Deck 6: Interest Rate Risk Measurement: the Duration Model

Question 1

The duration gap can be used to measure how changes in the interest rate affect an FI's:

A) net worth.
B) maturity gap strategy.
C) liquidity strategy.
D) All of the listed options are correct.

Answer 1

A

Question 2

The statement that a portfolio is immunised using duration matching:

A) means that the FI is entirely hedged against interest rate risks.
B) is misleading as duration matching is a dynamic process and only hedges the FI against instantaneous interest rate changes.
C) is misleading as duration matching is a dynamic process and only hedges the FI against interest rate changes that occur within a month.
D) None of the listed options are correct.

Answer 2

B

Question 3

With increasing maturity of a fixed-income asset or liability the asset or liability's duration:

A) increases, but at a decreasing rate.
B) decreases.
C) increases at an increasing rate.
D) increases at a constant rate.

Answer 3

A

Question 4

The leverage adjusted duration gap measures:

A) the change in an FI's net worth if interest rates change.
B) the degree of duration mismatch in an FI's profit and loss statement.
C) the degree of duration mismatch in an FI's balance sheet.
D) All of the listed options are correct.

Question 5

As interest rates increase the price of an asset or liability:

A) remains constant.
B) decreases.
C) increases.
D) increases and it increases at a faster rate.

Question 6

The effect of interest rate changes on the market value of an FI's net worth breaks down into three effects, these being the leverage adjusted duration gap, the:

A) size of the FI and the reputation of the FI.
B) size of the FI and the size of the interest rate shock.
C) reputation of the FI and the size of the interest rate shock.
D) size of the FI and the direction of the interest rate changes.

Question 7

The special feature of consol bonds is that:

A) their duration equals their maturity.
B) their maturity is infinite, while their duration is finite.
C) their maturity is finite, while their duration is infinite.
D) both, their maturity and their duration, are infinite.

Question 8

The modified duration is defined as:

A) duration multiplied by (1 + R).
B) duration divided by (1 + R).
C) duration minus (1 + R).
D) duration plus (1 + R).

Question 9

Duration is seen as a more complete measure of an asset or a liability's interest rate sensitivity than maturity because it takes into account the:

A) size of cash flows.
B) timing of cash flows.
C) size of cash flows and the asset or liability's time to maturity.
D) time of arrival of all cash flows plus the asset or liability's maturity.

Question 10

Duration is a direct measure of the interest rate sensitivity of an asset or liability, which means that:

A) the smaller the duration, the more sensitive the price of that asset or liability.
B) the larger the duration, the less sensitive the price of that asset or liability.
C) the larger the duration, the more sensitive the price of that asset or liability.
D) None of the listed options are correct.

Question 11

The larger an FI's absolute leverage adjusted duration gap:

A) the less exposed the FI is to interest rate shocks.
B) the more exposed the FI is to interest rate shocks.
C) the lower the FI's net worth.
D) None of the listed options are correct.

Question 12

Immunising the balance sheet to protect equity holders from the effects of interest rate risk occurs when:

A) the maturity gap is zero.
B) the repricing gap is zero.
C) the duration gap is zero.
D) the effect of a change in the level of interest rates on the value of the assets of the FI is exactly offset by the effect of the same change in interest rates on the liabilities of the FI.

Question 13

Convexity is defined as:

A) the degree of curvature of the price-yield curve around some maturity level.
B) the degree of curvature of the price-yield curve around some price level.
C) the degree of curvature of the price-yield curve around some interest rate level.
D) None of the listed options are correct.

Question 14

Which of the following statements most appropriately responds to the critique that duration matching is costly and time consuming?

A) The critique is valid, however, the speed has been eased and transaction costs of balance sheet restructuring have been lowered due to growth of purchased funds, asset securitisation and loan sales markets.
B) The critique is valid and FIs should spend funds in order to develop more efficient interest rate risk management tools.
C) The critique is valid, particularly because it is not possible for managers to get the same results of direct duration matching by taking positions in derivatives markets.
D) None of the listed options are correct.

Question 15

Using the duration gap to measure the change in an FI's net worth in case of large interest rate shocks:

A) produces exact results.
B) only produces exact results if interest rates change instantaneously.
C) produces approximate results only due to concavity.
D) produces approximate results only due to convexity.

Question 16

The duration of an asset or a liability for which there are intervening cash flows between issue and maturity:

A) equals the asset or the liability's maturity.
B) exceeds the asset or the liability's maturity.
C) is smaller than the asset or the liability's maturity.
D) Not enough information to answer this question.

Question 17

The duration of a zero-coupon bond:

A) is smaller than its maturity.
B) exceeds its maturity.
C) equals its maturity.
D) depends on the size and timing of intervening cash flows between issue and maturity.

Question 18

Duration is defined as:

A) the weighted-average time to maturity of a series of cash flows, using the relative present values of the cash flows as weights.
B) the weighted-average present values of a series of cash flows using the timing of the cash flows as weights.
C) the standard deviation of the time to maturity of a series of cash flows.
D) an asset's or a liability's time to maturity.

Question 19

The lower the coupon or interest payment on a security:

A) the lower its duration.
B) coupon or interest payments have no impact on a security's duration.
C) the higher its duration.
D) None of the listed options are correct.

Question 20

Duration is a less accurate predictor for the change in an FI's net worth in case of large interest rate shocks because it assumes a:

A) linear relationship between the change in an asset or liability's price and the change in the interest rate, while the true relationship is convex.
B) linear relationship between the change in an asset or liability's price and the change in the interest rate, while the true relationship is concave.
C) convex relationship between the change in an asset or liability's price and the change in the interest rate, while the true relationship is linear.
D) concave relationship between the change in an asset or liability's price and the change in the interest rate, while the true relationship is linear.

Question 21

How can a negative duration gap of 0.21 years be interpreted?

A) The FI is exposed to decreasing interest rates because it has a negative duration gap of 0.21 years.
B) The FI is exposed to increasing interest rates because it has a negative duration gap of 0.21 years.
C) The FI is not exposed to interest rate changes since it is running a matched book.
D) The FI's exposure will depend on its maturity gap.

Question 22

Consider an asset with a current market value of $250 000 and a duration of 3.3 years. Assume the asset is partially funded through zero-coupon bonds which currently sells for $225 000 and has a maturity of 4 years. The current discount rate is 15 per cent. Calculate the duration gap for this scenario:

A) -0.3 years
B) 0.3 years
C) -0.7 years
D) 0.7 years

Question 23

Consider a consol bond with a required yield to maturity of 9 per cent. What is the consol bond's duration (round to two decimals)?

A) Infinite as the bond has no maturity
B) 0 years
C) 9.33 years
D) 12.11 years

Question 24

For large interest rate shocks and large convexity of a fixed-income security or portfolio:

A) the error will not change compared to smaller interest rate shocks and lower convexity.
B) the error will be smaller compared to smaller interest rate shocks and lower convexity.
C) the error will be greater compared to smaller interest rate shocks and lower convexity.
D) there will be no error as duration measures changes accurately.

Question 25

Assume that the required yield to maturity on a consol bond increases from 6 per cent to 12 per cent. What is the impact on the consol bond's duration?

A) As there are no intervening cash flows between issue and maturity, the duration will always equal the bond's maturity.
B) As interest rates rise, the duration of consol bonds falls.
C) As interest rates rise, the duration of consol bonds rises.
D) There will be no impact on the bond's duration.

Question 26

Consider a security with a face value of $100 000, which is to be repaid at maturity. The security pays an annual coupon of 8 per cent and has a maturity of three years. The current discount rate is 10 per cent. What is the security's duration (round to two decimals)?

A) 2.78 years
B) 3 years
C) 0.36 years
D) 1.94 years

Question 27

Consider a security with a face value of $100 000, which is to be repaid at maturity. The security pays an annual coupon of 8 per cent and has a maturity of three years. The current discount rate is 10 per cent. What is the security's current price (round to two decimals)?

A) $124 000
B) $95 026.30
C) $19 894.82
D) $100 000

Question 28

Consider a security with a duration of 2.78 years. The current interest rate level is 10 per cent p.a. How does the price of the security change if interest rates decrease by 100 basis points (round to two decimals)?

A) The price of the security will decrease by 1 per cent.
B) The price of the security will increase by 1 per cent.
C) The price of the security will decrease by 2.50 per cent.
D) The price of the security will increase by 2.50 per cent.

Question 29

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?

A) 0.9000 years
B) 0.9600 years
C) 0.9756 years
D) 0.8844 years

Question 30

What is the duration of a 5-year par value zero coupon bond yielding 10 per cent annually?

A) 0.50 years
B) 2 years
C) 4.40 years
D) 5 years

Question 31

Immunisation of a portfolio implies that changes in _______ will not affect the value of the portfolio.

A) book value of assets
B) maturity
C) interest rates
D) duration

Question 32

In order to achieve a zero duration gap, an FI can:

A) change the duration of its assets only.
B) change the duration of its liabilities only.
C) change the duration of both, assets and liabilities.
D) All of the listed options are correct.

Question 33

Which of the following statements is true?

A) The optimal duration gap is zero.
B) Duration gap measures the impact of unanticipated changes in interest rates on the market value of equity.
C) The shorter the maturity of the FI's securities, the greater the FI's interest rate risk exposure.
D) The duration of all floating rate debt instruments is equal to the time to maturity.

Question 34

Which of the following statements is true?

A) All assets and liabilities are convex.
B) All fixed income securities, including those with special option features, are convex.
C) All assets are convex, all liabilities are convex and all fixed income securities, including those with special option features, are convex.
D) None of the listed options are correct.

Question 35

Consider a security with a face value of $100 000 to be repaid at maturity. The maturity of the security is 3 years. The coupon rate is 9 per cent p.a. and coupon payments are made semi-annually. The current discount rate is 12 per cent p.a. What is the security's price (round your answer to two decimals)?

A) $127 000.00
B) $100 000.00
C) $76 046.08
D) $92 624.01

Question 36

Which of the following statements is true?

A) Convexity is desirable because the larger the convexity the greater the interest rate protection against interest rate decreases and the greater the potential gains following increasing interest rates.
B) Convexity is desirable because the larger the convexity the greater the interest rate protection against interest rate rises and the greater the potential gains following decreasing interest rates.
C) Convexity is undesirable because the larger the convexity the lower the interest rate protection against interest rate rises and the smaller the potential gains following decreasing interest rates.
D) Convexity is undesirable because the larger the convexity the lower the interest rate protection against interest rate decreases and the smaller the potential gains following increasing interest rates.

Question 37

Consider an asset with a current market value of $250 000 and a duration of 3.3 years. Assume the asset is partially funded through zero-coupon bonds which currently sells for $225 000 and has a maturity of 4 years. The current discount rate is 15 per cent. Which of the following statements is true?

A) The FI is benefiting from increasing interest rates as it has a negative duration gap of 0.3 years.
B) The FI is exposed to increasing interest rates as it has a negative duration gap of 0.3 years.
C) The FI is exposed to increasing interest rates as it has a positive duration gap of 0.3 years.
D) The FI is exposed to decreasing interest rates as it has a positive duration gap of 0.3 years.

Question 38

Consider an asset with a current market value of $250 000 and a duration of 3.3 years. Assume the asset is partially funded through zero-coupon bonds which currently sells for $225 000 and has a maturity of 4 years. The current discount rate is 15 per cent and interest rates are expected to increase by 150 basis points. Which of the following statements is true?

A) The current net worth of the position is $25 000 and if interest rates increase the net worth will not be affected.
B) The current net worth of the position is $25 000 and if interest rates increase the net worth will increase, too.
C) The current net worth of the position is $25 000 and if interest rates increase the net worth will decrease.
D) The current net worth of the position cannot be determined, however, if interest rates increase the net worth will increase, too.

Question 39

An FI purchases at par value a $100 000 Treasury bond paying 10 per cent interest with a 7.5 year duration. If interest rates rise by 4 per cent, calculate the bond's new value. Recall that Treasury bonds pay interest semi-annually. Use the duration valuation equation.

A) +$28 571.43
B) -$20 864.46
C) +$20 864.46
D) -$28 571.43

Question 40

Consider a security with a face value of $100 000 to be repaid at maturity. The maturity of the security is 3 years. The coupon rate is 9 per cent p.a. and coupon payments are made semi-annually. The current discount rate is 12 per cent p.a. What is the security's duration (round your answer to two decimals)?

A) 2.68 years
B) 2.68 half-years
C) 3 years
D) 0.38 years

Question 41

It is not possible to measure the duration of a perpetuity as a perpetuity has no maturity.

Question 42

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

A) duration mismatch
B) immunisation effect
C) net worth exposure
D) net interest income

Question 43

Calculating modified duration involves:

A) dividing the value of duration by the change in the market interest rate.
B) dividing the value of duration by 1 plus the interest rate.
C) dividing the value of duration by discounted change in interest rates.
D) multiplying the value of duration by discounted change in interest rates.

Question 44

Which of the following statements are incorrect?

A) Convexity is a desirable effect to a portfolio manager because it is easy to measure and price.
B) All fixed-income assets exhibit convexity in their price-yield relationships.
C) The greater is convexity, the more insurance a portfolio manager has against interest rate increases and the greater potential gain from rate decreases.
D) The fact that the capital gain effect for rate decreases is greater than the capital loss effect for rate increases is caused by convexity in the yield-price relationship.

Question 45

The leverage adjusted duration gap reflects the degree of duration mismatch in an FI's balance sheet.

Question 46

An FI has a leverage-adjusted duration gap of 1.21 years, $60 million in assets, 7 per cent equity to assets ratio, and market rates are 8 per cent. What is the impact on the dealer's market value of equity per $100 of assets if the relative change in all interest rates is an increase of 0.5 per cent [i.e., R/(1+R) = 0.5 per cent]?

A) +$336 111
B) -$0.605
C) -$336 111
D) +$0.605

Question 47

As interest rates increase (decrease) the value of an asset or a liability decreases (increases).

Question 48

Which of the following statements about leverage adjusted duration gap is true?

A) It is equal to the duration of the assets minus the duration of the liabilities.
B) The larger the gap in absolute terms, the more exposed the FI is to interest rate shocks.
C) It reflects the degree of maturity mismatch in an FI's balance sheet.
D) It indicates the dollar size of the potential net worth and its value is equal to duration divided by (1+R).

Question 49

Duration measures changes in an FI's net worth inaccurately if interest rate changes are large.

Question 50

Which of the following is indicated by high numerical value of the duration of an asset?

A) Low sensitivity of an asset price to interest rate shocks.
B) High interest inelasticity of a bond.
C) High sensitivity of an asset price to interest rate shocks.
D) Lack of sensitivity of an asset price to interest rate shocks.

Question 51

Duration matching is a desirable interest rate risk management tool as it captures changes in interest rates over long periods of time.

Question 52

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

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.

Question 53

The bank has a negative maturity gap. Is the bank exposed to interest rate increases or decreases and why?

A) Interest rate increases because the value of its assets will rise more than its liabilities.
B) Interest rate increases because the value of its assets will fall more than its liabilities.
C) Interest rate decreases because the value of its assets will rise less than its liabilities.
D) Interest rate decreases because the value of its assets will fall more than its liabilities.

Question 54

The larger the numerical value of the duration of an asset or liability, the less sensitive the price of that asset or liability is to changes in the interest rate.

Question 55

The maturity of a fixed-income security is always smaller than its duration.

Question 56

In simple words, duration measures the average life of an asset or liability.

Question 57

Which of the following statements are incorrect?

A) Investing in a zero-coupon asset with a maturity equal to the desired investment horizon is one method of immunising against changes in interest rates.
B) Investing in a zero-coupon asset with a maturity equal to the desired investment horizon removes interest rate risk from the investment management process.
C) Buying a fixed-rate asset whose duration is exactly equal to the desired investment horizon immunises against interest
D) Using a fixed-rate bond to immunisea desired investment horizon means that the reinvested coupon payments are not affected by changes in market interest rates.

Question 58

Using the leverage adjusted duration gap, it is possible to measure the effect of changing interest rates on an FI's net worth.

Question 59

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

A) equity.
B) asset value.
C) liability value.
D) duration value.

Question 60

The duration of a zero-coupon bond is always smaller than its maturity.

Question 61

Proof the following three propositions using a simple numerical example for each of the cases.
a. The duration of an asset or liability with intervening cash flows between issue and maturity is smaller than its maturity.
b. The duration of an asset or liability without any intervening cash flows between issue and maturity equals its maturity.
c. Despite the fact that perpetuities such as consol bonds have no maturity, it is possible to calculate their duration.

Question 62

Would you consider convexity of a fixed-income security to be desirable or undesirable for an FI? Explain your opinion.

Question 63

One method of changing the positive leverage adjusted duration gap for the purpose of immunising the net worth of a typical depository institution is to increase the duration of the assets and to decrease the duration of the liabilities.

Question 64

The greater is convexity, the more insurance a portfolio manager has against interest rate increases and the greater potential gain from rate decreases.

Question 65

Discuss the following proposition: While in theory duration matching allows an FI to immunise against interest rate risk, the reality is that it is too costly and too time-consuming to be useful.