Appendix_8A the Maturity Model

8A-1

Appendix 8A The Maturity Model As mentioned in the chapter, a weakness of the repricing model is its reliance on book values rather than market values of assets and liabilities. Indeed, in most countries, FIs report their bal-ance sheets by using book value accounting. This method records the historic values of securities purchased, loans made, and liabilities sold. For example, investment assets (i.e., those expected to be held to maturity) are recorded at book values, while those assets expected to be used for trad-ing (trading securities or available-for-sale secu-rities) are reported according to market value. 1

The recording of market values means that assets and liabilities are revalued to reflect current mar-ket conditions. Thus, if a fixed-coupon bond had been purchased at $100 per $100 of face value in a low-interest rate environment, a rise in cur-rent market rates reduces the present value of the cash flows from the bond to the investor. Such a

rise also reduces the pricesay, to $97at which the bond could be sold in the secondary market today. That is, the market value accounting approach reflects economic reality, or the true values of assets and liabilities if the FIs portfolio were to be liquidated at todays securities prices rather than at the prices when the assets and liabilities were originally purchased or sold. This practice of valuing securities at their market value is referred to as marking to market. We discuss book value ver-sus market value accounting and the impact that the use of the alternative methods has in measur-ing the value of an FI in more detail in Chapter 20. In the maturity and duration model, developed below and in Chapter 9, the effects of interest rate changes on the market values of assets and liabilities are explicitly taken into account. This contrasts with the repricing model, discussed in Chapter 8, in which such effects are ignored.

EXAMPLE 8A1

Fixed-Income Assets and the Maturity Model

Consider the value of a bond held by an FI that has one year to maturity, a face value of $100 ( F ) to be paid on maturity, one single annual coupon at a rate of 10 percent of the face value ( C ), and a current yield to maturity ( R ) (reflecting current interest rates) of 10 percent. The

fair market price of the one-year bond, P1B , is equal to the present value of the cash flows on

the bond:

P1B5

F 1 C11 1 R 2

5100 1 10

1.15 100

Suppose the Bank of Canada tightens monetary policy so that the required yield on the bond rises instantaneously to 11 percent. The market value of the bond falls to

P1B 5

100 1 101.11

5 99.10

Thus, the market value of the bond is now only $99.10 per $100 of face value, while its origi-nal book value was $100. The FI has suffered a capital loss ( P 1 ) of $0.90 per $100 of face value in holding this bond, or

P1 5 99.10 2 100 5 2$0.90

Also, the percentage change in the price is

P1 599.10 2 100

1005 20.90%

1 More accurately, they are reported at the lower of cost or current market value (LOCOM).

8A-2 Appendix 8A The Maturity Model

Suppose the FI in the example above issued a one-year deposit with a promised interest rate of 10 percent and principal or face value of $100. 2 When the current level of interest rates is 10 percent, the market value of the liability is 100:

P1D 5

100 1 1011.1 2

5 100

Should interest rates on new one-year deposits rise instantaneously to 11 percent, the FI has gained by locking in a promised interest payment to depositors of only 10 percent. The market value of the FIs liability to its depositors would fall to $99.10; alternatively, this would be the price the FI would need to pay the depositor if it repurchased the deposit in the sec-ondary market:

P1D 5

100 1 1011.11 2

5 99.10

That is, the FI gained from paying only 10 percent on its deposits rather than 11 percent if they were newly issued after the rise in interest rates.

EXAMPLE 8A2

Fixed-Rate Liabilities and the Maturity Model

This example simply demonstrates the fact that

PR6 0

A rise in the required yield to maturity reduces the price of fixed-income securities held in FI portfo-lios. Note that if the bond under consideration was issued as a liability by the FI (e.g., a fixed-interest

deposit such as a GIC) rather than being held as an asset, the effect would be the samethe market value of the FIs deposits would fall. However, the economic interpretation is different. Although rising interest rates that reduce the market value of assets are bad news, the reduction in the market value of liabilities is good news for the FI. The economic intuition is illustrated in the following example.

2 In this example we assume for simplicity that the promised interest rate on the deposit is 10 percent. In reality, for returns to intermediation to prevail, the promised rate on deposits would be less than the promised rate (coupon) on assets.

As a result, in a market value accounting framework, rising interest rates generally lower the market values of both assets and liabilities on

an FIs balance sheet. Clearly, falling interest rates have the reverse effect: They increase the market values of both assets and liabilities.

In the preceding examples, both the bond and the deposit were of one-year maturity. We can easily show that if the bond or deposit had a two-year maturity with the same annual coupon rate, the same increase in market interest rates from 10 to 11 percent would have had a more negative effect on the market value of the bonds (and deposits) price. That is, before the rise in required yield:

P2B 5

1011.1 2

110 1 100

11.1 225 100

After the rise in market yields from 10 to 11 percent:

P2B 5

1011.11 2

110 1 100

11.11 225 98.29

and

P2B 5 98.29 2 100 5 21.71

EXAMPLE 8A3

Impact ofMaturity on Change inBond Value

Appendix 8A The Maturity Model 8A-3

This example demonstrates another general rule of portfolio management for FIs: The longer the maturity of a fixed-income asset or liability, the larger its fall in price and market value for any given increase in the level of market interest rates. That is,

P1R

6P2R

6 6P30R

Note that while the two-year bonds fall in price is larger than the fall of the one-year bonds, the dif-ference between the two price falls, % P 2 % P 1 , is 1.71% ( 0.9%) 0.81%. The fall in the three-year, 10 percent coupon bonds price when yield increases to 11 percent is 2.44 percent. Thus, % P 3 % P 2 2.44% ( 1.71%) 0.73%. This establishes an important result: While P 3 falls

more than P 2 and P 2 falls more than P 1 , the size of the capital loss increases at a diminishing rate as we move into the higher maturity ranges. This effect is graphed in Figure 8A1 .

So far, we have shown that for an FIs fixed-income assets and liabilities:

1. A rise (fall) in interest rates generally leads to a fall (rise) in the market value of an asset or liability.

2. The longer the maturity of a fixed-income asset or liability, the larger the fall (rise) in marketvalue for any given interest rate increase (decrease).

3. The fall in the value of longer-term securities increases at a diminishing rate for any given increase in interest rates.

The resulting percentage change in the bonds value is

%P2B 5 198.29 2 100 2 >100 5 21.71%

If we extend the analysis one more year, the market value of a bond with three years to maturity, a face value of $100, and a coupon rate of 10 percent is

P3B 5

1011.1 2

110

11.1 221

10 1 100

11.1 235 100

After the rise in market rates from 10 to 11 percent, market value of the bond is

P3B 5

1011.11 2

110

11.11 221

10 1 100

11.11 235 97.56

This is a change in the market value of

P3B 5 97.56 2 100 5 22.44

or

%P3B 597.56 2 100

1005 22.44%

FIGURE 8A1 The Relationship between R, Maturity, and P (Capital Loss)

$.90

$1.71$2.44

P(Capital loss)

0Maturity ofthe bond

1 2 3


amounts of relatively longer-term, fixed-income assets such as conventional mortgages, consumer loans, business loans, and bonds, while issuing shorter-term liabilities, such as GICs with fixed-interest payments promised to the depositors. 3

Consider the simplified portfolio of a represen-tative FI in Table 8A1 and notice that all assets and liabilities are marked to market; that is, we are using a market value accounting framework. Note that in the real world, reported balance sheets dif-fer from Table 8A2 because historic or book value accounting rules are used. In Table 8A2 the dif-ference between the market value of the FIs assets ( A ) and the market value of its liabilities such as deposits ( L ) is the net worth or true equity value ( E ) of the FI. This is the economic value of the FI owners stake in the FI. In other words, it is the money the owners would get if they could liqui-date the FIs assets and liabilities at todays prices in the financial markets by selling off loans and bonds and repurchasing deposits at the best prices. This is also clear from the balance sheet identity:

E 5 A 2 L As was demonstrated earlier, when interest

rates rise, the market values of both assets and lia-bilities fall. However, in this example, because the maturity on the asset portfolio is longer than the maturity on the liability portfolio, for any given increase in interest rates, the market value of the asset portfolio ( A ) falls by more than the market value of the liability portfolio ( L ). For the balance sheet identity to hold, the difference between the changes in the market value of its assets and

The Maturity Model with a Portfolio of Assets and Liabilities The preceding general rules can be extended beyond an FI holding an individual asset or liabil-ity to a portfolio of assets and liabilities. Let M A be the weighted-average maturity of an FIs assets and M L the weighted-average maturity of an FIs liabilities such that

Mi 5 Wi1Mi1 1 Wi2Mi2 1 1 WinMin

where M i Weighted-average maturity of an FIs

assets (liabilities), i A or L W ij Importance of each asset (liability) in

the asset (liability) portfolio as mea-sured by the market value of that asset (liability) position relative to the market value of all the assets (liabilities)

M ij Maturity of the j th asset (or liability), j 1 n

This equation shows that the maturity of a portfo-lio of assets or liabilities is a weighted average of the maturities of the assets or liabilities that constitute that portfolio. In a portfolio context, the same three principles prevail as for an individual security:

1. A rise in interest rates generally reduces the market values of an FIs asset and liability portfolios.

2. The longer the maturity of the asset or liabil-ity portfolio, the larger the fall in value for any given interest rate increase.

3. The fall in value of the asset or liability port-folio increases with its maturity at a diminish-ing rate.

Given the preceding, the net effect of rising or falling interest rates on an FIs balance sheet depends on the extent and direction in which the FI mismatches the maturities of its asset and liability portfolios. That is, the effect depends on whether its maturity gap, M A M L , is greater than, equal to, or less than zero.

Consider the case in which M A M L > 0; that is, the maturity of assets is longer than the maturity of liabilities. This is the case of mostcommercial banks. These FIs tend to hold large

Assets Liabilities

Long-term assets (A) Short-term liabilities (L)Net worth (E)

TABLE 8A1 The Market Value Balance Sheet of an FI

TABLE 8A2 Initial Market Values of an FIs Assets and Liabilities ($ millions)

Assets Liabilities

A $100 (MA 3 years) $ 90 L (ML 1 year) 10 E

$100 $100

3 These assets generate periodic interest payments such as coupons that are fixed over the assets life. In Chapter 9 we discuss interest payments fluctuating with market interest rates, such as on a variable-rate mortgage.


liabilities must be made up by the change in the market value of the FIs equity or net worth:

E 5 A1Change in FI 1Change in market

net worth 2 value of assets 2

2 L1Change in marketvalue of liabilities 2

To see the effect on FI net worth of having lon-ger-term assets than liabilities, suppose that ini-tially the FIs balance sheet looks like the one in Table 8A2 . The $100 million of assets is invested in three-year, 10 percent coupon bonds, and the lia-bilities consist of $90 million raised with one-year deposits paying a promised interest rate of 10 per-cent. We showed earlier that if market interest rates rise 1 percent, from 10 to 11 percent, the value of three-year bonds falls 2.44 percent while the value of one-year deposits falls 0.9 percent.4 Table 8A3 depicts this fall in asset and liability market values and the associated effects on FI net worth.

Because the FIs assets have a three-year matu-rity compared with its one-year maturity liabili-ties, the value of its assets has fallen by more than has the value of its liabilities. The FIs net worth declines from $10 million to $8.37 million, a loss of $1.63 million, or 16.3 percent! Thus, it is clear that with a maturity gap of two years:

MA 2 ML 5 2 years

13 2 2 11 2

a 1 percentage point rise in interest rates can cause the FIs owners or stockholders to take a big hit to their net worth. Indeed, if a 1 percent rise in inter-est rates leads to a fall of 16.3 percent in the FIs net worth, it is not unreasonable to ask how large an interest rate change would need to occur to ren-der the FI economically insolvent by reducing its

owners equity stake or net worth to zero. That is, what increase in interest rates would make E fall by $10 million so that all the owners net worth would be eliminated? For the answer to this ques-tion, look at Table 8A4 . If interest rates were to rise a full 7 percent, from 10 to 17 percent, the FIs equity ( E ) would fall by just over $10 million,rendering the FI economically insolvent.5

Given this example, it is not surprising that financial institutions with 25-year fixed-rate mortgages as assets and shorter-term deposits as liabilities suffered badly during the 19791982 period, when interest rates rose dramatically. At the time, deposit-taking institutions measured interest rate risk almost exclusively according to the repricing model, which captures the impact of interest rate changes on net interest income only. Regulators monitoring this measure only, rather

TABLE 8A3 An FIs Market Value Balance Sheet after a Rise in Interest Rates of 1 Percent with Longer-Term Assets

Assets Liabilities

A $97.56 L $89.19E 8.37

$97.56 $97.56or E A L $1.63 ($2.44) ($0.81)

TABLE 8A4 An FI Becomes Insolvent aftera 7 Percent Rate Increase

Assets Liabilities

A $84.53 L $84.62E 0.09

$84.53 $84.53or E A L $10.09 ($15.47) ($5.38)

4 The market value of deposits ($ millions) is initially

P1D 5

9 1 901.1

5 90

When rates increase to 11 percent, the market value decreases:

P1D 5

9 1 901.11

5 89.19

The resulting change is

P1D 589.19 2 90

905 20.90%

5 Here we are talking about economic insolvency. The legal and regulatory definition may vary, depending on what type of accounting rules are used.


than a market valuebased measure, were unable to foresee the magnitude of the impact of rising interest rates on the market values of these FIs assets and thus on their net worth.

From the preceding examples, you might infer that the best way for an FI to immunize, or pro-tect, itself from interest rate risk is for its man-agers to match the maturities of its assets and liabilities, that is, to construct its balance sheet so that its maturity gap, the difference between the weighted-average maturity of its assets and liabilities, is zero ( M A M L 0). However, as we

discuss next, maturity matching does not always protect an FI against interest rate risk.

WEAKNESSES OF THE MATURITY MODEL The maturity model has two major shortcomings: (1) It does not account for the degree of leverage in

Suppose the FI had adopted an even more extreme maturity gap by investing all its assets in 30-year fixed-rate bonds paying 10 percent coupons while continuing to raise funds by issuing one-year deposits with promised interest payments of 10 percent, as shown in Table 8A5 . Assuming annual compounding and a current level of interest rates of 10 percent, the market price of the bonds ($ millions) is initially

P30B 5

$1011.1 2

1$10

11.1 221 1

$10

11.1 2291

$10 1 $100

11.1 2305 $100

If interest rates were to rise by 1.5 percent to 11.5 percent, the price ($ millions) of the30-year bonds would fall to

P30B 5

$1011.115 2

1$10

11.115 221 1

$10

11.115 2291

$10 1 $100

11.115 2305 $87.45

a drop of $12.55, or as a percentage change, %P30B 5 1$87.45 2 $100 2 >$100 5 212.55%.

The market value of the FIs one-year deposits would fall to

P1D 5

$9 1 $901.115

5 $88.79

a drop of $1.21 or ($88.79 $90)/$90 1.34%. Look at Table 8A6 to see the effect on the market value balance sheet and the FIs net

worth after a rise of 1.5 percent in interest rates. It is clear from Table 8A6 that when the mismatch in the maturity of the FIs assets and liabilities is extreme (29 years), a mere 1.5 percent increase in interest rates completely eliminates the FIs $10 million in net worth and renders it completely and massively insolvent (net worth is $1.34 million after the rise in rates). In contrast, a smaller maturity gap (such as the two years from above) requires a much larger change in interest rates (i.e., 7 percent) to wipe out the FIs equity. Thus, interest rate risk increases as the absolute value of the maturity gap increases.

EXAMPLE 8A4

ExtremeMaturity Mismatch

TABLE 8A5 An FI with an Extreme Maturity Mismatch

Assets Liabilities

A $100 (MA 30 years) L $ 90 (ML 1 year)E 10

$100 $100

TABLE 8A6 The Effect of a 1.5 Percent Rise in Interest Rates on the Net Worth of an FI with an Extreme Asset and Liability Mismatch

Assets Liabilities

A $87.45 L $88.79E 1.34

$87.45 $87.45or E A L $11.34 ($12.55) ($1.21)


the FIs balance sheet, and (2) it ignores the timing of the cash flows from the FIs assets and liabili-ties. As a result of these shortcomings, a strategy of matching asset and liability maturities moves the FI in the direction of hedging itself against interest rate risk, but it is easy to show that this strategy does not always eliminate all interest rate risk for an FI.

To show the effect of leverage on the ability of the FI to eliminate interest rate risk using the maturity model, assume that the FI is initially set up as shown in Table 8A7 . The $100 million in assets is invested in one-year, 10 percent cou-pon bonds, and the $90 million in liabilities is in one-year deposits paying 10 percent. The maturity gap ( M A M L ) is now zero. A 1 percent increase in interest rates results in the balance sheet in Table 8A8 . In Table 8A8 , even though the matu-rity gap is zero, the FIs equity value falls by $0.10 million. The drop in equity value is due to the fact that not all the assets (bonds) were financed with deposits; rather, equity was used to finance a por-tion of the FIs assets. As interest rates increased, only $90 million in deposits were directly affected, while $100 million in assets were directly affected.

We show next, using a simple example, that an FI choosing to directly match the maturities and values of its assets and liabilities (so that M A M L and $ A $ L ) does not necessarily achieve per-fect immunization, or protection, against inter-est rate risk. Consider the example of an FI that

issues a one-year GIC to a depositor. This GIC has a face value of $100 and an interest rate promised to depositors of 15 percent. Thus, on maturity at the end of the year, the FI has to repay the bor-rower $100 plus $15 interest, or $115, as shown in Figure 8A2 .

Suppose the FI lends $100 for one year to a corporate borrower at a 15 percent annual inter-est rate (thus, $ A $ L ). However, the FI contrac-tually requires half of the loan ($50) to be repaid after six months and the last half to be repaid at the end of the year. Note that although the matu-rity of the loan equals the maturity of the deposit of one year and the loan is fully funded by deposit liabilities, the cash flow earned on the loan may be greater or less than the $115 required to pay off depositors, depending on what happens to inter-est rates over the one-year period. You can see this in Figure 8A3 .

At the end of the first six months, the FI receives a $50 repayment in loan principal plus $7.5 in interest (100 1/2 year 15 percent), for a total mid-year cash flow of $57.5. At the end of the year, the FI receives $50 as the final repayment of loan principal plus $3.75 interest ($50 1/2 year 15 percent) plus the reinvestment income earned from re-lending the $57.5 received six months ear-lier. If interest rates do not change over the period, the FIs extra return from its ability to reinvest part of the cash flow for the last six months will be ($57.5 1/2 15 percent) 4.3125. We summarize

TABLE 8A7 Initial Market Values of an FIs Assets and Liabilities with a Maturity Gap of Zero ($ millions)

Assets Liabilities

A $100 (MA 1 years) L $ 90 (ML 1 year)E 10

$100 $100

TABLE 8A8 FIs Market Value Balance Sheet after a 1 Percent Rise in Interest Rates($ millions)

Assets Liabilities

A $99.09 L $89.19E 9.90

$99.09 $99.09or E A L 0.10 0.91 (0.81)

FIGURE 8A2 One-Year GIC Cash

Flows FI borrows$100

FI pays principalplus interest todepositor = $115

0 1 year


the total cash flow on the FIs one-year loan in Table 8A9 .

As you can see, by the end of the year, the cash paid in on the loan exceeded the cash paid out on the deposit by $0.5625. The reason for this is the FIs ability to reinvest part of the principal and interest over the second half of the year at 15 percent. Suppose that interest rates, instead of staying unchanged at 15 percent throughout the whole one-year period, had fallen to 12 percent over the last six months in the year. This fall in rates would affect neither the promised deposit rate of 15 percent nor the promised loan rate of 15 percent because they are set at time 0 when the deposit and loan were originated and do not change throughout the year. What is affected is the FIs reinvestment income on the $57.5 cash flow received on the loan at the end of six months. It can be re-lent for the final six months of the year only at the new, lower interest rate of 12 percent (see Table 8A10 ).

The only change to the asset cash flows for the bank comes from the reinvestment of the $57.5 received at the end of six months at the lower

Cash Flow at 1/2 Year

Principal $ 50.00 Interest 7.50

Cash Flow at 1 year

Principal $50.00 Interest 3.75 Reinvestment income 4.3125 $115.5625

TABLE 8A9 Cash Flow on a Loan with a 15 Percent Interest Rate

Cash Flow at 1/2 Year

Principal $ 50.00 Interest 7.50

Cash Flow at 1 year

Principal $50.00 Interest 3.75 Reinvestment income 3.45 $114.70

TABLE 8A10 Cash Flow on the Loan When the Beginning Rate of 15 Percent Falls to 12 Percent

interest rate of 12 percent. This produces the smaller reinvestment income of $3.45 ($57.5 1/2 12 percent) rather than $4.3125 when rates stayed at 15 percent throughout the year. Rather than making a profit of $0.5625 from intermedia-tion, the FI loses $0.3. Note that this loss occurs as a result of interest rates changing, even when the FI had matched the maturity of its assets and lia-bilities ( M A M L 1 year), as well as the dollar amount of loans (assets) and deposits (liabilities) (i.e., $ A $ L ).

Despite the matching of maturities, the FI is still exposed to interest rate risk because the timing of the cash flows on the deposit and loan are not per-fectly matched. In a sense, the cash flows on the loan are received, on average, earlier than cash flows are paid out on the deposit, where all cash flows occur at the end of the year. Chapter 9 shows that only by matching the average lives of assets and liabilitiesthat is, by considering the precise timing of arrival (or payment) of cash flowscan an FI immunize itself against interest rate risk.

Loan$100

Receive$50 principal+ interest ($3.75)+ interest onreinvestment of cashflow received inmonth 6 = $53.75 plusinterest on cash flowsreceived in month 6

Receive$50 principal+ interest ($7.5)= $57.5

6 months 1 year0FIGURE 8A3 One-Year Loan Cash Flows


1. What is a maturity gap? How can the maturity model be used to immunize an FIs portfolio? What is the critical requirement that allows matu-rity matching to have some success in immunizing the balance sheet of an FI?

2. Nearby Bank has the following balance sheet($ millions):

What is the maturity gap for Nearby Bank? Is Nearby Bank more exposed to an increase or a decrease in interest rates? Explain why.

3. County Bank has the following market value bal-ance sheet ($ millions, all interest at annual rates). All securities are selling at par equal to book value.

a. What is the maturity gap for County Bank? b. What will be the maturity gap if the interest rates

on all assets and liabilities increase 1 percent? c. What will happen to the market value of the

equity? 4. If a bank manager is certain that interest rates

are going to increase within the next six months, how should the bank manager adjust the banks maturity gap to take advantage of this antici-

pated increase? What if the manager believed rates would fall? Would your suggested adjustments be difficult or easy to achieve?

5. Consumer Bank has $20 million in cash and a $180 million loan portfolio. The assets are funded with demand deposits of $18 million, a $162 million GIC, and $20 million in equity. The loan portfolio has a maturity of two years, earns interest at an annual rate of 7 percent, and is amortized monthly. The bank pays 7 percent annual interest on the GIC, but the interest will not be paid until the GIC matures at the end of two years.

a. What is the maturity gap for Consumer Bank? b. Is Consumer Bank immunized, or protected,

against changes in interest rates? Why or why not?

c. Does Consumer Bank face interest rate risk? That is, if market interest rates increase or decrease 1 percent, what happens to the value of the equity?

d. How can a decrease in interest rates create inter-est rate risk?

6. FI International holds seven-year Acme Interna-tional bonds and two-year Beta Corporation bonds. The Acme bonds are yielding 12 percent and the Beta bonds are yielding 14 percent under current market conditions.

a. What is the weighted-average maturity of FIs bond portfolio if 40 percent is in Acme bonds and 60 percent is in Beta bonds?

b. What proportion of Acme and Beta bonds should be held to have a weighted-average yield of 13.5 percent?

c. What will be the weighted-average maturity of the bond portfolio if the weighted-average yield is realized?

7. An insurance company has invested in the fol-lowing fixed-income securities: (a) $10,000,000 of five-year Treasury notes paying 5 percent interest and selling at par value, (b) $5,800,000 of 10-year bonds paying 7 percent interest with a par value of $6,000,000, and (c) $6,200,000 of 20-year subordi-nated debentures paying 9 percent interest with a par value of $6,000,000.

a. What is the weighted-average maturity of this portfolio of assets?

b. If interest rates change so that the yields on all the securities decrease 1 percent, how does the weighted-average maturity of the portfolio change?

Assets Liabilities and Equity

Cash $ 20 Demand deposits $10015-year commercial loan at 10% interest, balloon payment 160

5-year GICs at 6% interest, balloon payment 210

25-year mortgages at 8% interest, balloon payment 300

20-year debentures at 7% interest 120Equity 50

Total assets $480Total liabilities and equity $480


Cash $ 60 Demand deposits $1405-year Canada notes 60 1-year GICs 16025-year mortgages 200 Equity 20


Questions and Problems


c. Explain the changes in the maturity values if the yields increase 1 percent.

d. Assume that the insurance company has no other assets. What will be the effect on the mar-ket value of the companys equity if the interest rate changes in (b) and (c) occur?

8. The following is a simplified FI balance sheet:

The average maturity of loans is four years, and the average maturity of deposits is two years. Assume that loan and deposit balances are reported as book value, zero-coupon items.

a. Assume that the interest rate on both loans and deposits is 9 percent. What is the market value of equity?

b. What must be the interest rate on deposits to force the market value of equity to be zero? What economic market conditions must exist to make this situation possible?

c. Assume that the interest rate on both loans and deposits is 9 percent. What must be the aver-age maturity of deposits for the market value of equity to be zero?

9. Gunnison Insurance has reported the following balance sheet ($ thousands):

All securities are selling at par equal to book value. The two-year notes are yielding 5 percent, and the 15-year provincial bonds are yielding 9 percent. The one-year commercial paper pays 4.5 percent, and the five-year notes pay 8 percent. All instru-ments pay interest annually.

a. What is the weighted-average maturity of the assets for Gunnison?

b. What is the weighted-average maturity of the liabilities for Gunnison?

c. What is the maturity gap for Gunnison? d. What does your answer to part (c) imply

about the interest rate exposure of Gunnison Insurance?

e. Calculate the values of all four securities of Gunnison Insurances balanc e sheet, assuming that all interest rates increase 2 percent. What is the dollar change in the total asset and total liability values? What is the percentage change in these values?

f. What is the dollar impact on the market value of equity for Gunnison? What is the percentage change in the value of the equity?

g. What would be the impact on Gunnisons mar-ket value of equity if the liabilities paid interest semiannually instead of annually?

10. Scandia Bank has issued a one-year, $1 million GIC paying 5.75 percent to fund a one-year loan paying an interest rate of 6 percent. The principal of the loan will be paid in two instalments: $500,000 in six months and the balance at the end of the year.

a. What is the maturity gap of Scandia Bank? According to the maturity model, what does this maturity gap imply about the interest rate risk exposure faced by Scandia Bank?

b. What is the expected net interest income at the end of the year?

c. What would be the effect on annual net interest income of a 2 percent interest rate increase that occurred immediately after the loan was made? What would be the effect of a 2 percent decrease in rates?

d. What do these results indicate about the ability of the maturity model to immunize portfolios against interest rate exposure?

11. EDF Bank has a very simple balance sheet. Assets consist of a two-year, $1 million loan that pays an interest rate of LIBOR plus 4 percent annually. The loan is funded with a two-year deposit on which the bank pays LIBOR plus 3.5 percent interest annually. LIBOR currently is 4 percent, and both the loan and the deposit principal will be paid at maturity.

a. What is the maturity gap of this balance sheet? b. What is the expected net interest income in year

1 and year 2? c. Immediately prior to the beginning of year 2,

LIBOR rates increase to 6 percent. What is the expected net interest income in year 2? What would be the effect on net interest income of a 2 percent decrease in LIBOR?

12. What are the weaknesses of the maturity model?


2-year Canada note $175

1-year commercial paper $135

15-year provincial bonds 165 5-year note 160

Equity 45



Loans $1,000 Deposits $ 850Equity 150

Total assets $1,000Total liabilities and equity $1,000

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/CreateJDFFile false /Description > /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ > /FormElements false /GenerateStructure true /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles true /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /NA /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /LeaveUntagged /UseDocumentBleed false >> ]>> setdistillerparams> setpagedevice

Documents

Appendix_8A the Maturity Model