interest rates and changes in net interest income when CGAP is positive? When CGAP is negative?CGAP effect describe the relationship between changes in interest rates and changes in net interest income.CGAP > 0, RSA > RSL, expose to reinvestment risks. CGAP < 0, RSA < RSL, expose to refinancing risks. The CGAP effect describes the relation between changes in interest rates and changes in net interest income. According to the CGAP effect, when CGAP is positive the change in NII is positively related to the change in interest rates. Thus, an FI would want its CGAP to be positive when interest rates are expected to rise. According to the CGAP effect, when CGAP is negative the change in NII is negatively related to the change in interest rates. Thus, an FI would want its CGAP to be negative when interest rates are expected to fall. If a bank manager was quite certain that interest rates were going to rise within the next six months, how should the bank manager adjust the bank’s six-month repricing gap to take advantage of this anticipated rise? What if the manger believed rates would fall in the next six months.134388638926489293277R NII , if CGAP > 0 1261499571564579512024R NII , if CGAP < 0 When interest rates are expected to rise, a bank should set its repricing gap to a positive position. In this case, as rates rise, interest income will rise by more than interest expense. The result is an increase in net interest income. When interest rates are expected to fall, a bank should set its repricing gap to a negative position. In this case, as rates fall, interest income will fall by less than interest expense. The result is an increase in net interest income. Calculate the value of MMC’s rate-sensitive assets, rate sensitive liabilities, and repricing gap over the next year.RSA: 2, 4, 5, 8, 62.5 + 37.5 + 43.75+50 = 193.75 RSL: 4, 5, 6, 7, 50+ 25+ 75+ 25 = 175 b). Calculate the expected change in the net interest income for the bank if interest rates rise by 1 percent on both RSAs and RSLs. If interest rates fall by 1 percent on both RSAs and RSLs.CGAP = 193.75 – 175 = 18.75 ΔNII=18.75 * 0.01 = 187,500 ΔNII=18.75 * -0.01 = -187,500 C). Calculate the expected change in the net interest income for the bank if interest rates rise by 1.2 percent on RSAs and by 1 percent on RSLs. If interest rates fall by 1.2 percent on RSAs and by 1 percent on RSLs.ΔNII=193.75*0.012-175*0.01=575, 000ΔNII=193.75*-0.012-175*-0.01=-26325000+1750000=-24575000 1). 30 days: RSA = 72 RSL = 170 GAP = -95 2). 3 months: RSA = 75 + 75 = 150 RSL = 170 GAP = -20 3). 2 years: RSA = 75 + 75 + 50 + 25 = 225RSL = 170 GAP = 55 b. What is the impact over the next 30 days on net interest income if interest rates increase 50 basis points? Decrease 75 basis points? ΔNII=-95*0.005 ΔNII=-95*-0.075 c). The following one-year runoffs are expected: $10 million for two-year T-notes and $20 million for eight-year T-notes. What is the one-year repricing gap?RSA = 75 + 75 + 10 + 20 +25 = 205 RSL = 170 CGAP = 35 d). If runoffs are considered, what is the effect on net interest income at year-end if interest rates increase 50 basis points? Decrease 75 basis points?35 * 0.005 = 0.175 35* -0.0075 = -0.2625 Chapter 9 questions What are the two different general interpretations of the concept of duration, and what is the technical definition of this term? How does duration differ from maturity?Duration measures the weighted-average life of an asset or liability in economic terms. As such, duration has economic meaning as the interest rate sensitivity (or interest elasticity) of an asset’s value to changes in the interest rate. Duration differs from maturity as a measure of interest rate sensitivity because duration takes into account the time of arrival and the rate of reinvestment of all cash flows during the assets life. Technically, duration is the weighted-average time to maturity using the relative present values of the cash flows as the weights.A one-year, $100,000 loan carries a coupon rate and a market interest rate of 12 percent. The loan requires payment of accrued interest and one-half of the principal at the end of six months. The remaining principal and accrued interest are due at the end of the year.a). What will be the cash flows at the end of six months and at the end of the year? b). What is the present value of each cash flow discounted at the market rate? What is the total present value?c). What proportion of the total present value of cash flows occurs at the end of six months? What proportion occurs at the end of the year?d). What is the duration of this loan? ................
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