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BUFN 722

BUFN 722. ch-8 Interest Rate Risk Re-pricing model; Maturity Model. Overview. This chapter discusses the interest rate risk associated with financial intermediation: Federal Reserve policy Repricing model Maturity model Duration model *Term structure of interest rate risk

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BUFN 722

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  1. BUFN 722 ch-8 Interest Rate Risk Re-pricing model; Maturity Model BUFN722- Financial Institutions

  2. Overview • This chapter discusses the interest rate risk associated with financial intermediation: • Federal Reserve policy • Repricing model • Maturity model • Duration model • *Term structure of interest rate risk • *Theories of term structure of interest rates BUFN722- Financial Institutions

  3. M1, etc WSJ Fri 2/8/02 p. C14 Federal Reserve Data - Monetary Aggregates (daily average in $bil) • one week ended Jan 28 2002 Jan 21 change • M1 s.a. 1186.8 1185.1 + • M2 s.a. 5462.1 5465.3 - $___ bil • M3 s.a. 8060.9 8047.6 + $___ bil • 2 weeks ended Feb 6 ’02 Jan. 23 • Total Reserves(2 wks ended 2/6/02& 1/21) 43,359 42,024 • Nonborrowed reserves (sa) 43,333 41,996 • Required reserves 42,002 40,775 • Excess reserves 1,356 1,270 • Borrowings from Fed (nsa) 26 28 • Free reserves (nsa) 1,330 1,242 • Monetary base 641,008 642,662 BUFN722- Financial Institutions

  4. M1, etc WSJ Fri 9/28/01 p. C15 Federal Reserve Data - Monetary Aggregates (daily average in $bil) • one week ended Sep 17 Sep 10 change • M1 s.a. 1254.2 1139.4 + • M2 s.a. 5480.0 5315.5 + $174.5 bil • M3 s.a. 7865.8 7701.7 + $___ bil • 2 weeks ended Sep 19 ’01 Sep. 5 • Total Reserv(2 wks ended 9/19/01& 9/5) 76,773 40,236 • Nonborrowed reserves (sa) 70,057 40,080 • required reserves 37,741 38,705 • excess reserves 39,032 1,530 • borrowings from Fed (nsa) 6,717 156 • Free reserves (nsa) 32,315 1,374 • Monetary base 658,484 618,772 BUFN722- Financial Institutions

  5. ER & NBR & NFR & Fed Funds • NBR- when high, banks reluctant to lend or buy new investments • loans at Fed discount window < 15 days • so must accumulate ER to repay Fed- so not lend or invest • if bank lends ER to another bank for short period of time, it sells Fed Funds to it & transfers some of its reserve deposits to the borrowing bank through the Fed’s wire transfer system • The next day, selling bank will get its reserve deposits back when the borrowing bank repays the Fed Funds loan plus interest (at Fed Funds rate) by redepositing money in selling banks reserve deposit at the Fed • “Fed funds sold” are lent to other bank - so no longer avail to meet bank’s reserve requirements & not part of that bank’s Reserves • if not sell ER to another bank, can lend them or buy securities - if ER high, banks may be more willing to lend - so interest rates may fall • banks with ER will not lend freely if have borrowed from Fed & need to repay that debt - so analysts may look at NFR (net free reserves) = ER-BR - not just ER BUFN722- Financial Institutions

  6. History of Fed Policy Procedures • Targeting Monetary Aggregates: 1970s • 1. Fed funds rate as operating target with narrow band • 2. Procyclical Ms • New Operating Procedures: 1979-82 • 1. De-emphasis on fed funds rate • 2. Non-borrowed reserves operating target • 3. Fed still using interest rates to affect economy & inflation • De-emphasis of Monetary Aggregates: 1982 -Early 1990s • 1. Borrowed Reserves (DL) operating target • Fed Funds Targeting Again • 1. since 1994, Fed funds target now announced – “Transparency” • International Considerations • 1. M in 1985 to lower exchange rate, M in 1987 to raise it • 2. International policy coordination BUFN722- Financial Institutions

  7. Inflation Targeting • Lessons from Monetary Targeting • 1. Success requires correcting overshoots • 2. Operating procedures not critical • 3. Breakdown of relationship between M and goals made M-targeting untenable: Led to inflation targeting • Inflation Targeting: New Zealand, U.K., Canada, ECB • 1. Announcement of numerical π goal • 2. Commitment to price stability • 3. Communication with "Inflation Report" • Lessons from Inflation Targeting • 1. Decline in π still led to output loss • 2. Worked to keep π low • 3. Kept π in public eye: reduced political pressures for inflationary policy BUFN722- Financial Institutions

  8. Central Bank Independence • Factors making Fed independent • 1. Members of Board have long terms • 2. Fed is financially independent: This is most important • Factors making Fed dependent • 1. Congress can amend Fed legislation • 2. President appoints Chairmen and Board members and can influence legislation • Overall: Fed is quite independent • Other Central Banks • 1. Bank of Canada and Bank of Japan: fair degree of independence, but not all on paper • 2. Bank of England and Bank of Japan made more independent in 1997 and 1998, respectively. • 3. European Central Bank most independent • 4. Trend to greater independence

  9. Explaining Central Bank Behavior • Theory of Bureaucratic Behavior • 1. Is an example of principal-agent problem • 2. Bureaucracy often acts in own interest • Implications for Central Bank Behavior: • 1. Act to preserve independence • 2. Try to avoid controversy: often plays games • 3. Seek additional power over banks BUFN722- Financial Institutions

  10. Explaining Central Bank Behavior • Should Fed Be Independent? • Case For: • 1. Independent Fed likely has longer run objectives, politicians don't: evidence is that get better policy outcomes • 2. Avoids political business cycle • 3. Less likely budget deficits will be inflationary • Case Against: • 1. Fed may not be accountable • 2. Hinders coordination of monetary & fiscal policy • 3. Fed has often performed badly BUFN722- Financial Institutions

  11. Using a Fed Watcher • Do we need a Fed watcher if “transparency”? • Fed watcher predicts monetary tightening, i 1. Acquire funds at current low i 2. Buy $ in FX market • Fed watcher predict monetary loosening, i 1. Make loans now at high i 2. Buy bonds, price rise in future 3. Sell $ in FX market BUFN722- Financial Institutions

  12. International Monetary Policiesand Strategies • Foreign Exchange Intervention • commitments between countries about the institutional aspects of their intervention in the foreign exchange markets • similar to open market purchases and sales of Treasury securities BUFN722- Financial Institutions

  13. Central Bank Policy and Interest Rate Risk • Japan: March 2001 announced it would no longer target the uncollateralized overnight call rate. • New target: Outstanding current account balances at BOJ • Targeting of bank reserves in U.S. proved disastrous BUFN722- Financial Institutions

  14. Central Bank and Interest Rate Risk • Effects of interest rate targeting. • Lessens interest rate risk • October 1979 to October 1982, nonborrowed reserves target regime. • Implications of return to reserves target policy: • Increases importance of measuring and managing interest rate risk. BUFN722- Financial Institutions

  15. Federal Funds Rate and Money Growth Before and After October 1979 BUFN722- Financial Institutions

  16. Repricing Model • Repricing or funding gap model based on book value. • Contrasts with market value-based maturity and duration models recommended by the Bank for International Settlements (BIS). • Rate sensitivity means time to repricing. • Repricing gap is the difference between the rate sensitivity of each asset and the rate sensitivity of each liability: RSA - RSL. BUFN722- Financial Institutions

  17. Maturity Buckets • Commercial banks must report repricing gaps for assets and liabilities with maturities of: • One day. • More than one day to three months. • More than 3 three months to six months. • More than six months to twelve months. • More than one year to five years. • Over five years. BUFN722- Financial Institutions

  18. Repricing Gap Example AssetsLiabilitiesGap Cum. Gap 1-day $ 20 $ 30 $-10 $-10 >1day-3mos. 30 40 -10 -20 >3mos.-6mos. 70 85 -15 -35 >6mos.-12mos. 90 70 +20 -15 >1yr.-5yrs. 40 30 +10 -5 >5 years 10 5 +5 0 BUFN722- Financial Institutions

  19. Applying the Repricing Model • DNIIi = (GAPi) DRi = (RSAi - RSLi) Dri Example: In the one day bucket, gap is -$10 million. If rates rise by 1%, DNIIi = (-$10 million) × .01 = -$100,000. BUFN722- Financial Institutions

  20. Applying the Repricing Model • Example II: If we consider the cumulative 1-year gap, DNIIi = (CGAPi) DRi = (-$15 million)(.01) = -$150,000. BUFN722- Financial Institutions

  21. Rate-Sensitive Assets • Examples from hypothetical balance sheet: • Short-term consumer loans. If repriced at year-end, would just make one-year cutoff. • Three-month T-bills repriced on maturity every 3 months. • Six-month T-notes repriced on maturity every 6 months. • 30-year floating-rate mortgages repriced (rate reset) every 9 months. BUFN722- Financial Institutions

  22. Rate-Sensitive Liabilities • RSLs bucketed in same manner as RSAs. • Demand deposits and passbook savings accounts warrant special mention. • Generally considered rate-insensitive (act as core deposits), but there are arguments for their inclusion as rate-sensitive liabilities. BUFN722- Financial Institutions

  23. CGAP Ratio • May be useful to express CGAP in ratio form as, CGAP/Assets. • Provides direction of exposure and • Scale of the exposure. • Example: • CGAP/A = $15 million / $270 million = 0.56, or 5.6 percent. BUFN722- Financial Institutions

  24. Equal Changes in Rates on RSAs and RSLs • Example: Suppose rates rise 2% for RSAs and RSLs. Expected annual change in NII, NII = CGAP ×  R = $15 million × .01 = $150,000 With positive CGAP, rates and NII move in the same direction. BUFN722- Financial Institutions

  25. Unequal Changes in Rates • If changes in rates on RSAs and RSLs are not equal, the spread changes. In this case, NII = (RSA ×  RRSA ) - (RSL ×  RRSL ) BUFN722- Financial Institutions

  26. Unequal Rate Change Example • Spread effect example: RSA rate rises by 1.2% and RSL rate rises by 1.0% NII =  interest revenue -  interest expense = ($155 million × 1.2%) - ($155 million × 1.0%) = $310,000 BUFN722- Financial Institutions

  27. Restructuring Assets and Liabilities • The FI can restructure its assets and liabilities, on or off the balance sheet, to benefit from projected interest rate changes. • Positive gap: increase in rates increases NII • Negative gap: decrease in rates increases NII BUFN722- Financial Institutions

  28. Weaknesses of Repricing Model • Weaknesses: • Ignores market value effects and off-balance sheet cash flows • Overaggregative • Distribution of assets & liabilities within individual buckets is not considered. Mismatches within buckets can be substantial. • Ignores effects of runoffs • Bank continuously originates and retires consumer and mortgage loans. Runoffs may be rate-sensitive. BUFN722- Financial Institutions

  29. The Maturity Model • Explicitly incorporates market value effects. • For fixed-income assets and liabilities: • Rise (fall) in interest rates leads to fall (rise) in market price. • The longer the maturity, the greater the effect of interest rate changes on market price. • Fall in value of longer-term securities increases at diminishing rate for given increase in interest rates. BUFN722- Financial Institutions

  30. Maturity of Portfolio • Maturity of portfolio of assets (liabilities) equals weighted average of maturities of individual components of the portfolio. • Principles stated on previous slide apply to portfolio as well as to individual assets or liabilities. • Typically, MA - ML > 0 for most banks and thrifts. BUFN722- Financial Institutions

  31. Effects of Interest Rate Changes • Size of the gap determines the size of interest rate change that would drive net worth to zero. • Immunization and effect of setting MA - ML = 0. BUFN722- Financial Institutions

  32. Interest Rate Risk Measurement • Repricing or funding gap • GAP: the difference between those assets whose interest rates will be repriced or changed over some future period (RSAs) and liabilities whose interest rates will be repriced or changed over some future period (RSLs) • Rate Sensitivity • the time to reprice an asset or liability • a measure of an FI’s exposure to interest rate changes in each maturity “bucket” • GAP can be computed for each of an FI’s maturity buckets BUFN722- Financial Institutions

  33. Calculating GAP for a Maturity Bucket NIIi = (GAP)i Ri = (RSAi - RSLi) Ri where NIIi = change in net interest income in the ith maturity bucket GAPi = dollar size of the gap between the book value of rate-sensitive assets and rate- sensitive liabilities in maturity bucket i Ri = change in the level of interest rates impacting assets and liabilities in the ith maturity bucket BUFN722- Financial Institutions

  34. Simple Bank Balance Sheet and Repricing Gap Assets Liabilities 1. Cash and due from $ 5 1. Two-year time deposits $ 40 2. Short-term consumer 50 2. Demand deposits 40 loans (1 yr. maturity) 3. Long-term consumer 25 3. Passbook Savings 30 loans (2 yr. maturity) 4. Three-month T-bills 30 4. Three-month CDs 40 5. Six-month T-notes 35 5. Three-month banker’s 20 acceptances 6. Three-year T-bonds 60 6. Six-month commercial 60 7. 10-yr. Fixed-rate mort. 20 7. One-year time deposits 20 8. 30-yr. Floating-rate m. 40 8. Equity capital (fixed) 20 9. Premises 5 $270 $270 BUFN722- Financial Institutions

  35. RSA & RSL • One year RSA (p. 618) $155 million • One year RSL (p. 619) $140 million • Cumulative one year repricing gap (CGAP) = 155m – 140 m = $15 m • Gap ratio =CGAP/A = $15m/$270 m = 5.6% • With a positive CGAP, when interest rates rise, NII rises BUFN722- Financial Institutions

  36. Weakness in the Repricing Model • Four major weaknesses • it ignores market value effects of interest rate changes • it ignores cash flow patterns within a maturity bucket • it fails to deal with the problem of rate-insensitive asset and liability cash flow runoffs and prepayments • it ignores cash flows from off-balance-sheet activities BUFN722- Financial Institutions

  37. Duration Model Duration gap - a measure of overall interest rate risk exposure for an FI D = - % in market value of a security  R/(1 + R) BUFN722- Financial Institutions

  38. Managing Interest-Rate Risk-example First National Bank Assets Liabilities --------------------------------------------------------------------------------------------------------------------- Reserves and cash items $ 5 m | Checkable deposits $ 15 m | Securities | Money market deposit accounts $ 5 m less than 1 year $ 5 m | 1 to 2 year $ 5 m | Savings deposits $ 15 m greater than 2 year $ 10 m | | CDs: Variable-rate $10 m Residential mortgages | less than 1 year $ 15 m Variable rate $ 10 m | 1 to 2 year $ 5 m Fixed rate (30 year) $ 10 m | greater than 2 year $ 5 m | Commercial Loans | Fed funds $ 5 m less than 1 year $ 15 m | 1 to 2 year $ 10 m | Borrowings: less than 1 year $10 m greater than 2 year $ 25 m | 1 to 2 year $ 5 m | greater than 2 year $ 5 m Physical capital $ 5 m | | Bank capital $ 5 m BUFN722- Financial Institutions

  39. Income Gap Analysis Rate-Sensitive Assets = $5m + $ 10m + $15m + 20% x $20m RSA = $32 m Rate-Sensitive Liabs = $5m + $25m + $5m+ $10m + 10% x $15m + 20%x$15m RSL = $49.5 m i  5%  ΔAsset Income = + 5% x $32.0m = + $ 1.6m ΔLiability Costs = + 5% x $49.5m = + $ 2.5m ΔIncome = $ 1.6m - $ 2.5 = - $0.9m If RSL > RSA, iNIM, Income GAP = RSA - RSL = $32.0m - $49.5m = -$17.5m ΔIncome = GAP x Δi = - $17.5m x 5% = -$0.9m BUFN722- Financial Institutions

  40. Maturity Matching and Interest Rate Exposure • If MA - ML = 0, is the FI immunized? • Extreme example: Suppose liabilities consist of 1-year zero coupon bond with face value $100. Assets consist of 1-year loan, which pays back $99.99 shortly after origination, and 1¢ at the end of the year. Both have maturities of 1 year. • Not immunized, although maturities are equal. • Reason: Differences in duration. BUFN722- Financial Institutions

  41. Duration • The average life of an asset or liability • The weighted-average time to maturity using present value of the cash flows, relative to the total present value of the asset or liability as weights. BUFN722- Financial Institutions

  42. *Term Structure of Interest Rates YTM YTM Time to Maturity Time to Maturity Time to Maturity Time to Maturity BUFN722- Financial Institutions

  43. *Unbiased Expectations Theory • Yield curve reflects market’s expectations of future short-term rates. • Long-term rates are geometric average of current and expected short-term rates. __~~ RN = [(1+R1)(1+E(r2))…(1+E(rN))]1/N - 1 BUFN722- Financial Institutions

  44. *Liquidity Premium Theory • Allows for future uncertainty. • Premium required to hold long-term. *Market Segmentation Theory • Investors have specific needs in terms of maturity. • Yield curve reflects intersection of demand and supply of individual maturities. BUFN722- Financial Institutions

  45. Pertinent Websites • For information related to central bank policy, visit: Bank for International Settlements www.bis.org Federal Reserve www.federalreserve.gov Bank of Japan www.boj.or.jp BUFN722- Financial Institutions

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