Deck 8: Managing Interest Rate Risk: Duration Gap and Economic Value of Equity

Question 1

Duration gap analysis:

A) applies he the concept of duration to the bank's entire balance sheet.
B) applies he the concept of duration to the bank's entire income statement.
C) applies he the concept of duration to the bank's retained earnings.
D) indicates the difference in the GAP in the time it takes to collect on loan payments versus the time to attract deposits.
E) estimates when embedded options will be exercised.

Answer 1

A

Question 2

Which of the following is true regarding duration gap analysis?

A) The magnitude of the duration gap is related to the amount of interest rate risk a bank is subject to. b. Management can adjust the duration gap to speculate on future interest rate changes.
C) A positive duration gap means a bank's market value of equity will decrease with an increase in interest rates.
D) All of the above are true.
E) a. and c.

Answer 2

D

Question 3

Which of the following allows a security's cash flows to change when interest rates change?

A) Modified duration
B) Macaulay's duration
C) Effective duration
D) Balance sheet duration
E) Income statement duration

Answer 3

C

Question 4

Macaulay's duration:

A) is a weighted average of the time until cash flows are received.
B) is always greater than maturity.
C) is never equal to maturity.
D) directly indicates how much the price of a security will change given a change in interest rates.
E) estimates when embedded options will be used.

Question 5

Which of the following would generally be considered price sensitive?

A) Fed funds purchased
B) Fed funds sold
C) Repurchase agreements
D) Demand deposits
E) A 20-year zero coupon bond

Question 6

A 30-year zero coupon bond with a face value of $5,000 is currently selling for $1,156.88 and has a market rate of interest of 5%. Using the bond's modified duration, what is the approximate change in the price of the bond if interest rates fall to 4.25%?

A) Increase of $285.70
B) Increase of $247.90
C) Decrease of $285.70
D) Decrease of $247.90
E) Not enough information is given to answer the question.

Question 7

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 150 & && \text {Time Deposits } & \$ 500 & 4 \% & 1.25 \\\hline \text { Loans } & \$ 675 & 10 \% & 2.50 &\text { CDs } & \$ 400 & 6 \% & 3.00 \\\hline\text { T-Bonds }&\$175&5\%&5.00&\text { Equity }&\$100&&\\\hline\text { Total }&\$1,000&&&&\$1,000\\\hline\end{array}$

-What is the weighted average duration of assets?

A) 2.56 years
B) 3.75 years
C) 4.85 years
D) 5.00 years
E) 7.50 years

Question 8

A 10-year annual coupon bond is currently selling for its par value of $1,000 with an annual yield of 5%. If the bond is callable at par, what is the effective duration of the bond, if the interest rates change by 1%? The price of the bond at a 6% interest rate equals $926.40.

A) 10 years
B) 7.36 years
C) 5.52 years
D) 4.60 years
E) 3.68 years

Question 9

Put the following steps in duration gap analysis in the proper order.
I. Estimate the economic value of assets, liabilities and equity.
II. Forecast the change in the economic value of equity for various interest rates.
III. Forecast future interest rates.
IV. Estimate the duration of assets and liabilities.

A) III, I, IV, II
B) I, II, III, IV
C) III, IV, I, II
D) IV, I, II, III
E) II, IV, I, III

Question 10

EVE analysis: is essentially a _____________ analysis.

A) profitability
B) quality
C) liquidity
D) liquidation
E) earnings

Question 11

Modified duration:

A) estimates when embedded options will be used. b. directly indicates how much the price of a security will change given a change in interest rates.
C) is always greater than maturity.
D) All of the above
E) a. and b.

Question 12

Effective duration:

A) estimates when embedded options will be used.
B) directly indicates how much the price of a security will change given a change in interest rates.
C) is always greater than maturity.
D) is a weighted average of the time until cash flows are received.
E) All of the above

Question 13

What does a bank's duration gap measure?

A) The duration of short-term buckets minus the duration of long-term buckets.
B) The duration of the bank's assets minus the duration of its liabilities.
C) The duration of all rate-sensitive assets minus the duration of rate-sensitive liabilities.
D) The duration of the bank's liabilities minus the duration of its assets.
E) The duration of all rate-sensitive liabilities minus the duration of rate-sensitive assets.

Question 14

Which of the following is false regarding duration gap analysis?

A) Duration gap analysis does not classify assets as rate-sensitive.
B) Duration gap analysis indicates the potential change in a bank's net interest income.
C) Duration gap accounts for bank leverage.
D) Duration gap accounts for the present value of cash flows associated with all liabilities.
E) Duration gap analysis indicates the potential change in a bank's market value of equity.

Question 15

A bond has a Macaulay's duration of 26.56 years. If rates rise from 6.25% to 6.50%, the bonds price will:

A) increase by approximately 6.25%.
B) decrease by approximately 6.25%.
C) increase by approximately 6.50%.
D) decrease by approximately 6.50%.
E) Not enough information is given to answer the question.

Question 16

A bond has a Macaulay's duration of 21 years. If rates rise from 5% to 5.5%, the bonds price will:

A) increase by approximately 1%.
B) decrease by approximately 1%.
C) increase by approximately 10%.
D) decrease by approximately 10%.
E) Not enough information is given to answer the question.

Question 17

A 20-year annual coupon bond is currently selling for its par value of $10,000 with an annual yield of 7%. If the bond is callable at par, what is the effective duration of the bond, assuming rates change by 2%? The price of the bond at a 9% interest rate equals $8,174.29.

A) 25.00 years
B) 20.00 years
C) 5.52 years
D) 4.56 years
E) 3.68 years

Question 18

Which of the following is likely to have a negative effective duration?

A) A high coupon, interest only mortgage-backed security that is pre-paying at a high rate.
B) A low coupon U.S. Treasury bond.
C) Fed Funds purchased.
D) Demand deposits
E) None of the above can have a negative effective duration.

Question 19

A bond has a Macaulay's duration of 10.7 years. If rates fall from 7% to 6%, the bonds price will:

A) increase by approximately 1%.
B) decrease by approximately 1%.
C) increase by approximately 10%.
D) decrease by approximately 10%.
E) Not enough information is given to answer the question.

Question 20

A 20-year zero coupon bond with a face value of $1,000 is currently selling for $214.55 and has a market rate of interest of 8%. Using the bond's modified duration, what is the approximate change in the price of the bond if interest rates rise to 9%?

A) Increase of $39.73
B) Increase of $18.52
C) Decrease of $39.73
D) Decrease of $18.52
E) Not enough information is given to answer the question.

Question 21

Economic value of equity analysis focuses on net interest income.

Question 22

Which of the following will not affect a bank's duration estimate for the year?

A) Prepayments on loans that exceed expectations.
B) A 20-year corporate bond that is unexpectedly called in 6 months.
C) Certificates of deposit that are withdrawn early.
D) Holding a 30-year Treasury bond until maturity.
E) All of the above will affect a bank's estimated duration for the year.

Question 23

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 200 & && \text {Time Deposits } & \$ 600 &2.0 \% & 1.500 \\\hline \text { Loans } & \$ 800 & 8.0 \% & 3.750 &\text { CDs } & \$ 500 & 4.5 \% & 3.125 \\\hline\text { T-Bonds }&\$250&4.0\%&7.250&\text { Equity }&\$150&&\\\hline\text { Total }&\$1,250&&&&\$1,250\\\hline\end{array}$

-What is the weighted average duration of assets?

A) 2.56 years
B) 3.85 years
C) 4.85 years
D) 5.00 years
E) 7.50 years

Question 24

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 150 & && \text {Time Deposits } & \$ 500 & 4 \% & 1.25 \\\hline \text { Loans } & \$ 675 & 10 \% & 2.50 &\text { CDs } & \$ 400 & 6 \% & 3.00 \\\hline\text { T-Bonds }&\$175&5\%&5.00&\text { Equity }&\$100&&\\\hline\text { Total }&\$1,000&&&&\$1,000\\\hline\end{array}$

-If interest rates rise 1% for all assets and liabilities, what is the approximate expected change in the economic value of equity?

A) -$2.56
B) $5.84
C) -$5.84
D) $6.78
E) -$6.78

Question 25

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 150 & && \text {Time Deposits } & \$ 500 & 4 \% & 1.25 \\\hline \text { Loans } & \$ 675 & 10 \% & 2.50 &\text { CDs } & \$ 400 & 6 \% & 3.00 \\\hline\text { T-Bonds }&\$175&5\%&5.00&\text { Equity }&\$100&&\\\hline\text { Total }&\$1,000&&&&\$1,000\\\hline\end{array}$

-What is the weighted average duration of liabilities?

A) 1.25 years
B) 2.03 years
C) 2.12 years
D) 3.00 years
E) 4.25 years

Question 26

Which of the following is NOT a weakness of duration gap analysis?

A) It is difficult to accurately compute duration.
B) Each future cash flow must be discounted by the appropriate future interest rate.
C) The duration of a portfolio must be constantly monitored.
D) It is difficult to estimate the duration on zero coupon bonds.
E) All of the above are weaknesses of duration gap analysis.

Question 27

For a bank that has a negative duration gap, a decrease in interest rates will cause a(n) _______ in the economic value of assets that is _______ than the _______ in the economic value of liabilities, and a(n) _______ in the economic value of equity.

A) increase, less, increase, decrease
B) increase, greater, increase, decrease
C) increase, less, decrease, increase
D) decrease, less, decrease, increase
E) decrease, greater, decrease, decrease

Question 28

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 150 & && \text {Time Deposits } & \$ 500 & 4 \% & 1.25 \\\hline \text { Loans } & \$ 675 & 10 \% & 2.50 &\text { CDs } & \$ 400 & 6 \% & 3.00 \\\hline\text { T-Bonds }&\$175&5\%&5.00&\text { Equity }&\$100&&\\\hline\text { Total }&\$1,000&&&&\$1,000\\\hline\end{array}$

-What is the bank's expected economic net interest income?

A) $14.75
B) $32.25
C) $44.00
D) $76.25
E) $120.25

Question 29

To perfectly immunize a bank's economic value of equity from changes in interest rate risk, it should:

A) adjust assets and liabilities such that its duration gap is equal to one.
B) adjust assets and liabilities such that its duration gap is greater than zero.
C) adjust assets and liabilities such that its duration gap is equal to zero.
D) adjust assets and liabilities such that its GAP is equal to zero.
E) adjust assets and liabilities such that its GAP is less than one.

Question 30

If the yield curve is inverted, a portfolio manager can take advantage of this by:

A) pricing more deposits on a fixed-rate basis.
B) buying more long-term securities
C) making variable-rate, callable loans.
D) increasing the number of rate-sensitive assets.
E) All of the above.

Question 31

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 150 & && \text {Time Deposits } & \$ 500 & 4 \% & 1.25 \\\hline \text { Loans } & \$ 675 & 10 \% & 2.50 &\text { CDs } & \$ 400 & 6 \% & 3.00 \\\hline\text { T-Bonds }&\$175&5\%&5.00&\text { Equity }&\$100&&\\\hline\text { Total }&\$1,000&&&&\$1,000\\\hline\end{array}$

-What is the bank's duration gap?

A) 0.53
B) 0.73
C) 0.91
D) 2.03
E) 4.58

Question 32

A liability sensitive bank decides to reduce risk by marketing 2-year CDs paying 5% instead of NOW accounts that pay 4%. The bank will benefit if:

A) the 2-year rate in one year is less than 5%.
B) the 1-year rate in one year is less than 6%.
C) the 1-year rate in one year is greater than 6%.
D) the 2-year rate in one year is greater than 6%.
E) Not enough information is given to determine the correct answer.

Question 33

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 200 & && \text {Time Deposits } & \$ 600 &2.0 \% & 1.500 \\\hline \text { Loans } & \$ 800 & 8.0 \% & 3.750 &\text { CDs } & \$ 500 & 4.5 \% & 3.125 \\\hline\text { T-Bonds }&\$250&4.0\%&7.250&\text { Equity }&\$150&&\\\hline\text { Total }&\$1,250&&&&\$1,250\\\hline\end{array}$

-What is the bank's duration gap?

A) 0.53
B) 0.73
C) 0.91
D) 1.88
E) 4.58

Question 34

For a bank that has a positive duration gap, a decrease in interest rates will cause a(n) _______ in the economic value of assets that is ______ than the _______ in the economic value of liabilities, and a(n) _______ in the economic value of equity.

A) increase, greater, decrease, increase
B) increase, less, increase, decrease
C) increase, greater, increase, increase
D) decrease, greater, decrease, increase
E) decrease, less, decrease, decrease

Question 35

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 200 & && \text {Time Deposits } & \$ 600 &2.0 \% & 1.500 \\\hline \text { Loans } & \$ 800 & 8.0 \% & 3.750 &\text { CDs } & \$ 500 & 4.5 \% & 3.125 \\\hline\text { T-Bonds }&\$250&4.0\%&7.250&\text { Equity }&\$150&&\\\hline\text { Total }&\$1,250&&&&\$1,250\\\hline\end{array}$

-If interest rates decrease 1% for all assets and liabilities, what is the approximate expected change in the economic value of equity?

A) -$2.56
B) $5.84
C) -$5.84
D) $22.19
E) -$22.19

Question 36

For a bank that has a negative duration gap, an increase in interest rates will cause a(n) _______ in the economic value of assets, that is _______ than the _________ in the economic value of liabilities, and a(n) _______ in the economic value of equity.

A) increase, less, increase, increase
B) increase, less, increase, decrease
C) increase, greater, increase, increase
D) decrease, less, decrease, increase
E) decrease, greater decrease, increase

Question 37

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 200 & && \text {Time Deposits } & \$ 600 &2.0 \% & 1.500 \\\hline \text { Loans } & \$ 800 & 8.0 \% & 3.750 &\text { CDs } & \$ 500 & 4.5 \% & 3.125 \\\hline\text { T-Bonds }&\$250&4.0\%&7.250&\text { Equity }&\$150&&\\\hline\text { Total }&\$1,250&&&&\$1,250\\\hline\end{array}$

-What is the weighted average duration of liabilities?

A) 2.0 years
B) 2.24 years
C) 3.25 years
D) 4.5 years
E) 6.5 years

Question 38

For a bank that has a positive duration gap, an increase in interest rates will cause a(n) _______ in the economic value of assets, that is _______ than the _________ in the economic value of liabilities, and a(n) _______ in the economic value of equity.

A) increase, greater, decrease, increase
B) increase, less, increase, decrease
C) increase, greater, increase, increase
D) decrease, less, decrease, increase
E) decrease, greater, decrease, decrease

Question 39

What is the strength of static GAP analysis relative to duration gap analysis?

A) Static GAP analysis recognizes the time value of money of each cash flow.
B) Static GAP analysis provides a measure of the total portfolio's interest rate risk.
C) Static GAP analysis is easier to understand.
D) Static GAP analysis takes the long-run view while duration gap analysis takes a shorter-run view.
E) The static GAP measure directly correlates with the risk of the bank, i.e., a bank with twice the static GAP is twice as risky.

Question 40

Use the following bank information for questions .
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline &\begin{array}{c}\text { Market } \\\text { Value }\end{array} &\text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} & \begin{array}{c}\text { Liabilities }\\\text { and } \\\text { Equity }\end{array} & \begin{array}{c}\text { Market } \\\text { Value }\end{array} & \text { Rate } & \begin{array}{c}\text { Duration } \\\text { (Years) }\end{array} \\\hline\text { Cash } & \$ 200 & && \text {Time Deposits } & \$ 600 &2.0 \% & 1.500 \\\hline \text { Loans } & \$ 800 & 8.0 \% & 3.750 &\text { CDs } & \$ 500 & 4.5 \% & 3.125 \\\hline\text { T-Bonds }&\$250&4.0\%&7.250&\text { Equity }&\$150&&\\\hline\text { Total }&\$1,250&&&&\$1,250\\\hline\end{array}$

-What is the bank's expected economic net interest income?

A) $34.5
B) $32.3
C) $39.5
D) $44.0
E) $120.5

Question 41

Effective duration considers a security's embedded options.

Question 42

An asset that is rate-sensitive is generally not price sensitive.

Question 43

How does effective duration differ from modified duration?

Question 44

What are the strengths and weaknesses of duration gap analysis?

Question 45

Duration gap analysis focuses on changes in net interest income.

Question 46

Why is it difficult to estimate the duration of demand deposits?

Question 47

The yield curve is typically inverted at the peak of the business cycle.

Question 48

Discuss the differences between assets and liabilities that are price sensitive and those that are rate sensitive.

Question 49

A bank with a duration gap of 1 is more sensitive to changes in the economic value of equity than a bank with a duration gap of -1.5.

Question 50

Duration of equity measures the dollar change in EVE with a 1% change in interest rates.

Question 51

Discuss why a bank may have to sacrifice yield to vary its duration gap.

Question 52

The duration of a liability that does not pay interest must be equal to 0.

Question 53

Banks should never assume any interest rate risk.

Question 54

An investor that matches the duration of an investment with her holding period balances price risk and reinvestment risk.