chapter 8 re-pricing model & maturity model. interest rate risk models –re-pricing model...
TRANSCRIPT
Chapter 8
Re-pricing Model & Maturity Model
Interest Rate Risk Models
– Re-pricing model– Maturity model– Duration model– In-house models
ProprietaryCommercial
13-2
Central Bank and Interest Rates
Target is primarily short term rates– Focus on Fed Funds Rate in particular
Interest rate changes and volatility increasingly transmitted from country to country– Statements by Ben Bernanke can have
dramatic effects on world interest rates.
Short-Term Rates 1954-2009
0
5
10
15
20
25
Fed Funds Rate
3 Mo T-bill
3Mo CD
13-4
Short-Term Rates 1997-2009
0
1
2
3
4
5
6
7
8
Fed Funds
3Mo T-Bill
3Mo CD
Short-Term Rates 2007-2009
0
1
2
3
4
5
6
7
Fed Funds
3Mo T-Bill
3Mo CD
13-6
Rate Changes Can Vary by Market
Note that there have been significant differences in recent years
If your asset versus liability rates change by different amounts, that is called “basis risk”– May not be accounted for in your
interest rate risk model
Re-pricing Model
Re-pricing 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).
Re-pricing Model
Rate sensitivity means time to re-pricing. Re-pricing gap is the difference between
the rate sensitivity of each asset and the rate sensitivity of each liability: RSA - RSL.
Refinancing risk (typical for banks) Reinvestment risk
Re-pricing Model
We are interested in the Re-pricing Model as an introduction to the importance of Net Interest Income– Variability of NII is really what we are
trying to protect– NII is the lifeblood of banks/thrifts
13-10
Maturity Buckets
Commercial banks must report re-pricing 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.
Note the cut-off levels
Re-pricing 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
13-13
IRR Commercial BankBalance Sheet $Millions Repricing Buckets
0 to 1 yr 1 yr to 2 yrs2 yrs to 5
yrs 5 yrs to 10 yrs >10 yrsAssets: Rate: Amount:
5 Year Prime-based Commercial Loans 6.0% 70 70 3 Year Auto Loans (3) 6.0% 60 60 7/1 Adjustable Rate Mortgages(1) 6.5% 50 50 9 Year Treasury Notes 5.5% 30 30 30 Year Fixed Rate Mortgages 8.0% 190 190 Total 400 70 0 60 80 190
Liabilities
Demand Deposits (2) 0.0% 30 21 9 18 Month CDs, interest paid annually 4.0% 150 150 36 Month CDs, interest paid annually 4.5% 80 80 72 Month CDs, interest paid annually 5.0% 20 20 Fed Funds Borrowed 2.0% 90 90 Equity (4) 0 30 Total 400 111 150 89 20 0
(1) 30 year term. Rate is fixed for first seven years and then adjusts annually.
(2) Assume for this exercise that 30% of demand deposits have a maturity and
duration of 5 years and the remaining 70% mature overnight.
(3) Auto loans are fully amortizing. For simplicity assume annual payments.
(4) for purposes of the repricing model, do not enter the amount of equiity
anywhere, so you will have a cumulative gap in cell J33 = +equity. Gap -41 -150 -29 60 190Cum Gap -41 -191 -220 -160 30
Re-pricing 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
Note this example is not realistic because asset = liabilities Usually assets > liabilities, final CGAP will be + Equity
13-14
Applying the Re-pricing Model
NIIi = (GAPi) Ri = (RSAi - RSLi) Ri
Example: In the one day bucket, gap is -$10
million. If rates rise by 1%, NII(1) = (-$10 million) × .01 = -
$100,000.
Applying the Re-pricing Model
Example II: If we consider the cumulative 1-year
gap,
NII = (CGAPone year) R = (-$15 million)(.01)
= -$150,000.
Rate-Sensitive Assets Examples from hypothetical balance
sheet:– Short-term consumer loans. If re-priced at
year-end, would just make one-year cutoff.– Three-month T-bills re-priced on maturity
every 3 months.– Six-month T-notes re-priced on maturity
every 6 months.– 30-year floating-rate mortgages re-priced
(rate reset) every 12 months.
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.
– FOR NOW, we will treat these as though they re-price overnightText assumes that they do not re-price
at all
CGAP Ratio
May be useful to express CGAP in ratio form as,
CGAP/Assets.– Provides direction of exposure and – Scale of the exposure.
Example- 12 month CGAP: – CGAP/A = -$15 million / $260 million = -
0.058, or -5.8 percent.
Equal Rate Changes on RSAs, RSLs
Example: Suppose rates rise 2% for RSAs and RSLs. Expected annual change in NII,
NII = CGAP × R= -$15 million × .02= -$300,000
With positive CGAP, rates and NII move in the same direction.
Change proportional to CGAP
Re-pricing 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
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
210 225>1yr.-5yrs. 40 30 +10 -5>5 years 10 5 +5 0
13-22
Equal Rate Changes on RSAs, RSLs
Example: Suppose rates rise 1% 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.
Change proportional to CGAP
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 )
Unequal Rate Change Example
Spread effect example: RSA rate rises by 1.0% and RSL rate rises by 1.0%
NII = interest revenue - interest expense
= ($210 million × 1.0%) - ($225 million × 1.0%)
= $2,100,000 -$2,250,000 = -$150,000
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
= ($210 million × 1.2%) - ($225 million × 1.0%)
= $2,520,000 -$2,250,000 = $270,000
13-26
Unequal Rate Change Example
Spread effect example: RSA rate rises by 1.0% and RSL rate rises by 1.2%
NII = interest revenue - interest expense
= ($210 million × 1.0%) - ($225 million × 1.2%)
= $2,100,000 -$2,700,000 = -$600,000
13-27
Simple Bank Repricing
Maturity Balance 0 to 1 >1
Securities 0.75 9,000 9,000
Consumer Loans 0.5 10,000 10,000
Consumer Loans 1.5 15,000 15,000
Consumer Loans 3 16,000 16,000
Prime-Based Loans 3 50,000 50,000
Total Assets 100,000 69,000
Demand Deposits - Fixed 5 15,000 15,000
Demand Deposits - Variable 0.01 35,000 35,000
CDs 0.5 30,000 30,000
CDs 0.75 5,000 5,000
CDs 2 5,000 5,000
Equity NA 10,000
Total Liabilities & NW 100,000 70,000
1 year Cum Gap -1,000
Change In Mkt Rates 1%
Change in NII -10
Chang in NII/ Assets -.01%
Re-pricing Model – 1 Year Cum Gap Analysis
Simple Bank Repricing
Maturity Balance 0 to 1 >1
Securities 0.75 9,000 9,000
Consumer Loans 0.5 10,000 10,000
Consumer Loans 1.5 15,000 15,000
Consumer Loans 3 16,000 16,000
Mortgage Loans 3 50,000 50,000
Total Assets 100,000 19,000
Demand Deposits - Fixed 5 15,000 15,000
Demand Deposits - Variable 0.01 35,000 35,000
CDs 0.5 30,000 30,000
CDs 0.75 5,000 5,000
CDs 2 5,000 5,000
Equity NA 10,000
Total Liabilities & NW 100,000 70,000
1 year Cum Gap -51,000
Change In Mkt Rates 1%
Change in NII -510
Chang in NII/ Assets -.51%
Re-pricing Model – 1 Year Cum Gap Analysis
Difficult Balance Sheet Items Equity/Common Stock O/S
– Ignore for re-pricing model, duration/maturity = 0
Demand Deposits– Treat as 30% re-pricing over 5 years/duration = 5
years 70% re-pricing immediately/duration = 0
Passbook Accounts– Treat as 20% re-pricing over 5 years/duration = 5
years 80% re-pricing immediately/duration = 0
Amortizing Loans– We will bucket at final maturity, but really should be
spread out in buckets as principal is repaid. Not a problem for duration/market value methods
Difficult Balance Sheet Items Prime-based loans Adjustable rate mortgages
– Put in based on adjustment date– Re-pricing/maturity/duration models cannot
cope with life-time cap
Assets with options– Re-pricing model cannot cope– Duration model does not account for option– Only market value approaches have the
capability to deal with options– Mortgages are most important class– Callable corporate bonds also
Prime Rate Vs Fed Funds 1955-2009
0
5
10
15
20
25
Fed Funds Rate
Prime Rate
Prime Rate Vs Fed Funds 1997-2009
0
1
2
3
4
5
6
7
8
9
10
Fed Funds
Prime Rate
Prime Rate Vs Fed Funds 2007-2009
0
1
2
3
4
5
6
7
8
9
Fed Funds
Prime Rate
Simple Bank Repricing
Maturity Balance 0 to 1 >1
Securities 0.75 9,000 9,000
Consumer Loans 0.5 10,000 10,000
Consumer Loans 1.5 15,000 15,000
Consumer Loans 3 16,000 16,000
Prime-Based Loans 3 50,000 50,000
Total Assets 100,000 69,000
Demand Deposits - Fixed 5 15,000 15,000
Demand Deposits - Variable 0.01 35,000 35,000
CDs 0.5 30,000 30,000
CDs 0.75 5,000 5,000
CDs 2 5,000 5,000
Equity NA 10,000
Total Liabilities & NW 100,000 70,000
1 year Cum Gap -1,000
Change In Mkt Rates 2%
Change in NII -20
Chang in NII/ Assets -.02%
Re-pricing Model – 1 Year Cum Gap Analysis
Simple Bank Repricing
Maturity Balance 0 to 1 >1
Securities 0.75 9,000 9,000
Consumer Loans 0.5 10,000 10,000
Consumer Loans 1.5 15,000 15,000
Consumer Loans 3 16,000 16,000
Prime-Based Loans 3 50,000 50,000
Total Assets 100,000 69,000
Demand Deposits - Fixed 5 15,000 15,000
Demand Deposits - Variable 0.01 35,000 35,000
CDs 0.5 30,000 30,000
CDs 0.75 5,000 5,000
CDs 2 5,000 5,000
Equity NA 10,000
Total Liabilities & NW 100,000 70,000
1 year Cum Gap -1,000
Change In Mkt Rates 6%
Change in NII -60
Chang in NII/ Assets -.07%
Re-pricing Model – 1 Year Cum Gap Analysis
Re-pricing Model – 1 Year Cum Gap Analysis
Simple S&L Repricing
Maturity Balance 0 to 1 >1
Securities 0.75 12,000 12,000
Consumer Loans 0.5 2,000 2,000
Consumer Loans 1.5 2,000 2,000
Consumer Loans 3 2,000 2,000
Fixed Rate Mortgages 30 82,000 82,000
Total Assets 100,000 14,000
Demand Deposits - Fixed 5 0 0
NOW Accounts 0.01 20,000 20,000
CDs 0.5 61,000 61,000
CDs 0.75 10,000 10,000
CDs 2 5,000 5,000
Equity NA 4,000
Total Liabilities & NW 100,000 91,000
1 year Cum Gap -77,000
Change In Mkt Rates 1%
Change in NII -770
Chang in NII/ Assets -.77%
Re-pricing Model – 1 Year Cum Gap Analysis
Simple S&L Repricing
Maturity Balance 0 to 1 >1
Securities 0.75 12,000 12,000
Consumer Loans 0.5 2,000 2,000
Consumer Loans 1.5 2,000 2,000
Consumer Loans 3 2,000 2,000
Fixed Rate Mortgages 30 82,000 82,000
Total Assets 100,000 14,000
Demand Deposits - Fixed 5 0 0
NOW Accounts 0.01 20,000 20,000
CDs 0.5 61,000 61,000
CDs 0.75 10,000 10,000
CDs 2 5,000 5,000
Equity NA 4,000
Total Liabilities & NW 100,000 91,000
1 year Cum Gap -77,000
Change In Mkt Rates 6%
Change in NII -4,620
Chang in NII/ Assets -4.62%
Comparison of 1980 Bank vs S&L
No Change in Rates No Change in Rates
Simple Bank Yield Balance Interest Simple S&L Yield Balance Interest
Assets 6.5% 100,000 6,500 Assets 7.0% 100,000 7,000
Liabilities 2.5% 90,000 -2,250 Liabilities 4.9% 96,000 -4,704
Equity 0 10,000 Equity 0 4,000
NII 4,250 NII 2,296
Operating Expenses -2,000 Operating Expenses -1,400
Pre-tax income 2,250 Pre-tax income 896
Taxes at 35% -788 Taxes at 35% -314
Net income 1,463 Net income 582
ROA 1.46% ROA 0.58%
ROE 14.6% ROE 14.6%
Comparison of 1980 Bank vs S&L
Rates Up 6% Rates Up 6%
Simple Bank Yield Balance Interest Simple S&L Yield Balance Interest
Assets 10.6% 100,000 10,640 Assets 7.8% 100,000 7,840
Liabilities 7.3% 90,000 -6,570 Liabilities 10.6% 96,000 -10,176
Equity 0 10,000 Equity 0 4,000
NII 4,070 NII -2,336
Operating Expenses -2,000 Operating Expenses -1,400
Pre-tax income 2,070 Pre-tax income -3,736
Taxes at 35% -725 Taxes at 35% 1,308
Net income 1,346 Net income -2,428
ROA 1.35% ROA -2.43%
ROE 13.5% ROE -60.7%
Restructuring Assets & 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 The “simple bank” we looked at does not
appear to be subject to much interest rate risk.
Let’s try restructuring for the “Simple S&L”
Weaknesses of Re-pricing Model
Weaknesses:– Ignores market value effects and off-
balance sheet (OBS) cash flows– Over-aggregative
Distribution of assets & liabilities within individual buckets is not considered. Mismatches within buckets can be substantial.
– Ignores effects of runoffsBank continuously originates and retires
consumer and mortgage loans and demand deposits/passbook account balances can vary. Runoffs may be rate-sensitive.
A Word About Spreads
Text example: Prime-based loans versus CD rates
What about libor-based loans versus CD rates?
What about CMT-based loans versus CD rates
What about each loan type above versus wholesale funding costs?
This is why the industry spreads all items to Treasury or LIBOR
*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.
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, maturity gap, MA - ML > 0 for most banks and thrifts.
*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.
*Maturities 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 maturity gap equals zero.
– Reason: Differences in duration** **(See Chapter 9)
*Maturity Model
Leverage also affects ability to eliminate interest rate risk using maturity model– Example:
Assets: $100 million in one-year 10-percent bonds, funded with $90 million in one-year 10-percent deposits (and equity)
Maturity gap is zero but exposure to interest rate risk is not zero.
Modified Maturity Model
Correct for leverage
to immunize, change: MA - ML = 0 to
MA – ML& E = 0 with ME = 0
(not in text)
13-49