Question 1

When does "duration" become a less accurate predictor of expected change in security prices?

Accepted Answer

A) As interest rate shocks increase in size. 
B) As interest rate shocks decrease in size. 
C) When maturity distributions of an FI's assets and liabilities are considered. 
D) As inflation decreases. 
E) When the leverage adjustment is incorporated. 
A) As interest rate shocks increase in size. 
B) As interest rate shocks decrease in size. 
C) When maturity distributions of an FI's assets and liabilities are considered. 
D) As inflation decreases. 
E) When the leverage adjustment is incorporated.

Question 2

An FI can immunize its portfolio by matching the maturity of its asset with its liabilities.

Accepted Answer

A) True 
 B)False

Question 3

Duration of commercial loans $$D = \frac { \sum _ { t = 1 } ^ { N } P V _ { t } \times t } { \sum _ { t = 1 } ^ { N } P _ { t } } = \frac { \left[ \frac { 40,000,000 } { ( 1.10 ) ^ { 1 } } \times 1 \right] + \left[ \frac { 40,000,000 + 400,000,000 } { ( 1.10 ) ^ { 2 } } \times 2 \right] } { 400,000,000 } = 1.9114$$
-What is the FI's leverage-adjusted duration gap?

Accepted Answer

A) 0.91 years. 
B) 0.83 years. 
C) 0.73 years. 
D) 0.50 years. 
E) 0 years. 
A) 0.91 years. 
B) 0.83 years. 
C) 0.73 years. 
D) 0.50 years. 
E) 0 years.

Question 4

For a given change in required yields, short-duration securities suffer a smaller capital loss or receive a smaller capital gain than do long-duration securities.

Accepted Answer

A) True 
 B)False

Question 5

Investing in a zero-coupon asset with a maturity equal to the desired investment horizon removes interest rate risk from the investment management process.

Accepted Answer

A) True 
 B)False

Question 6

The larger the interest rate shock, the smaller the interest rate risk exposure of an FI.

Accepted Answer

A) True 
 B)False

Question 7

Calculate the duration of a two-year corporate loan paying 6 percent interest annually, selling at par. The $30,000,000 loan is 100 percent amortizing with annual payments.

Accepted Answer

A) 2 years. 
B) 1.89 years. 
C) 1.94 years. 
D) 1.49 years. 
E) 1.73 years. 
A) 2 years. 
B) 1.89 years. 
C) 1.94 years. 
D) 1.49 years. 
E) 1.73 years.

Question 8

$1,000 face value, 9% annual coupon, 5 year maturity, 10% rate $$\begin{array} { | l | l | l | l | l | } 
\hline \mathrm { PV } = 962.09 & \mathrm { FV } = 1,000 & \mathrm { I } = 10 & \mathrm {~N} = 5 & \text { PMT } = 90 \
\hline
\end{array}$$
-Calculate the percentage change in this bond's price if interest rates on comparable risk securities decline to 7 percent. Use the duration valuation equation.

Accepted Answer

A) +8.58 percent 
B) +12.76 percent 
C) -12.75 percent 
D) +11.80 percent 
E) +11.52 percent 
A) +8.58 percent 
B) +12.76 percent 
C) -12.75 percent 
D) +11.80 percent 
E) +11.52 percent

Question 9

$$\begin{array} { | l | r | c | c | } 
\hline \text { Assets } & \text { Amount } & \text { Rate } & \text { Duration } \
\hline \text { Cash } & \$ 75 \text { million } & & \
\hline \text { Loans } & \$ 750 \text { million } & 12 \text { percent } & 1.75 \text { years } \
\hline \text { Treasuries } & \$ 175 \text { million } & 9 \text { percent } & 7.00 \text { years } \
\hline \text { Liabilities and Equity } & & & \
\hline \text { Time Deposits } & \$ 350 \text { million } & 7 \text { percent } & 1.75 \text { years } \
\hline \text { CDs } & \$ 575 \text { million } & 8 \text { percent } & 2.50 \text { years } \
\hline \text { Equity } & \$ 75 \text { million } & & \
\hline
\end{array}$$
-Calculate the leverage-adjusted duration gap to four decimal places and state the FI's interest rate risk exposure of this institution.

Accepted Answer

A) +1.0308 years; exposed to interest rate increases. 
B) -0.3232 years; exposed to interest rate increases. 
C) +0.8666 years; exposed to interest rate increases. 
D) +0.4875 years; exposed to interest rate increases. 
E) -1.3232 years; exposed to interest rate decreases. 
A) +1.0308 years; exposed to interest rate increases. 
B) -0.3232 years; exposed to interest rate increases. 
C) +0.8666 years; exposed to interest rate increases. 
D) +0.4875 years; exposed to interest rate increases. 
E) -1.3232 years; exposed to interest rate decreases.

Question 10

The duration of a consol bond is

Accepted Answer

A) less than its maturity. 
B) infinity. 
C) 30 years. 
D) more than its maturity. 
E) given by the formula D = 1/(1-R). 
A) less than its maturity. 
B) infinity. 
C) 30 years. 
D) more than its maturity. 
E) given by the formula D = 1/(1-R).

Question 11

The error from using duration to estimate the new price of a fixed-income security will be less as the amount of convexity increases.

Accepted Answer

A) True 
 B)False

Question 12

A key assumption of Macaulay duration is that the yield curve is flat so that all cash flows are discounted at the same discount rate.

Accepted Answer

A) True 
 B)False

Question 13

Buying a fixed-rate asset whose duration is exactly equal to the desired investment horizon immunizes against interest rate risk.

Accepted Answer

A) True 
 B)False

Question 14

A risk manager could restructure assets and liabilities to reduce interest rate exposure for this example by

Accepted Answer

A) increasing the average duration of its assets to 9.56 years. 
B) decreasing the average duration of its assets to 4.00 years. 
C) increasing the average duration of its liabilities to 6.78 years. 
D) increasing the average duration of its liabilities to 9.782 years. 
E) increasing the leverage ratio, k, to 1. 
A) increasing the average duration of its assets to 9.56 years. 
B) decreasing the average duration of its assets to 4.00 years. 
C) increasing the average duration of its liabilities to 6.78 years. 
D) increasing the average duration of its liabilities to 9.782 years. 
E) increasing the leverage ratio, k, to 1.

Question 15

As interest rates rise, the duration of a consol bond decreases.

Accepted Answer

A) True 
 B)False

Question 16

For small change in interest rates, market prices of bonds move in an inversely proportional manner according to the size of the

Accepted Answer

A) equity. 
B) asset value. 
C) liability value. 
D) duration value. 
E) Answers A and B only. 
A) equity. 
B) asset value. 
C) liability value. 
D) duration value. 
E) Answers A and B only.

Question 17

An FI has financial assets of $800 and equity of $50. If the duration of assets is 1.21 years and the duration of all liabilities is 0.25 years, what is the leverage-adjusted duration gap?

Accepted Answer

A) 0.9000 years. 
B) 0.9600 years. 
C) 0.9756 years. 
D) 0.8844 years. 
E) Cannot be determined. 
A) 0.9000 years. 
B) 0.9600 years. 
C) 0.9756 years. 
D) 0.8844 years. 
E) Cannot be determined.

Question 18

The larger the size of an FI, the larger the _________ from any given interest rate shock.

Accepted Answer

A) duration mismatch 
B) immunization effect 
C) net worth exposure 
D) net interest income 
E) risk of bankruptcy 
A) duration mismatch 
B) immunization effect 
C) net worth exposure 
D) net interest income 
E) risk of bankruptcy

Question 19

-What is the duration of the municipal notes (the value of x)?

Accepted Answer

A) 1.94 years. 
B) 2.00 years. 
C) 1.00 years. 
D) 1.81 years. 
E) 0.97 years. 
A) 1.94 years. 
B) 2.00 years. 
C) 1.00 years. 
D) 1.81 years. 
E) 0.97 years.

Question 20

Leverage-adjusted duration gap $$- \left[ D _ { A } - D _ { L } k \right] = - \left[ 1.21 - 0.25 \times \left( \frac { 800 - 50 } { 800 } \right) \right] = - [ 1.21 - 0.234375 ] = - 0.9756$$
-Calculate the duration of a two-year corporate bond paying 6 percent interest annually, selling at par. Principal of $20,000,000 is due at the end of two years.

Accepted Answer

A) 2 years. 
B) 1.91 years. 
C) 1.94 years. 
D) 1.49 years. 
E) 1.75 years. 
A) 2 years. 
B) 1.91 years. 
C) 1.94 years. 
D) 1.49 years. 
E) 1.75 years.

Exam 9: Interest Rate Risk II

When does "duration" become a less accurate predictor of expected change in security prices?

An FI can immunize its portfolio by matching the maturity of its asset with its liabilities.

For a given change in required yields, short-duration securities suffer a smaller capital loss or receive a smaller capital gain than do long-duration securities.

Investing in a zero-coupon asset with a maturity equal to the desired investment horizon removes interest rate risk from the investment management process.

The larger the interest rate shock, the smaller the interest rate risk exposure of an FI.

Calculate the duration of a two-year corporate loan paying 6 percent interest annually, selling at par. The $30,000,000 loan is 100 percent amortizing with annual payments.

$1,000 face value, 9% annual coupon, 5 year maturity, 10% rate =962.09 =1,000 =10 =5 PMT =90 -Calculate the percentage change in this bond's price if interest rates on comparable risk securities decline to 7 percent. Use the duration valuation equation.

The duration of a consol bond is

The error from using duration to estimate the new price of a fixed-income security will be less as the amount of convexity increases.

A key assumption of Macaulay duration is that the yield curve is flat so that all cash flows are discounted at the same discount rate.

Buying a fixed-rate asset whose duration is exactly equal to the desired investment horizon immunizes against interest rate risk.

A risk manager could restructure assets and liabilities to reduce interest rate exposure for this example by

As interest rates rise, the duration of a consol bond decreases.

For small change in interest rates, market prices of bonds move in an inversely proportional manner according to the size of the

An FI has financial assets of $800 and equity of $50. If the duration of assets is 1.21 years and the duration of all liabilities is 0.25 years, what is the leverage-adjusted duration gap?

The larger the size of an FI, the larger the _________ from any given interest rate shock.

-What is the duration of the municipal notes (the value of x)?

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