Answers to End of Chapter Questions
1. Basic steps:
a. Develop an interest rate forecast.
b. Estimate the market values of assets, liabilities, and stockholders’ equity.
2. Low coupon bonds have longer Macaulay’s durations because an investor has to wait longer to
receive any cash ,ow. With a coupon bond, an investor receives interim coupon payments before
3. The current price of the bond is $9,944.32.
a. Macaulay’s duration =
4.
a. If rates rise to 7.5% (3.75% semiannually), the price falls to $982,993 from $1 million.
5. Percentage change in prices using annual interest rates:
(1.08)
1
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periods semiannual 83.3
32.944,9$
81.121,38$
32.944,9$
4
)0305.1(
290,10$
3
(1.0305)
$290
2
)0305.1(
290$
1
)0305.1(
290$
D
4321
(1.08)
6. There is interest rate risk with this transaction. The liability is a zero coupon deposit that pays all
interest and principal at maturity in 5 years. Thus, the Macaulay’s duration of the deposit is 5 years.
7. With GAP analysis, it is easy to collect and update data and interpret .gures. Most managers and
analysts focus on earnings so GAP and earnings sensitivity results are highly intuitive. Duration gap
analysis, however, focuses on price sensitivity, which is oGen more confusing. It incorporates the
8. The statement is generally true. A bank with a negative GAP will have more RSLs than RSAs and will
typically lose when the level of rates rises. This is consistent with a bank having more .xed-rate
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9. Duration gap analysis
a. Average duration of assets = (102,000/500,000)1.8 + (375,000/500,000)1.5 = 1.492 years
b. Using an average earning asset yield of 9.72%:
Change in market value of assets:
Change in market value of liabilities:
c. Objective: To reduce (immunize against) risk, the bank needs to move DGAP closer to zero. This
involves increasing the average duration of assets relative to the average duration of liabilities. One
10. The objective is to reduce risk with DGAP > 0.
a. This transaction increases risk because the asset duration is longer than the liability duration.
11. The bank is positioned to gain if interest rates fall, especially if they fall 2%-3% below the base
12. EVE Sensitivity
a. If rates fall sharply, the bonds will be called. The bonds are likely callable around par, so the
3
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bank will not realize any gain or price appreciation when the bonds are liquidated. The bank loses in the
b. If rates move higher, customers may withdraw their funds early unless the bank agrees to pay
c. If rates fall sharply, the mortgages will prepay. The bank gives up a higher yield earning asset
and must reinvest the proceeds at lower rates. The bank again foregoes any real price appreciation of the
4
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accessible website, in whole or in part.