Class 5, Chap 8

Interest rate risk
 types
▪ Price risk
▪ Reinvestment risk
▪ Refinancing risk

Repricing gap – a simple measure
2

At bond funds
3
How do banks make their profits?

Margin = r(assets) – r(liabilities)
Why is the margin usually positive?




Assets are usually long-term loans – mortgages, C&I, consumer
Liabilities are usually short term – deposits, commercial paper, repos
Longer-term assets usually earn higher interest
Maturity Mismatch


The maturity of FI’s assets and liabilities do not match
Margin = r(assets) – r(liabilities)
Usually pay a higher rate because they are
long-term but the rate is usually fixed
Usually pay a lower rate because they are shortterm therefore their funding cost will vary
4

IRR is the risk that a firm will lose money if interest rates
change

This is a fundamental business risk that FI’s take on when they
choose to operate as a financial institution
 Asset transformation – transform short-term liabilities into long-term assets

Types of interest rate risk:
 Price Risk: Variation in market prices caused by unexpected changes in
interest rates. Think of gains or losses on a trading portfolio.
 Refinancing Risk: The risk that FI’s funding costs change. The interest
rate at which FIs can borrow e.g. the rate on deposits, commercial paper,
and repos
 Reinvestment Risk: The risk of a change in the rate the FI receives on
investments (mortgages, C&I loans, consumer loans)
5
Example: A bank has an outstanding 10 year interest only loan with principal of $100,000 maturing in 6
months. The interest rate on the existing loan is 7.3% pa. Currently, mortgage rates are at 6%. Suppose the
bank funds the loan with 1 year CDs that pay approximately 3%.
100,000
Assets
8
9
10
11
7.3%
12
6%
Liabilities
8
$100,000
CD 3%
9
$100,000
CD 3%
10
$100,000
CD 3%
Margin = 7.3% – 3% = 4.3%
11
$100,000
CD 3%
12
$100,000
CD 3%
Margin = 6% – 3% = 3%
6
Example: An FI has a 10 year $100,000 interest only loan outstanding. The interest rate on the existing
loan is 7.3% pa. Suppose the FI finances the asset with 1 year commercial paper.
7.3%
Assets
5
6
7
8
9
5
6
7
8
9
Liabilities
$100,000
CP 2.5%
$100,000
CP 5%
$100,000
CP 3.3%
$100,000
CP 3.7%
Margin =
Margin =
Margin =
Margin =
Margin =
7.3% – 3%
7.3%–2.5%
7.3%–5%
7.3%–3.3%
7.3%–3.7%
= 4.3%
= 4.8%
= 2.3%
= 4%
= 3.6%
$100,000
CP 3%
7
REPRICING GAP
21

Repricing Gap Model:
 Basic Idea: measure how a change in interest rates will change the net
interest income for the company over a specific time horizon
Net Interest
Income (NII)
=
Interest income
from assets
-
Interest expense
from liabilities
 The time horizon is called the repricing interval

Repricing interval: is a time interval; any asset or liability that is
“repriced” during this period is said to be Rate Sensitive and is
included in the repricing gap for that horizon
22

Liabilities:
 Refinancing - A loan issued to the FI at 10% interest comes due and
must be refinanced at 12%
 Variable Rate - An FI holds a variable rate loan – the loan is repriced
when the rate adjusts

Assets:
 Reinvestment - A mortgage issued by the FI at 7% matures and a new
mortgage can be issued at 9%
 Variable Rate - The FI has issued a variable rate mortgage the asset is
repriced whenever rate adjusts
23
1.
Define repricing interval(s)
2.
Identify rate sensitive assets and liabilities for each
interval
3.
Sum book values of rate sensitive assets (RSA)
and liabilities (RSL) in each interval
4.
Calculate the repricing gap for each interval
5.
Calculate the change in NII with respect to a
change in interest rates for each interval

2 cases r(RSA) = r(RSL) & r(RSA) ≠ r(RSL)
24

Recently the Federal Reserve has required commercial banks
to report quarterly (in call reports) repricing gaps for assets
and liabilities with maturities of:
 One day
 More than one day to three months
 More than three months to six months
 More than six months to twelve months
 More than one year to five years
 Over five years
25
Sample Balance Sheet
Assets
ST Loans (6-month maturity)- 50
LT Loans (2-year maturity) - 25
3-month Treasuries - 30
6-month Treasuries - 35
3-year Treasuries - 70
30-year Mortgages - 20
30-year Mortgages (adjustable every 9
months) – 40
Liabilities & Equity
Demand Deposits - 40
Savings Deposits - 30
3-month CDs - 40
3-month banker acceptances - 20
6-month commercial paper - 60
One-year CDs - 20
Two-year CDs - 40
Equity Capital – 20
Total: $270
Total: $270
26
One day
Assets = $0M
Liabilities = $0M
Assets (millions)
ST Loans (6-month maturity)- $50
LT Loans (2-year maturity) - 25
3-month Treasuries - 30
6-month Treasuries - 35
3-year Treasuries - 70
30-year Mortgages - 20
30-year Mortgages (adjustable every 9
months) – 40
Liabilities (millions)
Demand Deposits - 40
Savings Deposits - 30
3-month CDs - 40
3-month banker acceptances - 20
6-month commercial paper - $60
One-year CDs - 20
Two-year CDs - 40
Equity Capital – 20
Total: $270
Total: $270
27
More than one day to three months
Assets = $30M
Liabilities = $60M
Assets (millions)
ST Loans (6-month maturity)- 50
LT Loans (2-year maturity) - 25
3-month Treasuries - 30
6-month Treasuries - 35
3-year Treasuries - 70
30-year Mortgages - 20
30-year Mortgages (adjustable every 9
months) – 40
Liabilities (millions)
Demand Deposits - 40
Savings Deposits - 30
3-month CDs - 40
3-month banker acceptances - 20
6-month commercial paper - 60
One-year CDs - 20
Two-year CDs - 40
Equity Capital – 20
Total: $270
Total: $270
28
More than 3 months to 6 months
Assets = $85M
Liabilities = $60M
Assets (millions)
ST Loans (6-month maturity)- 50
LT Loans (2-year maturity) - 25
3-month Treasuries - 30
6-month Treasuries - 35
3-year Treasuries - 70
30-year Mortgages - 20
30-year Mortgages (adjustable every 9
months) – 40
Liabilities (millions)
Demand Deposits - 40
Savings Deposits - 30
3-month CDs - 40
3-month banker acceptances - 20
6-month commercial paper - 60
One-year CDs - 20
Two-year CDs - 40
Equity Capital – 20
Total: $270
Total: $270
29
More than 6 months to 12 months
Assets = $40M
Liabilities = $20M
Assets (millions)
ST Loans (6-month maturity)- 50
LT Loans (2-year maturity) - 25
3-month Treasuries - 30
6-month Treasuries - 35
3-year Treasuries - 70
30-year Mortgages - 20
30-year Mortgages (adjustable every 9
months) – 40
Liabilities (millions)
Demand Deposits - 40
Savings Deposits - 30
3-month CDs - 40
3-month banker acceptances - 20
6-month commercial paper - 60
One-year CDs - 20
Two-year CDs - 40
Equity Capital – 20
Total: $270
Total: $270
30
More than 1 year to 5 years
Assets = $95M
Liabilities = $40M
Assets (millions)
ST Loans (6-month maturity)- 50
LT Loans (2-year maturity) - 25
3-month Treasuries - 30
6-month Treasuries - 35
3-year Treasuries - 70
30-year Mortgages - 20
30-year Mortgages (adjustable every 9
months) – 40
Liabilities (millions)
Demand Deposits - 40
Savings Deposits - 30
3-month CDs - 40
3-month banker acceptances - 20
6-month commercial paper - 60
One-year CDs - 20
Two-year CDs - 40
Equity Capital – 20
Total: $270
Total: $270
31
More than 5 year
Assets = $20M
Liabilities = $0M
Assets (millions)
ST Loans (6-month maturity)- 50
LT Loans (2-year maturity) - 25
3-month Treasuries - 30
6-month Treasuries - 35
3-year Treasuries - 70
30-year Mortgages - 20
30-year Mortgages (adjustable every 9
months) – 40
Liabilities (millions)
Demand Deposits - 40
Savings Deposits - 30
3-month CDs - 40
3-month banker acceptances - 20
6-month commercial paper - 60
One-year CDs - 20
Two-year CDs - 40
Equity Capital – 20
Total: $270
Total: $270
32
Assets
(RSA)
sum
Liabilities
(RSL)
sum
One day
$0M
$0M
More than 1 day to 3 months
$30M
$60M
More than 3 months to 6 months
$85M
$60M
More than 6 months to 12 months
$40M
$20M
More than 1 year to 5 years
$95M
$40M
Over 5 years
$20M
$0M
Repricing
Gap
(RSA-RSL)
Cumulative
GAP
33
Assets
(RSA)
sum
Liabilities
(RSL)
sum
Repricing
Gap
(RSA-RSL)
Cumulative
GAP
One day
$0M
$0M
$0M
$0M
More than 1 day to 3 months
$30M
$60M
$-30M
$-30M
More than 3 months to 6 months
$85M
$60M
$25M
$-5M
More than 6 months to 12 months
$40M
$20M
$20M
$15M
More than 1 year to 5 years
$95M
$40M
$55M
$70M
Over 5 years
$20M
$0M
$20M
$90M
Positive Gap – Reinvestment Risk: More assets than liabilities are being
repriced
Negative Gap – Refinancing Risk: More liabilities than assets are being
repriced
34
Assets
(RSA)
sum
Liabilities
(RSL)
sum
Repricing
Gap
(RSA-RSL)
Cumulative
GAP
One day
$0M
$0M
$0M
$0M
More than 1 day to 3 months
$30M
$60M
$-30M
$-30M
More than 3 months to 6 months
$85M
$60M
$25M
$-5M
More than 6 months to 12 months
$40M
$20M
$20M
$15M
More than 1 year to 5 years
$95M
$40M
$55M
$70M
Over 5 years
$20M
$0M
$20M
$90M
Cumulative Gap (CGAP)- Is the gap for one day to T (the given time period):
• A common cumulative GAP (CGAP) of interest is one-year repricing gap
includes all assets that will be repriced within one year
35
Alternative 1 year CGAP calculation
Assets
Liabilities
ST Loans (6-month maturity) - $50
Demand Deposits – $40 ??
LT Loans (2-year maturity) - $25
Savings Deposits – $30 ??
3-month Treasuries - $30
3-month CDs - $40
6-month Treasuries - $35
3-month banker acceptances - $20
3-year Treasuries - $70
6-month commercial paper - $60
30-year Mortgages - $20
One-year CDs - $20
30-year Mortgages (adjust. every 9 months) – Two-year CDs - $40
$40
Equity Capital - $20
RSA=50+30+35+40=$155M.
RSL=40+20+60+20=$140M.
CGAP=155 -140=$15M
Gap Ratio: CGAP/Assets=15/270=5.6%
36
Basic Case – Interest rates for assets and liabilities change by the
same amount

Suppose rates increase 1% for both RSAs and RSLs.
Expected annual change in net interest income (NII):
NII = CGAP ×  R
= $15 million × 0.01
= $150,000

Suppose rates fall 1% for both RSAs and RSLs. Expected
annual change in NII:
NII = CGAP ×  R
= $15 million × -0.01
= $-150,000
37
Interest rates for assets and liabilities change by different amounts

If changes in rates on RSAs and RSLs are not equal,
NII = (RSA ×  RRSA ) - (RSL ×  RRSL )
= Interest Revenue - Interest Expense

Example: Suppose that in the previous example, rates increase
by 1.2% on RSAs and by 1% on RSLs:
NII = (RSA ×  RRSA ) - (RSL ×  RRSL )
= Interest Revenue - Interest Expense
= ($155 million × 1.2%) - ($140 million ×1%)
= $460,000
.
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Given the following balance sheet:
a) Calculate the value of 1 year rate-sensitive assets
b) Calculate the value of 1 year rate-sensitive liabilities
c) Calculate the cumulative 1 yr repricing gap
d) Find the 1 year GAP ratio
e) Calculate the change in net interest income (NII)
i. For a 3% rate increase (both assets & liab.)
ii. For a change of 2% asset, -1% liabilities
Assets
Short-tem loans (1yr)
Long-term loans
3 month T-bills
6 month T-notes
3 year T-bonds
10 year mortgage
(fixed rate)
30 year mortgage
(adjusts every 9 months)
Liabilities
150
125
130
135
170
120
140
970
Equity Capital
Demand Deposits
Passbook savings
220
40
130
3 month CDs
6 month CP
Bankers Acceptance
(3 month)
1 year time deposits
2 year time deposits
140
160
120
120
40
970
39

Ignores the market value effect
 Assets and liabilities are recorded at their book-values which is
the original cost or sale price (historical) – this value is
constant
 In fact, present values of virtually all assets and liabilities on a
balance sheet change as interest rates change.
 Ex: A 5 year zero coupon bond was bought with YTM of 9.7%
currently the YTM is 5% but the book value is still 9.7%

Over-aggregative!
 Distribution of assets & liabilities within individual buckets is not
considered. Mismatches within buckets can be substantial.
40

Ignores effects of runoffs
 Banks continuously originate and retire consumer and
mortgage loans. Runoffs may be rate-sensitive.
▪ A 30 year mortgage could only have one year left to maturity. However, since it
is a 30 year mortgage, it is listed on the books as a 30 year mortgage and would
not be considered a RSA at the one year horizon

Ignores off-balance sheet instruments, which are also affected
by interest rate changes.
41

Types of interest rate risk
 Price risk
 Refinancing risk
 Reinvestment risk

Repricing GAP – measures a banks exposure
to interest rate risk
42