BNFN 501ASSET AND LIABILITY MANAGEMENT

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BNFN 501-ASSET AND LIABILITY MANAGEMENT

• WEEK 4
• HEMPEL(1999), CHP. 4
• FOUNDATIONS OF VALUE IN BANKING

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WHAT IS ASSET AND LIABILITY MANAGEMENT?

• ASSET AND LIABILITY MANAGEMENT (ALM) IS THE
  FINANCIAL RISK MANAGEMENT OF ANY FINANCIAL
  INSTITUTION. THIS INCLUDES RISK ASSESSMENTS IN
  ALL DIMENSIONS
• POLICY SETTING,
• STRUCTURING OF THE BANKS REPRICING AND
• MATURITY SCHEDULES,
• UNDERTAKING FINANCIAL HEDGE POSITIONS,
• CAPTIAL BUDGETING, AND
• INTERNAL PROFITABILITY MEASURMENTS.

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RISK AND RETURN TRADEOFF IN ALM

• THERE IS NO WAY TO SIMULTANEOUSLY MAXIMIZE
  RETURNS (OR PROFITS) AND MINIMIZE RISKS. BANKS
  CAN ONLY MAKE RISK/RETURN TRADEOFFS AND ATTEMPT
  TO MAXIMIZE RETURNS FOR WHATEVER AGGREGATE LEVEL
  OF RISK THEY CHOOSE TO UNDERTAKE.
• THE GOAL OF ALM IS TO MAXIMIZE THE
  RISK-ADJUSTED RETURNS TO SHAREHOLDERS OVER THE
  LONG RUN

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FOUNDATIONS OF VALUE IN BANKING

• We can use accounting data to analyze past bank
  performance, such as profit margin, return on
  equity, or return on assets, etc. However, such
  data is backward looking. They give us historical
  values of assets and liabilities.
• Value is a forward-looking concept. Changes in
  market conditions may change the economic values
  in banking. Therefore, we need to determine
  economic values under new market conditions in
  order to measure economic performance.

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ASSETS AND LIABILITIES OF BANKS ARE PRESENT
VALUES OF FUTURE CASH FLOWS

• The economic values of asset and liability
  nominal contracts do not come from historical
  monetary values. The values of assets and
  liabilities should be viewed as present values.
• The time value of money principle defines
  present values as the values of future cash flows
  to be received or paid, discounted by the rate of
  return investors expect to earn during the period
  of each particular cash flow.

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VALUE CHANGES IN BANKING

• Several factors may cause present values to
  change unexpectedly. (for example, loan default,
  changes in the timing of payment, or changes in
  interest rates)
• In this chapter we will study the value changes
  in banking that are caused by changes in
  interest rates.

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TIME VALUE OF MONEY AND INTEREST RATE SENSITIVITY

• The value (price) of a government bond is found
  from
• P0 present bond price
• CFt cash flow received by investor at time t
• n time of the final cash flow
  (maturity)
• r risk free discount rate per period
• Rn the final payment that redeems the par
  value of
• the bond

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• The values of longer-term bonds are more
  interest rate sensitive than short-term ones.
  This means that assets with longer-term cash
  flows, holding the coupon rate constant, produce
  larger decreases or increases in value when
  market discount rates rise or fall.

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EXAMPLE

• TABLE 4.1 - Interest Rate Sensitivities Base on
  Maturity
• Percent
• r 6 r 7 Change
• 1-year 1000.00 990.65 -0.94
• 5-year 1000.00 959.00 -4.10
• 30-year 1000.00 875.10 -12.40

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Interest Sensitivity is asymetrical

• The loss from a 1 increase in interest rate is
  not the same as the gain from a 1 decrease in
  the rate. Prices rose by a larger amount for a
  decrease in interest than they fell for the same
  increase in interest.
• Example a 5 year bond with different interest
  rates
• r 6, P 1000
• r 5, P 1,043.29 4.33 increase
• r 7, P 959.00 -4.10 decrease

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Figure 4.1. Price Curve for 5-year, 6 Coupon
Bond
Price
Price gain is greater from falling interest rates
than the loss from rising rates
6
5
7
Interest Rate
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BALANCE SHEET MATURITY MISMATCHING

• The market value of a financial institutions
  balance sheet is the value of its assets minus
  the value of its liabilities. It is critical for
  a financial services firm to understand how this
  value can be impacted by interest rate
  sensitivity.
• If the interest rate movements have a different
  effect on assets than they do on liabilities, the
  value of the firm must change.
• This difference in effect is caused by
  differences in the maturities of assets and
  liabilities known as maturity mismatching.

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• Example Treadwater Bank is started up by
  enthusiastic investors who put in 1 million in
  equity capital. The new bank raises an additional
  9 million in one year certificates of deposit
  (CDs) bearing 6 interest. The bank now invests
  all 10 million in a 5- year term loan, also
  yielding 6. Treadwater has no other costs or
  revenues.
• The historical cost accounting represents
  Treadwaters balance sheet as below
• Assets Liabilities and Equity Capital
• Loans 10,000,000 Deposits 9,000,000
• Equity Capital 1,000,000
• 10,000,000 10,000,000

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A Market Value Balance Sheet

• A market value balance sheet reflects changes in
  future earnings and cash flows due to interest
  rate changes.
• Let us create the market value balance sheet of
  Treadwater Bank under two different assumptions
• 1) Assume that there is no change in the market
  interest rate, i.e. r 6.
• 2) Assume that interest rates increased from 6
  to 7 .

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Table 4.2. Treadwater Banks Five-Year Projected
Earnings with Constant 6 interest Rate
1st Year 2nd Year 3rd Year 4th Year 5th
Year Int. income 600,000 600,000 600,000
600,000 600,000 Int. expense 540,000 540,000
540,000 540,000 540,000 __________
__________ __________ __________
__________ Net earnings 60,000 60,000
60,000 60,000 60,000
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Table 4.3. Treadwater Banks Five-Year Projected
Earnings with Initial 6 Interest Rate and
Rates Rise Immediately to 7 .
1st Year 2nd Year 3rd Year 4th Year 5th
Year Int. income 600,000 600,000 600,000
600,000 600,000 Int. expense 540,000 630,000
630,000 630,000 630,000 __________
__________ __________ __________
__________ Net earnings 60,000 - 30,000 -
30,000 - 30,000 - 30,000
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Treadwater Banks discounted cash flows by the
higher new one-year interest rate.

• Assets
• -Liabilities
• Equity Capital

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After the increase in interest rates, Tereadwater
Banks market value balance sheet becomes

• Assets Liabilities and Equity Capital
• Loans 9,589,980 Deposits 8,915,888
• Equity Capital 674,092
• 9,589,980
  9,589,980

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• Economic value of the balance sheet ( market
  value balance sheet)
• market value of assets market value of
  liabilities
• Interest rate sensitivity shows up in both
  earnings effect and economic balance sheet
  valuation effects. Combined, these to elements
  comprise total interest rate risk.
• Total returns Earnings Changes in value
• Total interest
• rate risk Earnings risk Economic (value
  risk)

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• It is risky to mismatch asset and liability
  maturities on bank balance sheets. However, it is
  not possible to quantify this risk on the basis
  of asset and liability maturities. For example,
  a 30 year assets sensitivity is 13.2 times that
  of a one year asset, not the 30 times ratio of
  their maturities.
• Duration analysis allows us to make more accurate
  characterization of interest rate sensitivity
  than we are allowed with maturity.

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MEASURING INTEREST RATE SENSITIVITY DURATION

• Single-Payment Assets
• The value of a financial asset with a single
  payment of Cn dollars to be received in n years
  is
• Cn
• Po
• (1r)n
• The price volatility of assets with a single
  payment can be found by
• It is only in the case of single payment assets
  that maturity n is an exact index of the assets
  respective interest rate risks.

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Multipayment Assets

• The index n of a single-payment asset is also its
  duration. Maturity and duration are equal only
  for single-payment assets.
• Duration can be derived as an index of interest
  rate risk for multipayment assets as well.
  Duration is a reliable index for multipayment
  assets but maturity is not.
• An approximation for the price changes of a bond
  when the interest rate changes by a small amount
  is

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Table 4.4. Duration and Modified Duration for
6 Coupon, Five-year Bond Priced at Par
(1) (2) (3) (4) (5) Year Cash Flow Present
Value Present Value Weighted Cash of 1 at
6 of Cash Flow Flows (1) ? (4)
1 60 0.9434 56.60 56.60 2 60 0.8900
53.40 106.80 3 60 0.8936
50.38 151.13 4 60 0.7921 47.53 190.10 5 1060
0.7473 792.09 3,960.45 ___________
_____________ 1000.00 4,465.08 Duration (D)
Weighted cash flows/present value (price)
4,465/1,000 4.465 years Modified duration
(DM) 4.212 years
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• Duration provides a convenient estimator of
  interest sensitivity. For example, if the market
  rate shifts from 6 to 7
• ?P0 .01
• -4.465 ( ) -4.212 P 1.06
• The estimate for ?P is -42.12, which indicates
  an estimate that the bonds price will fall from
  1,000 to 957.88.

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Duration and Coupon Effect

• Duration helps to resolve another interest rate
  sensitivity problem known as the coupon effect.
  The coupon effect is another reason that bond
  maturity is not a workable index of sensitivity.
• For a given maturity bond, the smaller the coupon
  the greater the price change for a chance in
  interest rates. Duration distinguishes between
  these two levels of coupons for bonds with the
  same maturity

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• Example Duration for a 6 coupon, five year
  bond at a market discount rate of 6 equals 4.465
  years, whereas the duration of a 12 coupon,
  5-year bond is 4.14.

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THE DURATION GAP

• Duration can help us understand how a financial
  institutions balance sheet net asset value- the
  market value of balance sheet equity- is affected
  by changes in interest rates.
• A bank can control the interest rate exposure of
  its equity value by approximately matching the
  duration of its portfolio of assets with that of
  its portfolio of liabilities.
• Duration gap measure the mismatch between the
  aggregate durations of assets and liabilities.
  Duration gap provides a unitary index of equity
  values exposure to interest rates.

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CALCULATION OF DURATION GAP

• The estimated price volatility equation
• ?P - D ?r
• DM ?r
• P 1 r
• The estimated price volatility equation is
  applied to both assets and liabilities
• ?A ? r
• - DA ( )
• A (1r)
• ?L ? r
• - DL ( )
• L (1r)

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Transposing these two expressions gives

• ? r
• ?A - DA A ( )
• (1r)
• ? r
• ?L - DL L ( )
• (1r)
• A market value of assets
• L market value of liabilities
• DA duration of assets
• DL duration of liabilities

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• The change in equity value of the bank (E) is
  found in the form of changes in the market values
  of assets, liabilities, and equity.
• ?A ?L ?E
• ?E ?A - ?L
• The duration Gap is
• L
• DG (DA - DL )
• A
• In this expression the duration of liabilities is
  weighted by the ratio of the market values of
  liabilities to assets. This adjust for the fact
  that the difference in these two magnitudes
  affects the relative amounts each will change
  with a change in interest rates.

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• The change in equity value of the bank (E) is
  found in the form of changes in the market values
  of assets, liabilities, and equity. When we
  solve directly for ?E
• ? r
• ?E - DG ? ? A
• (1 r)

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Table 4.5 Interest Rate exposure to Snow Banks
Balance Sheet

• Present Years
  Economic Value after
• Economic Value Duration
  2 Rate Increase
• Assets
• Securities
• Liquid 150 0.5 148.6
• Investment 100 3.5 93.6
• Loans
• Floating 400 0 400.0
• Fixed-rate 350 2.0 337.3
• _________________ _________________
  _________________
• Total assets 1,000 1.125 979.5
• Liabilities and net worth
• Transaction deposits 400 0 400.0
• CDs and other time deposits
• Short-term 350 0.4 347.5
• Long-term 150 2.5 143.7
• Net worth 100 _________________ 83.3a
• _________________ _________________
• Total liabilities and net worth 1,000 0.572
  979.5

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Example

• Snow bank found that the duration of its total
  assets is DA 1.125, and total liabilities DL
  0.572 . Given a 2 increase in interest rate
  and assuming an initial rate ( r ) of 10, what
  is the estimated change in equity value?
• ? r
• ?E -DG ? ? A
• (1r)
• 0.2
• -0.610 X X
  1,000,000,000 -11,100,000
• (10.10)

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YIELD TO MATURITY

• For assets with multiple payments, we assumed
  that the rate of discount is constant. We
  refer to this constant rate as the yield to
  maturity. This measure blends the discrete
  discount rates that differ for each maturity of
  an assets multiple cash flows.
• The relationship between yield and the timing of
  securities cash flows is known as the term
  structure of interest rates.

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• Yield to maturity is the unique discount rate
  which, when applied to all of a securitys cash
  flows, correctly produces the securitys price.