ch8 1

1
BUFN 722

• ch-8
• Interest Rate Risk
• Re-pricing model Maturity Model

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

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

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

5
ER NBR NFR Fed Funds

• NBR- when high, banks reluctant to lend or buy
  new investments
• loans at Fed discount window
• 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 Feds 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 banks reserve requirements
  not part of that banks 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

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

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 p goal
• 2. Commitment to price stability
• 3. Communication with "Inflation Report"
• Lessons from Inflation Targeting
• 1. Decline in p still led to output loss
• 2. Worked to keep p low
• 3. Kept p in public eye reduced political
  pressures for inflationary policy

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

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

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

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

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

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.

15
Federal Funds Rate and Money Growth Before and
After October 1979
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.

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.

18
Repricing Gap Example

• Assets Liabilities Gap 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

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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.

20
Applying the Repricing Model

• Example II
• If we consider the cumulative 1-year gap,
• DNIIi (CGAPi) DRi (-15 million)(.01)
• -150,000.

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.

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.

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.

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.

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 )

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

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

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.

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.

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.

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.

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 FIs exposure to interest rate
  changes in each maturity bucket
• GAP can be computed for each of an FIs maturity
  buckets

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
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 bankers 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
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

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

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)
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

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
• 20x15m
• RSL 49.5 m
• i ? 5 ?
• ?Asset Income 5 x 32.0m 1.6m
• ?Liability Costs 5 x 49.5m 2.5m
• ?Income 1.6m - 2.5 - 0.9m
• If RSL RSA, i ? NIM ?, Income ?
• GAP RSA - RSL
• 32.0m - 49.5m -17.5m
• ?Income GAP x ?i
• - 17.5m x 5 -0.9m

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.

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.

42
Term Structure of Interest Rates

• YTM

YTM
Time to Maturity
Time to Maturity
Time to Maturity
Time to Maturity
43
Unbiased Expectations Theory

• Yield curve reflects markets expectations of
  future short-term rates.
• Long-term rates are geometric average of current
  and expected short-term rates.
• _ _
• RN (1R1)(1E(r2))(1E(rN))1/N - 1

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.

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