CHAPTER 8.rtf by handongqp


									                                         CHAPTER 11


Goal of This Chapter: To learn what the nature and purpose is of a bank's portfolio of investment
securities and to discover what factors or elements bankers must consider before they buy or sell
securities for their banks.

                             Key Terms Presented in This Chapter

                  Money-Market Instruments                Yield to Maturity (YTM)
                  Capital-Market Instruments              Holding-Period Yield (HPY)
                  U.S. Treasury Bill                      Tax Swap
                  Treasury Notes                          Portfolio Shifting
                  Treasury Bonds                          Interest-Rate Risk
                  Federal Agency Securities               Credit Risk
                  Certificate of Deposit (CD)             Business Risk
                  Bankers' Acceptances                    Liquidity Risk
                  Commercial Paper                        Call Risk
                  Municipal Bonds                         Prepayment Risk
                  Corporate Notes                         Inflation Risk
                  Corporate Bonds                         Pledging
                  Securitized Assets                      Yield Curve
                  Mortgage-Backed Bond                    Duration
                  Stripped Security

                                        Chapter Outline

I.     Introduction: The Roles Performed by Investment Securities in Bank Portfolios
II.    Investment Instruments Available to Banks
       A.     Money-Market Instruments
              1.     Treasury Bills
              2.     Short-Term Treasury Notes and Bonds
              3.     Federal Agency Securities
              4.     Certificates of Deposit (CDs)
              5.     International Eurocurrency Deposits
              6.     Bankers' Acceptances
              7.     Commercial Paper
              8.     Short-Term Municipal Obligations
       B.     Capital Market Instruments
              1.     Treasury Notes and Bonds Over One Year to Maturity
              2.     Municipal Notes and Bonds
              3.     Corporate Notes and Bonds
III.   Other Investment Instruments Developed More Recently

        A.     Structured Notes
        B.     Securitized Assets
        C.     Stripped Securities
IV.     Investment Securities Actually Held by Banks
V.      Factors Affecting the Choice Among Investment Securities
        A.     Expected Rate of Return
        B.     Tax Exposure (Tax Swapping and Portfolio Shifting)
        C.     Interest-Rate Risk
        0.     Credit or Default Risk
        E.     Business Risk
        F.     Liquidity Risk
        G.     Call Risk
        H.     Prepayment Risk
        I.     Inflation Risk
        J.     Pledging Requirements
VI.     Investment Maturity Strategies
        A.     The Ladder or Spaced-Maturity Policy
        B.     The Front-End Loaded Maturity Policy
        C.     The Back-End Loaded Maturity Policy
        D.     The Barbell Strategy
        E.     The Rate Expectations Approach
VII.    Maturity Management Tools
        A.     The Yield Curve
        B.     Duration and Immunization
VIII.   Summary of the Chapter

                                         Concept Checks

11-1. Why do banks choose to devote a significant proportion of their assets to investments in
securities? What roles do investments play in the management of a bank?

Investments perform many different roles that act as a necessary complement to the advantages
loans provide. Investments generally have less credit risk than loans, allow the bank to diversify
into different localities than most of its loans permit, provide additional liquid reserves in case
more cash is needed, provide collateral as called for by law and regulation to back government
deposits, help to stabilize bank income over the business cycle, and aid banks in reducing their
exposure to taxes.

11-2. What are the principal money market and capital market instruments available to banks

Banks purchase a wide range of investment securities. The principal money market instruments
available to banks today are Treasury bills, federal agency securities, CD's issued by other
depository institutions, Eurodollar deposits, bankers' acceptances, commercial paper, and
short-term municipal obligations. Capital market instruments available to banks include Treasury

notes and bonds, state and local government notes and bonds, mortgage-backed securities, and
corporate notes and bonds.

11-3. What types of investment securities do banks prefer the most?

Banks clearly prefer these major types of investment securities: United States Treasury securities,
federal agency securities, and state and local government (municipal) bonds and notes. They hold
small amounts of equities and other debt securities (mainly corporate notes and bonds).

11-4. What are securitized assets? Why have they grown so rapidly over the past two decades?
What special risks do securitized assets present to banks investing in them?

Securitized assets are loans that are placed in a pool and, as the loans generate interest and
principal income, that income is passed on to the holders of securities representing an interest in
the loan pool. These loan-backed securities are attractive to many banks because of their higher
yields and frequent federal guarantees (in the case, for example, of most home-mortgage-backed
securities) as well as their relatively high liquidity and marketability. However, securitized assets
often carry substantial interest-rate risk and prepayment risk, which arises when certain loans in
the securitized-asset pool are paid off early by the borrowers (usually because interest rates have
fallen and new loans can be substituted for the old loans at cheaper loan rates) or are defaulted.
Prepayment risk can significantly decrease the values of securities backed by loans and change
their effective maturities.

11-5. What are structured notes and stripped securities? What unusual features do they have?

Structured notes usually are packaged investments assembled by security dealers that offer
customers flexible yields in order to protect their customers' investments against losses due to
inflation and changing interest rates. Most structured notes are based upon government or federal
agency securities.

Stripped securities consist of either principal payments or interest payments from a debt security.
The expected cash flow from a Treasury bond or mortgage-backed security is separated into a
stream of principal payments and a stream of interest payments, each of which may be sold as a
separate security maturing on the day the payment is due. Some of these stripped payments are
highly sensitive in their value to changes in interest rates.

11-6. How is the expected yield on most bonds held by banks determined?

For most bonds, this requires the calculation of the yield to maturity (YTM) if the bond is to be
held to maturity or the planned holding period yield (HPY) between point of purchase and point of
sale. YTM is the expected rate of return on a bond held until its maturity date is reached, based on
the bond's purchase price, promised interest payments, and redemption value at maturity. HPY is
a rate of discount bringing the current price of a bond in line with its stream of expected cash
inflows and its expected sale price at the end of the bank's holding period.

11-7. If a government bond is expected to mature in two years and has a current price of $950,
what is the bond's YTM if it has a par value of $1,000 and a promised coupon rate of 10 percent.
Suppose this bond is sold one year after purchase for a price of $970. What would this investor's
holding period yield be?

The relevant formula is:

             $100          $100         $1000
$950 =                            
         (1  YTM) 1
                       (1  YTM) 2
                                     (1  YTM) 2

Therefore, using the present value and annuity tables inside the text's front cover, we find the
bond's YTM to be:

                   $966 - $950
YTM = 12% +                      * 2  12.99%
                  $966  $933.60

If the bond is sold after one year, the formula entries change to:

             $100          $970
$950 =               
         (1  YTM) 1
                       (1  YTM) 1

and the YTM is:

                  $955.51- $950
YTM = 12% +                        * 2  12.64%
                 $955.51 - $938.39

11-8. What forms of risk affect bank security investments?

The following forms of risk affect bank security investments: interest-rate risk, credit risk,
business risk, liquidity risk, prepayment risk, call risk, and inflation risk. Interest-rate risk captures
the sensitivity of the value of investments to interest-rate movements, while credit risk reflects the
risk of default on either interest or principal payments. Business risk refers to the impact of credit
conditions and the economy, while liquidity risk focuses on the price stability and marketability of
investments. Prepayment risk is specific to certain types of investments and focuses on the fact
that some loans which the securities are based on can be paid off early. Call risk refers to the early
retirement of securities and inflation risk refers to their possible loss of purchasing power.

11-9. How has the tax exposure of various U.S. bank security investments changed in recent

In recent years, the government has treated interest income and capital gains from most bank
investments as ordinary income for tax purposes. In the past, only interest was treated as ordinary
income and capital gains were taxed at a lower rate. Tax reform in the United States has also had a
major impact on the relative attractiveness of state and local government bonds as bank

investments, limiting bankers ability to deduct borrowing costs for tax purposes when borrowing
money to buy municipal securities.

11-10. Suppose a corporate bond that a bank's investment officer would like to purchase for her
bank has a before-tax yield of 8.98 percent and the bank is in the 35 percent federal income tax
bracket. What is the bond's after-tax gross yield?

          Gross Yield                   = 8.98%(1 - 0.35) = 5.84%.
       on Corporate Bond

A prospective loan must generate a comparable yield to that of the bond to be competitive.
However, granting a loan to a corporation may have the added advantage of bringing in additional
service business for the bank that merely purchasing a corporate bond would not do. In this case
the bank would accept a somewhat lower yield on the loan compared to the bond in anticipation of
getting more total revenue from the loan relationship due to the sale of other bank services.

11-11. What is the net after-tax return on a qualified municipal security whose nominal gross
return is 6 percent, the cost of borrowed funds is 5 percent, and the bank is in the 35 percent tax
bracket? What is the tax-equivalent gross yield (TEY) on this tax-exempt security?

Net After-Tax Return = (.06 - .05) + (0.35 x 0.80 x .05) = 0.024 or 2.4%

The security's tax-equivalent yield in gross terms is 6%/(1-0.35) or 9.23%.

11-12. Spiro National Bank holds 6-percent bonds with an original cost of $5 million and a current
market value of $3.9 million. Comparable quality bonds today are trading at 8 percent. What are
the advantages to this bank of from selling the government bond bearing a 6 percent promised
yield and buying some 8 percent bonds?

In this instance the bank could sell the 6-percent bonds, buy the 8 percent bonds, and experience an
extra 2 percent in yield. The bank would experience a capital loss of $1.1 million from the bond's
book value, but the after-tax loss would be only $1.1 million * (1-0.35) or $0.715 million.

11-13 What is tax swapping? What is portfolio shifting? Give an example of each?

A tax swap involves exchanging one type of investment security for another when it is
advantageous to do so in reducing the bank's current or future tax exposure. For example, the bank
may sell investment securities at a loss to offset high taxable income on loans or to replace taxable
securities with tax-exempt securities. Portfolio switching which involves selling certain securities
out of a bank's portfolio, often at a loss, and replacing them with other securities, is usually carried
out to gain additional current income, add to future income, or to minimize a bank's current or
future tax liability. For example, the bank may shift its holdings of investment securities by selling
off selected lower-yielding securities at a loss, and substituting higher-yielding securities in order
to offset large amounts of loan income.

11-14. Why do banks face pledging requirements when they accept government deposits?

Pledging requirements are in place to safeguard the deposit of public funds. The first $100,000 of
public deposits is covered by federal deposit insurance, the rest must be backed up by bank
holdings of U.S. Treasury and federal agency securities valued at their par values.

11-15. What types of securities are used to meet bank collateralization requirements?

When a bank borrows from the discount window of its district Federal Reserve bank, it must
pledge either federal government securities or other collateral acceptable to the Fed. Typically,
banks will use U.S. Treasury securities to meet these collateral requirements. If the bank raises
funds through repurchase agreements (RPs), banks must pledge securities, typically U.S. Treasury
and federal agency issues, as collateral in order to borrow at the low RP interest rate.

11-16. What factors affect a bank's decision regarding the different maturities of securities it
should hold?

In choosing among various maturities of short-term and long-term securities to hold, the bank
needs to carefully consider the use of two key maturity management tools - the yield curve and
duration. These two tools help the bank's management understand more fully the consequences
and potential impact on bank earnings and risk of any particular maturity mix of securities they

11-17. What maturity strategies do banks employ in managing their investment portfolios?

In choosing the maturity distribution of securities to be held in the bank's investment portfolio one
of the following strategies typically is chosen by most banks:

A.     The Ladder or Spread-Maturity Strategy
B.     The Front-End Load Maturity Strategy
C.     The Back-End Load Maturity Strategy
D.     The Bar Bell Strategy
E.     The Rate-Expectation Approach

The ladder or spaced-maturity strategy involves equally spacing out a bank's security holdings
over its preferred maturity range to stabilize investment earnings. The front-end load maturity
strategy implies that a bank will pile up its security holdings into the shortest maturities to have
maximum liquidity and minimize the risk of loss due to rising interest rates. The back-end loaded
maturity policy calls for placing all security holdings at the long-term end of the maturity spectrum
to maximize potential gains if interest rates fall and to earn the highest average yields. In contrast,
the bar-bell strategy places a portion of the bank's security holdings at the short-end of the maturity
spectrum and the rest at the longest maturities, thus providing both liquidity and maximum income
potential. Finally, the rate expectations approach calls for shifting maturities toward the short end
if rates are expected to rise and toward the long-end of the maturity scale if interest rates are
expected to fall.

11-18 Bacone National Bank has structured its investment portfolio, which extends out to
four-year maturities, so that it holds about $11 million each in one-year, two-year, three-year and
four-year securities. In contrast, Dunham National Bank and Trust holds $36 million on one- and
two-year securities and about $30 million in 8- to 10-year maturities. What investment maturity
strategy is each bank following? Why do you believe that each of these banks has adopted the
particular strategy it has reflected in the maturity structure of its portfolio?

Bacone National Bank has structured its investment portfolio to include $11 million equally in
each of four one-year maturity intervals. This is clearly a spaced maturity or ladder policy. In
contrast, Dunham National Bank holds $36 million in one and two-year securities and about $30
million in 8 and 10-year maturities, which is clearly a barbell strategy. Dunham National Bank
pursues its strategy to provide both liquidity (from the short maturities) and high income (from the
long maturities), while Bacone National is a small bank that needs a simple-to-execute strategy.

11-19. How can the yield curve and duration help a bank's investment officer choose which
securities to acquire or sell?

Yield curves possibly provide a forecast of the future course of short-term rates, telling us what the
current average expectation is in the market. The yield curve also provides an indication of
equilibrium yields at varying maturities and, therefore, gives an indication if there are any
significantly underpriced or overpriced securities. Finally, the yield curve's shape gives the bank's
investment officer a measure of the yield trade-off - that is, how much yield will change, on
average, if a security portfolio is shortened or lengthened in maturity.

Duration tells a bank about the price volatility of its earning assets and liabilities due to changes in
interest rates. Higher values of duration imply greater risk to the value of assets and liabilities held
by a bank. For example, a loan or security with a duration of 4 years stands to lose twice as much
in terms of value for the same change in interest rates as a loan or security with a duration of 2

11-20. A bond currently selling for $950 with a $1,000 par value and which pays $100 in interest
for 3 years before being retired. Current YTMs on comparable-quality bonds are 12 percent. The
bond's duration must be:

                              Present         Present
                               Value          Value of          Present
               Cash           Factor           Cash              Value           Duration
 Year          Flow           at 12%           Flow             + Price         Components

   1           $100          0.893           $89.30            0.0940            0.0940
   2            100          0.797            79.70            0.0839            0.1678
   3           1100          0.712           783.20            0.8244            2.4733
                                                                                 2.7351 years

Clearly the bond's duration is 2.7351 years. If interest in the market fall to 10 percent, the
approximate percentage change in the bond's price will be:

Percentage Change in Price =  D x            x 100%
                                      (1  i)
                                             - .02
                              - 2.7351 x           x 100%  4.884 percent
                                          (1  .12)


11-1. A 10-year U.S. Treasury bond (par value, $1000) trading at $775 bears a 9-percent coupon
rate. What is this bond's expected yield to maturity?

(Hint - the following relationships can help in solving for the yield:

                If price < par value, then yield > coupon rate;
                If price = par value, then yield = coupon rate;
                If price > par value, then yield < coupon rate.)

Since the bond is selling at a discount, that is, price < par value, the yield will be greater than the
coupon rate, or a yield > 9%.

By trial and error, we search for two yields, one that makes the price greater than the target value of
$775 and another one that makes the price less than the target value of $775.

The relevant formula is:

             $90            $90                 $90           $1000
$775 =                             ...               
         (1  YTM) 1
                       (1  YTM) 2
                                           (1  YTM) 10
                                                          (1  YTM) 10

or $775 = $90 [$1 Annuity for 10 years at YTM%] + $1000 [PV of $1 at YTM%].

From the annuity and present-value tables we try 12% for YTM, giving:

$90 (5.650] + $1000 [0.322] = $508.50 +$322 = $830.50 > $775.

At YTM = 14% we find:

$90 {5.216] + $1000 [0.270] = $469.44 +$270 = $739.44 < $775.

The true yield to maturity is approximately:

                  $830.50 - $775                $55.50
YTM = 12% +                        * 2%  12%         * 2%  12%  1.22%
                 $830.50  $739.44              $91.06

 =       13.22% (By financial calculator, the solution is 13.18%.)

Alternative Scenario 1:

What is the holding-period yield for the U.S. Treasury bond if it is purchased today at $775 and
sold at the end of 3 years for $880?

The holding-period yield formula is:

$775 = $90 [Annuity of $1 for 3 years at HPY%] +$880 [PV of $1 in 3 years at HPY%].

At an estimated HPY of 14 percent we would have:

$90 [2.322]+ $880 [0.675] = $208.98 + $594 = $802.98 > $775.

At an estimated HPY of 16% we get:

$90 [2.246] + $880 [0.641] = $202.14 + $564.08 = $766.22 < $775.

The true holding-period yield is approximately:

                  $802.98- $775                $27.98
HPY= 14% +                        * 2%  14%         * 2%  14%  0.76% * 2%  15.52%
                $802.98  $766.22              $36.76

Alternative Scenario 2:

Suppose the bank later repurchases the same Treasury bond on the open market, this time paying
$940. The bond now has a remaining term to maturity of 4 years. What is the bond's yield to

The relevant formula, again, is:

             $90            $90                 $90         $1000
$940 =                             ...              
         (1  YTM) 1
                       (1  YTM) 2
                                           (1  YTM) 4
                                                         (1  YTM) 4

$940 = $90 [$1 Annuity for 4 years at YTM%] + $1000 [PV of $1 at YTM%].

From the annuity and present-value tables we try 10% for YTM, giving:

$90 [3.170] + $1000 [0.683] = $285.30 + $683 = $968.30 > $940.

At YTM = 12% we find:

$90 (3:037] + $1000 [0.636] = $273.33 + $636 = $909.33 < $940.

The true yield to maturity is approximately:

                  $968.30 - $940                $28.30
YTM = 10% +                        * 2%  10%         * 2%  10%  .96%  10.96%
                 $968.30  $909.33              $58.97

11 -2. A state government bond is selling today for $962.77 and has a $1,000 face (par) value. Its
yield to maturity is 6 percent, and the bond promises its holders $55 per year in interest for the next
10 years. What is the bond's duration?

              Annual                     PV of            Time                  Time-
              Interest       PV         Annual            Period               Weighted
  Year        Income        at 6%       Interest         Recorded                PV

     1       $ 55           0.943        51.87       x        1        =            $51.87
     2       $ 55           0.890        48.95       x        2        =            $97.90
     3       $ 55           0.840        46.20       x        3        =           $138.60
     4       $ 55           0.792        43.56       x        4        =           $174.24
     5       $ 55           0.747        41.09       x        5        =           $205.45
     6       $ 55           0.705        38.78       x        6        =           $232.68
     7       $ 55           0.665        36.58       x        7        =           $256.06
     8       $ 55           0.627        34.49       x        8        =           $275.92
     9       $ 55           0.592        32.56       x        9        =           $293.04
    10       $ 55           0.558        30.69       x       10        =           $306.90
    10       $1000          0.558       558.00       x       10        =          $5580.00
                                        $962.77                                   $7612.66

Then duration = $ 7612.66 / $962.77 = 8.186.years

Alternative Scenario 1:

If the bond's price falls to $950, its duration is approximately: $7612.66 / $950 = 8.013, which is a
change in duration of -0.173.

Alternative Scenario 2:

If the bank buys the bond at $950 and holds it to maturity, its after-tax yield to maturity will be
determined from:

             $55            $55                 $55           $1000
$950 =                             ...               
         (1  YTM) 1
                       (1  YTM) 2
                                           (1  YTM) 10
                                                          (1  YTM) 10

$950 = $55 [$1 Annuity for 10 years at YTM%] + $1000 [PV of $1 at YTM%].

From the annuity and present-value tables we try 6% for y, giving:

$55 [7.360] + $1000 [0.558] = $404.80 + $558 = $962.80 > $950.

At y = 8% we find:

$55{6.710] + $1000 [0.4631 = $369.05 + $463 = $832.05 < $950.

The true yield to maturity is approximately:

               $962.80 - $950               $12.80
YTM = 6%+                       * 2%  6%          * 2%  6%  .20%  6.20%
              $962.80  $832.05             $130.75

This is a before-tax yield. Since the income on this bond is tax exempt, we calculate the after-tax
equivalent yield as though this were a taxable bond as:

A.T. yield = 6.2% / (1 - .35) = 9.54%.

11-3. Calculate the yield to maturity of a 10-year U.S. Government bond that is currently selling
for $800 in today's market and carries a 10-percent coupon rate with interest paid semiannually.

              $50             $50                    $50             $1000
$800 =                                 ...                 
         (1  YTM/2) 1
                         (1  YTM/2) 2
                                               (1  YTM/2) 20
                                                                (1  YTM/2) 20

At a YTM/2 of 6% for 20 time periods we have:

$50 [11.470] + $1000 [0.312] = $573.50 + $312 = $885.50 > $800.

At a YTM/2 of 8% for 20 time periods we have:

$50 [9.818] + $1000 [0.215] = $490.90 + $215 = $705.90 < $800.

Therefore, the correct YTM / 2 yield is approximately:

               $885.50 - $800              $85.50
YTM = 6%+                      * 2%  6%          * 2%  6%  0.476* 2%  6.95%
              $885.5 - $705.90             $179.60

Then YTM= 2 (YTM/ 2) = 2 (6.95%) = 13.90%.

Alternative Scenario 1:

Suppose a bank purchases the 10-year bond at $800 and five years hence is compelled to sell it for
$900. What holding period yield can the bank expect after five years?

If the bond is sold after 5 years for $900 its estimated holding-period yield can be derived from:

$800 = $50 [annuity (10 periods) at HPY%] + $900 [PV in 10 periods at HPY%].

If HPY/2 is estimated at 6%, we have:

$50 [7.360] + $900 [0.558] = $368 + $502.20 = $870.20 > $800.

If HPY/2 is 8% we get:

$50 [6.710] + $900 [0.463] = $335.50 + $416.70 = $752.20 < $800.

Then the true HPY is:

       $870.20 - $800               $70.20
6%+                     * 2%  6%         * 2%  6%  .595* 2%  7.19%
      $870.20 - $752.20              $118

Therefore, the true holding-period yield is close to: HPY=2(HPY/2)=2 (7.19%)=14.38%.

Alternative Scenario 2:

Suppose the bond purchased at $800 suddenly rises to a premium of $1,100 after two years and the
bank alters its plan, selling the bond immediately to capture the premium. What will the holding
period return be?

If the bond is sold after 2 years for $1,100 its estimated holding-period yield can be derived from

$800 = $50 [Annuity (4 periods) at HPY%] + $1,100 [PV in 4 periods at HPY%].

If HPY/2 is estimated at 12%, we have:

$50 [3.465] + $l,100 [0.792]=$173.25+ $871.20 = $850.94 > $800.

If HPY/2 is estimated at 14% we have:

$50 [2.914] + $1,100 [0.592] = $145.70 + $651.20 = $796.60 < $800.

Then the true holding-period yield / 2 is about:

         $850.94 - $800                $50.94
12%+                      * 2%  12%         * 2%  12%  1.87%  13.87%
        $850.94 - $796.60              $54.34

Therefore, the true holding-period yield is close to: HPR = 2(HPR/2)=2 (13.87%)=27.75%.

Alternative Scenario 3:

Suppose First National Bank of Richland elected to purchase this 10-year Treasury bond and hold
it to its maturity date. If First National carries a 35 percent income tax rate, what expected after-tax
yield to maturity would result?

       After Tax Yield = Before Tax Yield * (1-0.35) = 13.90% (0.65) = 9.04%

This problem could also be solved by recalculating the interest income expected in each time
period in after-tax terms -- that is, $50 * (1 -0.35) -- and the capital gain in after-tax terms --that is,
($1,000 - $800) * (1 -0.35) in year 10.

11-4. A corporate bond being seriously considered for purchase by First Bank and Trust will
mature 20 years from today and promises a 12 percent interest payment once a year. Recent
inflation in the economy has driven the yield to maturity on this bond to 15 percent, and it carries a
face value of $1000. Calculate this bond’s duration.

              Annual                PV of             Time               Time-
              Interest      PV     Annual             Period           Weighted
  Year        Income      at 15%   Interest        X Recorded        =    PV
    1          $120       0.870  $104.40                 1               $104.40
    2           120       0.756    90.72                 2                181.44
    3           120       0.658    78.96                 3                235.88
    4           120       0.572    68.84                 4                274.56
    5           120       0.497    59.64                 5                298.20
    6           120       0.432    51.84                 6                311.04
    7           120       0.376    45.12                 7                315.84
    8           120       0.327    39.24                 8                313.92
    9           120       0.284    34.08                 9                306.72
   10           120       0.247    29.64                10                296.40
   11           120       0.215    25.80                11                283.80
   12           120       0.187    22.44                12                269.28
   13           120       0.163    19.56                13                254.28
   14           120       0.141    16.92                14                236.88
   15           120       0.123    14.76                15                221.40
   16           120       0.017    12.84                16                205.44
   17           120       0.093    11.16                17                189.72
   18           120       0.081      9.72               18                174.96
   19           120       0.070      8.40               19                159.60
   20           120       0.061      7.32               20                146.40
   20          1000       0.061    61.00                20               1220.00
                                  $812.2                               $6001.16

Therefore, the bond's duration is: $6001.16/$812.20 = 7.39 years.

Alternative Scenario:

Suppose the bank plans to hold the corporate bond described above for 12 years. Will this bond
carry market risk for the bank?

Yes, because interest rates may rise, lowering the bond's price.

How could the bank reduce its risk of loss from unfavorable interest rate movements? Please
explain carefully.

The bank could reduce its risk of loss from changing interest rates by holding, instead, a bond
whose duration matches its planned holding period of 12 years. This would immunize the bank
from interest rate changes. Because the duration of the bond equaled the planning horizon of the
bank the price and reinvestment risk would exactly offset each other and therefore the bank would
have the same dollar amount at the end of 12 years no matter what happened to interest rates.

11-5. City National Bank regularly purchases municipal bonds issued by small rural school
districts in its region of the state. At the moment, the bank is considering purchasing an $8 million
general obligation issue from the Youngstown school district, the only bond issue that district
plans this year. The bonds, which mature in 15 years, carry a nominal annual rate of return of
7.75%. City National, which is in the top corporate tax bracket of 35 percent, must pay an average
interest rate of 7.38% to borrow the funds needed to purchase the municipals. Would you
recommend purchasing these bonds?

Because these bonds were issued by a small governmental unit issuing less than $10 million in
securities annually, the interest cost the bank has to pay to acquire the funds needed to buy these
bonds is tax deductible. Therefore, their net after-tax return is:

       Net A.T.Y        =      (7.75% - 7.38%) + (0.80 x 0.35 x 7.38%)
                        =      7.75% -7.38% + 2.066%
                        =      2.436%

This net yield figure should be compared with other investments of comparable risk on an after-tax
basis. However, the tax-exempt status of the income coupled with the tax-deductibility of the
interest expense make these bonds a very attractive alternative.

Alternative Scenario:

What if the bank has to choose between the $8 million in municipals and a package of loans of an
equivalent amount that promises a before-tax return of 9.20 percent? Which use of the funds would
you recommend? Please explain.

The 9.20% before-tax return equates to a 5.98% after-tax return - that is, 9.20% * (1-0.35) or
5.98%. Clearly, the loan's after-tax return does not compare favorably with the municipal bonds.

An alternative solution would be: (Before-tax Gross Yield - Cost of Funds) * (1 - Tax Rate)
                       =     (9.2% - 7.38%) * (1 - .35)
                       =     1.82% X 0.65 = 1.18%

This 1.18% net after-tax yield does not compare favorably to the 2.44% net after-tax yield of the

11-6. Lakeway State Bank is interested in doing some investment portfolio shifting. Its loan
revenues this year have increased by 16 percent over last year’s level. The bank is subject to the 35
percent corporate income tax rate. The bank's investment officer has several options in the form of
bonds that have been held for some time in its portfolio:

       A.     Selling $4 million in 12-year City of Dallas bonds with a coupon rate of 7.5 percent
       and purchasing $4 million in bonds from Bexar County (also with 12-year maturities) with
       a coupon rate of 8% and issued at par. The Dallas bonds have a current market value of
       $3,750,000 but are listed on the bank's books at their $4 million par value.

       B.     Selling $4 million in 12-year U.S. Treasury bonds that carry a coupon rate of 12%
       and are recorded at par, which was the price when the bank purchased them. The market
       value of these bonds has risen to $4,330,000.

Which of these two portfolio shifts would you recommend? Is there a good reason for not selling
the Treasury bonds? What other information is needed to make the best decision? Please explain.

Under Option A the Lakeway bank will take an immediate $4 million - $3.75 million, or $250,000,
loss before taxes (or a loss of $162,500 after taxes) which can be used to help offset the high
taxable loan income earned this year. Moreover, the bank will be able to earn 8% on an investment
of $4 million, or $320,000, in annual interest income compared to only $300,000 with the bonds
currently held or a gain in tax-exempt income of $20,000 per year. (Of course, if the bank can only
afford to buy $3,750,000 in new municipals - the sale price of the old bonds - it will generate about
$300,000 in after-tax interest and have no net gain in tax-exempt interest income, but will still have
a tax-deductible loss on the sale of the old bonds.)

Under Option B the U.S. Treasury bonds must be sold for a gain of $330,000 which is taxable
income. Because the bank does not need additional taxable income, Option B is less desirable than
Option A. Besides, the Treasury bonds are selling at a premium above par which indicates their
coupon rate is higher than current interest rates on investments of comparable risk, suggesting the
wisdom of retaining these bonds in the bank's portfolio either until loan revenues decline and the
bank needs additional taxable income or until interest rates rise well above current levels and new
securities appear that promise significantly higher interest yields.

11-7. Current market yields on U.S. government securities are distributed by maturity as follows:

       3-month T bills         =      7.69 percent
       6-month T bills         =      7.49 percent
       1-year T notes =        7.77 percent
       2-year T notes =        7.80 percent
       3-year T notes =        7.80 percent
       5-year T notes =        7.81 percent
       7-year T notes =        7.86 percent
       10-year T notes=        7.87 percent
       30-year T bonds=        7.90 percent

Draw a yield curve for the above securities. What shape does the curve have? What significance
might this yield curve have for a bank with 75 percent of its investment portfolio in 7-year to
30-year Treasury bonds and 25 percent in U.S. government bills and notes under one year? What
would you recommend to the bank’s management?

The yield curve for U.S. Treasury bonds clearly slopes upward after the 6-month maturity point
and declines for 3- to 6-month maturities. Like most yield curves this curve becomes quite flat at
longer maturities, particularly over the 7- to 30-year maturity segment. The bank with 75 percent
of its portfolio in this 7- to 30-year range gains very little yield advantage over those banks holding
shorter maturities in the form of 3-month bills to 5-year notes. Yet, the longer-term bonds are less
liquid so that a bank holding 7+-year maturities faces substantially greater liquidity risk. This
bank would probably be better off to do some portfolio shifting into medium-term maturities.

11-8. A bond possesses a duration of 5.82 years. Suppose that market interest rates on
comparable bonds were 7 percent this morning but have now shifted upward to 7.5 percent. What
percentage change in the bond’s value occurred when interest rates moved .5 percent higher?

                                        0.50   2.91
 Percent Change in Value =       5.82                 2.72 percent
                                       1  .07  1.07

11-9. The investment officer for Sillistine State Bank in concerned about interest-rate risk
lowering the value of the bank’s bonds. A check of the bank’s bond portfolio reveals an average
duration of 4.5 years. How could this bond portfolio be altered in order to minimize interest rate
risk should interest rates change significantly within the next year.

The bank's bond portfolio has an average duration of 4.5 years. This is relatively long, subjecting
the bank to substantial interest-rate risk. Shortening the duration of the portfolio or the use of
hedging tools (such as futures and options) is recommended.

11-10. A bank’s economic department has just forecast accelerated growth in the economy with
GDP expected to grow at a 4.5 percent annual growth rate for at least the next two years. What are
the implications of this economic forecast for the bank’s investment officer? What types of
securities should the investment officer think most seriously about adding to the bank’s investment
portfolio? Why? Suppose the bank holds a security portfolio similar to the one described in Table
11-3 for all insured U.S. banks. Which type of securities might the bank want to think seriously
about selling if the projected economic expansion takes place? What losses might occur and how
could these be minimized?

This economic forecast suggests that the current yield curve should be upward sloping and that
interest rates will rise over the next two years. In addition, loan demand should increase as the
economy expands suggesting that the bank may have to sell some of its investment portfolio in the
future to meet that demand. The investment officer would probably shorten the maturities of the
investment portfolio. An exception to this might be if the investment officer wants to ride the yield
curve by selling shorter term securities at a premium today and replacing them with longer
maturity securities with higher coupon rates. However, the investment manager must take into

account the risk of capital losses for the future with this strategy. The investment manager can
      Types of Securities Held             %                   Types of Securities Held     %
      U.S. Treasury Securities           38.7                Securities Available for Sale 45.6
     Federal Agency Securities           35.2
 State and Local Govt. Obligations       15.5                 Securities with Maturities:
     Domestic Debt Securities             5.1                        Under 1 year          11.3
      Foreign Debt Securities             4.9                         1 to 5 years         37.9
               Equities                   0.6                        Over 5 years          50.8
reduce his risks with the appropriate hedging tools as discussed in previous chapters.

11-11. Contrary to the exuberant economic forecast described in the previous problem, suppose a
bank’s economic department is forecasting a significant recession in economic activity. Output
and employment are projected to decline significantly over the next 18 months. What are the
implications of this forecast for a bank’s investment portfolio manager? What is the outlook for
interest rates and inflation under the foregoing assumption? What types of securities would you
recommend during the period covered by the recession forecast and why? What other kinds of
information would you like to have about the bank’s current balance sheet and earnings report in
order to help you make the best quality decisions regarding the bank’s security portfolio?

This economic forecast suggests that the current yield curve should be flat or downward sloping
and interest rates and inflation should fall over the next 18 months. In addition, loan demand
should decline in the future as output and employment decline. The portfolio manager should
lengthen the maturities of the investment portfolio and lock in higher rates now. However, the
investment manager should look at the bank’s current interest-sensitive gap and duration gap
position as well as their current earnings and tax status and consider these aspects of the bank’s
balance sheet before making any decisions.

11-12. Arrington Hills National Bank, a $3.5 billion asset institution, holds the security portfolio
outlined below. The bank serves a rapidly growing money center into which substantial numbers
of businesses are relocating their corporate headquarters. Suburban areas around the city are also
growing rapidly as large numbers of business owners and managers along with retired
professionals are purchasing new homes and condominiums. Would you recommend any change
in the makeup of the security portfolio outlined below? Please explain why.

This bank is going to experience increasing loan demand in the future. This may mean increased
taxes in the future, increased liquidity risk and increased credit risk from its loan portfolio. To help
with the liquidity risk, the bank may want to consider shifting some of its portfolio from securities
with more than five years to maturity to shorter term securities. In terms of the increased taxes and
credit risk, it depends on which one of these is more important. The proportion of the municipal
bonds in this bank’s portfolio is already higher than the average bank of its size. The bank may
want to reduce its credit risk by reducing its municipal bond portfolio. However, this bank does

have other ways of reducing its credit risk and it may want to decrease its taxability by increasing
its investment in municipal bonds.

                                        Web Site Problems

1. As the investment officer for Bank of America, you have been informed by a member of the
bank’s board of directors that the investment policies you have followed over the past year have
been substandard relative to your competitors, including Citibank, Wells Fargo and Bank One.
You protest and observe that all banks have faced a tough market and, in your opinion, your bank
has done exceptionally well. Challenged, your CEO asks you to prepare a brief memo with
comparative investment facts, defending your bank’s investment portfolio performance against the
other banks mentioned. What web sites could you use to respond? What conclusion did you reach
after examining your bank’s relative investment performance over the preceeding four quarters?

The best web site to find comparative investment portfolio results for the above banks is the FDIC
web site and the UBPR for these banks. The table below shows the resuts for the 4 banks and their
peers for the four quarters of 2000. The FDIC certificate numbers for the banks are 3510 for BOA,
3511 for Wells Fargo, 7213 for Citibank and 6559 for Bank One. Knowing these numbers can
speed up the search for this information. There are many different pieces of information that could
be analyzed in response to this question. The analysis below uses the information about the total
yield on investment securities found on page 12 of the UBPR.

             Bank                      12-2000         9-2000     6-2000       3-2000      12-1999
        Bank of America                 5.95%          5.96%      5.91%        6.00%        6.10%
          Wells Fargo                   7.89%          7.46%      7.26%        7.00%        9.13%
           Citibank                     6.66%          6.33%      6.81%        7.22%        7.26%
           Bank One                     8.35%          8.32%      7.70%        7.41%        7.92%
        Peer Group One                  6.88%          6.86%      6.79%        6.53%        6.53%

From the above table it appears that bank of America does have a problem with its investments
portfolio. Its total yield is below the average for peer institutions and is below all of the banks
examined specifically. It appears that the investment manager needs to improve his or her

2. Which sites on the web seem especially good to you for help in evaluating the merits and
demerits of different types of securities that banks are allowed to add to their investment

One web site that looks good is This web
site allows investors to evaluate the risk of their portfolio compares to other indices and
benchmarks. In addition it examines the risk return tradeoff for a particular portfolio to determine
if the investor is being adequately compensated for additional risk. If an investor wants more
general information about bonds, what different types there are and other pertinent information
one good web site is This web site has a good glossary, bond
basics as well as information about current prices on various bonds.

3. If you want a summary of regulations applying to bank security portfolios where could you look
for this information?

The best web site for finding information about bank regulations regarding the bank’s security
portfolio is the FDIC web site at It has a section
on regulations and laws and you can do a search on a particular phrase or key word which would
allow you to find the specific laws regarding a bank’s security portfolio. This web site also has a
chronological list and summary of the important legislation regarding banks.


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