AssetLiability Management

1
Asset-Liability Management

• The Purpose of Asset-Liability Management is to
  Control a Banks Sensitivity to Changes in Market
  Interest Rates and Limit its Losses in its Net
  Income or Equity

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Yield to Maturity (YTM)
3
Bank Discount Rate (DR)
Where FV equals Face Value
4
Conversion of DR into YTM

• YTM equivalent yield
• (100 purchase price)/Purchase Price (365/days
  to maturity)
• Note that the DR ant the conversion to YTM
  equivalent yields are approximations that are
  popular with banks.

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Example

• Suppose that we purchase a money market security
  for 96. The security will mature in 90 days and
  its face value is 100.
• What is the DR, the YTM equivalent yield, and the
  actual YTM?

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Example

• DR (100 96)/100 360/90 0.16
• Equivalent YTM (100 96)/96 365/90 0.1690
• Actual YTM
• PV -96, FV 100, N 90/365, I ?
• I 18

7
Interest Rate Risk GAP Earnings Sensitivity

• When a banks assets and liabilities do not
  reprice at the same time, the result is a change
  in net interest income.
• The change in the value of assets and the change
  in the value of liabilities will also differ,
  causing a change in the value of stockholders
  equity

8
Interest Rate Risk

• Banks typically focus on either
• Net interest income or
• The market value of stockholders' equity
• GAP Analysis
• A static measure of risk that is commonly
  associated with net interest income (margin)
  targeting
• Earnings Sensitivity Analysis
• Earnings sensitivity analysis extends GAP
  analysis by focusing on changes in bank earnings
  due to changes in interest rates and balance
  sheet composition

9
Interest Rate Risk

• Price Risk
• When Interest Rates Rise, the Market Value of the
  Bond or Asset Falls
• Reinvestment Risk
• When Interest Rates Fall, the Coupon Payments on
  the Bond are Reinvested at Lower Rates

10
Interest Rate Risk Reinvestment Rate Risk

• If interest rates change, the bank will have to
  reinvest the cash flows from assets or refinance
  rolled-over liabilities at a different interest
  rate in the future.
• An increase in rates, ceteris paribus, increases
  a banks interest income but also increases the
  banks interest expense.
• Static GAP Analysis considers the impact of
  changing rates on the banks net interest income.

11
Interest Rate Risk Price Risk

• If interest rates change, the market values of
  assets and liabilities also change.
• The longer is duration, the larger is the change
  in value for a given change in interest rates.
• Duration GAP considers the impact of changing
  rates on the market value of equity.

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Measuring Interest Rate Risk with GAP

• Traditional Static GAP Analysis GAPt RSAt
  -RSLt
• RSAt
• Rate Sensitive Assets
• Those assets that will mature or reprice in a
  given time period (t)
• RSLt
• Rate Sensitive Liabilities
• Those liabilities that will mature or reprice in
  a given time period (t)

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What Determines Rate Sensitivity?

• An asset or liability is considered rate
  sensitivity if during the time interval
• It matures
• It represents and interim, or partial, principal
  payment
• It can be repriced
• The interest rate applied to the outstanding
  principal changes contractually during the
  interval
• The outstanding principal can be repriced when
  some base rate of index changes and management
  expects the base rate / index to change during
  the interval

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Interest-Sensitive Assets

• Short-Term Securities Issued by the Government
  and Private Borrowers
• Short-Term Loans Made by the Bank to Borrowing
  Customers
• Variable-Rate Loans Made by the Bank to Borrowing
  Customers

15
Interest-Sensitive Liabilities

• Borrowings from Money Markets
• Short-Term Savings Accounts
• Money-Market Deposits
• Variable-Rate Deposits

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Example

• A bank makes a 10,000 four-year car loan to a
  customer at fixed rate of 8.5. The bank
  initially funds the car loan with a one-year
  10,000 CD at a cost of 4.5. The banks initial
  spread is 4.
• What is the banks one year gap?

17
Example

• Traditional Static GAP Analysis
• What is the banks 1-year GAP with the auto loan?
• RSA1yr 0
• RSL1yr 10,000
• GAP1yr 0 - 10,000 -10,000
• The banks one year funding GAP is -10,000
• If interest rates rise (fall) in 1 year, the
  banks margin will fall (rise)

18
Measuring Interest Rate Risk with GAP

• Traditional Static GAP Analysis
• Funding GAP
• Focuses on managing net interest income in the
  short-run
• Assumes a parallel shift in the yield curve, or
  that all rates change at the same time, in the
  same direction and by the same amount.

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Other Gap Measurements
Relative Interest-Sensitive Gap
Interest Sensitivity Ratio
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Asset-Sensitive Bank Has

• Positive Dollar Interest-Sensitive Gap
• Positive Relative Interest-Sensitive Gap
• Interest Sensitivity Ratio Greater Than One

21
Liability Sensitive Bank Has

• Negative Dollar Interest-Sensitive Gap
• Negative Relative Interest-Sensitive Gap
• Interest Sensitivity Ratio Less Than One

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Net Interest Margin
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Factors Affecting Net Interest Income

• Changes in the level of interest rates
• Changes in the composition of assets and
  liabilities
• Changes in the volume of earning assets and
  interest-bearing liabilities outstanding
• Changes in the relationship between the yields on
  earning assets and rates paid on interest-bearing
  liabilities

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Example

• Consider the following balance sheet

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Examine the impact of the following changes

• A 1 increase in the level of all short-term
  rates?
• A 1 decrease in the spread between assets yields
  and interest costs such that the rate on RSAs
  increases to 8.5 and the rate on RSLs increase
  to 5.5?
• Changes in the relationship between short-term
  asset yields and liability costs
• A proportionate doubling in size of the bank?

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1 increase in short-term rates
With a negative GAP, more liabilities than assets
reprice higher hence NII and NIM fall
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1 decrease in the spread
NII and NIM fall (rise) with a decrease
(increase) in the spread. Why the larger change?
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Changes in the Slope of the Yield Curve

• If liabilities are short-term and assets are
  long-term, the spread will
• widen as the yield curve increases in slope
• narrow when the yield curve decreases in slope
  and/or inverts

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Proportionate doubling in size
NII and GAP double, but NIM stays the same.
What has happened to risk?
30
Changes in the Volume of Earning Assets and
Interest-Bearing Liabilities

• Net interest income varies directly with changes
  in the volume of earning assets and
  interest-bearing liabilities, regardless of the
  level of interest rates

31
RSAs increase to 540 while fixed-rate assets
decrease to 310 and RSLs decrease to 560 while
fixed-rate liabilities increase to 260
Although the banks GAP (and hence risk) is
lower, NII is also lower.
32
Changes in Portfolio Composition and Risk

• To reduce risk, a bank with a negative GAP would
  try to increase RSAs (variable rate loans or
  shorter maturities on loans and investments) and
  decrease RSLs (issue relatively more longer-term
  CDs and fewer fed funds purchased)
• Changes in portfolio composition also raise or
  lower interest income and expense based on the
  type of change

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Changes in Net Interest Income are directly
proportional to the size of the GAP

• If there is a parallel shift in the yield curve
• It is rare, however, when the yield curve shifts
  parallel
• If rates do not change by the same amount and at
  the same time, then net interest income may
  change by more or less.

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Summary of GAP and the Change in NII