Answers to Chapter 22
Questions:
1. Through its daily open market operations, such as buying and selling Treasury bonds and Treasury bills, the Fed
seeks to influence the money supply, inflation, and the level of interest rates. When the Fed finds it necessary to
2. The repricing gap is a measure of the difference between the dollar value of assets that will reprice and the dollar
value of liabilities that will reprice within a specific time period, where repricing can be the result of a roll over of an
3. The maturity bucket is the time window over which the dollar amounts of assets and liabilities are measured. The
length of the repricing period determines which of the securities in a portfolio are rate-sensitive. The longer the
4. The CGAP effect describes the relations between changes in interest rates and changes in net interest income.
5. According to the CGAP effect, when CGAP is positive the change in NII is positively related to the change in
interest rates. Thus, an FI would want its CGAP to be positive when interest rates are expected to rise.
a. Yes. This change will increase RSAs, which will increase GAP.
6. When rates rise, the bank manager would want to set the repricing gap greater than zero. As rates rise, interest
8. The gap to total assets ratio is the ratio of the cumulative gap position to the total assets of the FI. The cumulative
9. The spread effect is the effect that a change in the spread between rates on RSAs and RSLs has on net interest
10. a. The repricing model has four general weaknesses:
i. It ignores market value effects.
ii. It does not take into account the fact that the dollar value of rate sensitive assets and liabilities within a bucket are
11. Taking the first derivative of a bond’s (or any fixed-income security) price (P) with respect to the yield to
12. The change in the net worth of an FI for a change in interest rates is given by the following equation:
R) +(1
R
* A* k
D
–
D
– = E
LA
where k = L/A. Thus, three factors are important in determining ΔE:
14. When rates rise, the bank manager would want to set the duration gap less than zero. As rates rise, the value of
15. The three criticisms are:
i. Duration matching can be costly because it is not easy to restructure the balance sheet periodically, especially for
large FIs.
16. The duration model predicts that the relationship between an interest rate change (or shock) and a bond’s price
change will be proportional to the bond’s D (duration). By precisely calculating the true change in the bond’s price,
17. Book value accounting reports assets and liabilities at the original issue values. Market value accounting is an
economist=s definition of capital. Specifically, the economist=s definition of an FI=s capital, or owners= equity
18. The book value definition of capital is the value of assets minus liabilities as found on the balance sheet. This
amount often is referred to as accounting net worth. The economic definition of capital is the difference between the
market value of assets and the market value of liabilities.
a. The loss in value caused by credit risk is borne first by the equity holders, and then by the liability holders. With
b. Because book value accounting recognizes the value of assets and liabilities at the time they were placed on the
19. Market values produce a more accurate picture of the bank=s current financial position for both stockholders
and regulators. Stockholders could more readily see the effects of changes in interest rates on the bank=s equity. As
20. The market value of equity is more relevant than book value because in the event of a bankruptcy, the
liquidation (market) values will determine the FI’s ability to pay the various claimants.
Problems:
2. a. Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million.
b. After the 200 basis point interest rate increase, net interest income declines to:
d. After the unequal rate increases, net interest income will be 50(0.12) + 50(0.07) – 70(0.07) – 20(0.07) = $9.5m –
a.
c. The CGAP affect worked to increase net interest income. That is, the CGAP was positive while interest rates
increased. Thus, interest income increased by more than interest expense. The result is an increase in NII. The
6. a. Funding or repricing gap using a 30-day planning period = $75m – $170m = -$95 million.
8. a. Duration of the two-year liability = 1.897 years.
b. Change in net worth using leveraged adjusted duration gap is given by:
9. a. Duration of GBI’s fixed-rate loan portfolio:
c. Duration of GBI’s core deposits:
Since GBI’s duration gap is positive, an increase in interest rates will lead to a decline in net worth. For a 1%
increase, the change in net worth is:
10. a. The market value of the loan declines by $2.55 million, to $97.45 million.
b. The duration of the loan is 1.909 years.
c. The approximate change in the market value of the loan for a 150 basis points change is:
d. The market value of the liability declines $1.233 million, to $88.767 million.
e. The duration is one year because it is a pure discount (zero-coupon) instrument.
d. The market value of the equity will change by the following for an approximate 50 basis point change in interest
rates (i.e. ΔR/(1 + R) = 0.0050) for both assets and liabilities:
e. If instead, ΔR/(1 + R) is -0.0025, the change in the value of equity is:
12. a. For Bank A, an increase of 100 basis points in interest rate will cause the market values of assets and
liabilities to decrease as follows:
For Bank B:
b. The assets and liabilities of Bank A change in value by different amounts because the durations of the assets and
liabilities are not the same, even though the face values and maturities are the same. For Bank B, the maturities of
the assets and liabilities are different, but the current market values and durations are the same. Thus, the change in
interest rates causes a smaller change in value for both liabilities and assets.
c. Ten-year CD Bank B (values in thousands of $s)
The duration on the CD of Bank B is calculated above to be 7.00 years. Since the bond is a zero-coupon, the
duration is equal to the maturity of 7 years.
Using the duration formula to estimate the change in value:
estimation model. The difference in this estimate and the estimate found in part (a) above is due to the convexity of
the two financial assets.
The duration estimates for the loan and CD for Bank A are presented below:
Using the duration formula to estimate the change in value:
Loan: Value =
79501560000001
121
010
32826
1.,$,,$
.
.
.P
R
R
D
CD: Value =
45445610000001
101
010
75906
1.,$,,$
.
.
.P
R
R
D
The difference in the change in value of the assets and liabilities for Bank A is $4,943.66 using the duration
estimation model. The difference in this estimate and the estimate found in part (a) above is due to the convexity of
the two financial assets. The reason the change in asset values for Bank A is considerably larger than for Bank B is
because of the difference in the durations of the loan and CD for Bank A.