Deck 9: Interest Rate Risk II

Question 1

The economic meaning of duration is the interest elasticity of a financial assets price.

Answer 1

True

Question 2

Duration measures the average life of a financial asset.

Answer 2

True

Question 3

Duration considers the timing of all the cash flows of an asset by summing the product of the cash flows and the time of occurrence.

Answer 3

False

Question 4

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

Question 5

Duration is the weighted-average present value of the cash flows using the timing of the cash flows as weights.

Question 6

Duration normally is less than the maturity for a fixed income asset.

Question 7

Duration is related to maturity in a nonlinear manner through the current yield to maturity of the asset.

Question 8

For a given maturity fixed-income asset, duration decreases as the market yield increases.

Question 9

Duration increases with the maturity of a fixed-income asset at a decreasing rate.

Question 10

The difference between the changes in the market value of the assets and market value of liabilities for a given change in interest rates is, by definition, the change in the FI's net worth.

Question 11

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.

Question 12

For a given maturity fixed-income asset, duration increases as the promised interest payment declines.

Question 13

Marking-to-market accounting is a market value accounting method that reflects the purchase prices of assets and liabilities.

Question 14

In duration analysis, the times at which cash flows are received are weighted by the relative importance in present value terms of the cash flows arriving at each point in time.

Question 15

Larger coupon payments on a fixed-income asset cause the present value weights of the cash flows to be lower in the duration calculation.

Question 16

Duration is equal to maturity when at least some of the cash flows are received upon maturity of the asset.

Question 17

Duration of a fixed-rate coupon bond will always be greater than one-half of the maturity.

Question 18

Duration is related to maturity in a linear manner through the interest rate of the asset.

Question 19

Duration of a zero coupon bond is equal to the bond's maturity.

Question 20

In most countries FIs report their balance sheet using market value accounting.

Question 21

The duration of a portfolio of assets can be found by calculating the book value weighted average of the durations of the individual assets.

Question 22

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.

Question 23

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

Question 24

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

Question 25

For given changes in interest rates, the change in the market value of net worth of an FI is equal to the difference between the changes in the market value of the assets and market value of the liabilities.

Question 26

Immunization of an FIs net worth requires the duration of the liabilities to be adjusted for the amount of leverage on the balance sheet.

Question 27

Using a fixed-rate bond to immunize a desired investment horizon means that the reinvested coupon payments are not affected by changes in market interest rates.

Question 28

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

Question 29

Investing in a zero-coupon asset with a maturity equal to the desired investment horizon is one method of immunizing against changes in interest rates.

Question 30

The leverage adjusted duration of a typical depository institution is positive.

Question 31

One method of changing the positive leverage adjusted duration gap for the purpose of immunizing 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 32

Setting the duration of the assets higher than the duration of the liabilities will exactly immunize the net worth of an FI from interest rate shocks.

Question 33

The immunization of a portfolio against interest rate risk means that the portfolio will neither gain nor lose value when interest rates change.

Question 34

Perfect matching of the maturities of the assets and liabilities will always achieve perfect immunization for the equity holders of an FI against interest rate risk.

Question 35

Immunizing the balance sheet of an FI against interest rate risk requires that the leverage adjusted duration gap (D_A-kD_L) should be set to zero.

Question 36

Matching the maturities of assets and liabilities is not a perfect method of immunizing the balance sheet because the timing of the cash flows is likely to differ between the assets and liabilities.

Question 37

The value for duration describes the percentage increase in the price of an asset for a given increase in the required yield or interest rate.

Question 38

Deep discount bonds are semi-annual fixed-rate coupon bonds that sell at a market price that is less than par value.

Question 39

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

Question 40

The smaller the leverage adjusted duration gap, the more exposed the FI is to interest rate shocks.

Question 41

As the investment horizon approaches, the duration of an unrebalanced portfolio that originally was immunized will be less than the time remaining to the investment horizon.

Question 42

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.
E)equity and asset value.

Question 43

The cost in terms of both time and money to restructure the balance sheet of large and complex FIs has decreased over time.

Question 44

The duration of a consol bond is

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 45

Managers can achieve the results of duration matching by using these to hedge interest rate risk.

A)Rate sensitive assets.
B)Rate sensitive liabilities.
C)Coupon bonds.
D)Consol bonds.
E)Derivatives.

Question 46

The duration of all floating rate debt instruments is

A)equal to the time to maturity.
B)less than the time to repricing of the instrument.
C)time interval between the purchase of the security and its sale.
D)equal to time to repricing of the instrument.
E)infinity.

Question 47

Attempts to satisfy the objectives of shareholders and regulators requires the bank to use the same duration match in the protection of net worth from interest rate risk.

Question 48

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.
E)Smaller capital loss for a given change in interest rates.

Question 49

Immunizing the net worth ratio requires that the duration of the assets be set equal to the duration of the liabilities.

Question 50

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

Question 51

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)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.
E)Its value is equal to duration divided by (1 + R).

Question 52

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

Question 53

All fixed-income assets exhibit convexity in their price-yield relationships.

Question 54

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

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

Question 55

Immunizing net worth from interest rate risk using duration matching requires that the duration match must be realigned periodically as the maturity horizon approaches.

Question 56

Convexity is a desirable effect to a portfolio manager because it is easy to measure and price.

Question 57

The rate of change in duration values is less than the rate of change in maturity.

Question 58

Immunizing 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.
E)after-the-fact analysis demonstrates that immunization coincidentally occurred.

Question 59

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 60

The use of duration to predict changes in bond prices for given changes in interest rate changes will always underestimate the amount of the true price change.

Question 61

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.

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

Question 62

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

A)0.50 years.
B)2.00 years.
C)4.40 years.
D)5.00 years.
E)4.05 years.

Question 63

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.

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

Question 64

Consider a one-year maturity, $100,000 face value bond that pays a 6 percent fixed coupon annually. What is the price of the bond if market interest rates are 5 percent?

A)$100,952.38.
B)$101,238.10.
C)$100,963.71.
D)$100,000.00.
E)$101,108.27.

Question 65

Consider a one-year maturity, $100,000 face value bond that pays a 6 percent fixed coupon annually. What is the price of the bond if market interest rates are 7 percent?

A)$99,050.15.
B)$99,457.94.
C)$99,249.62.
D)$100,000.00.
E)$99,065.42.

Question 66

First Duration, a securities dealer, has a leverage-adjusted duration gap of 1.21 years, $60 million in assets, 7 percent equity to assets ratio, and market rates are 8 percent. What conclusions can you draw from the duration gap in your answer to the previous question?

A)The market value of the dealer's equity decreases slightly if interest rates fall.
B)The market value of the dealer's equity becomes negative if interest rates rise.
C)The market value of the dealer's equity decreases slightly if interest rates rise.
D)The market value of the dealer's equity becomes negative if interest rates fall.
E)The dealer has no interest rate risk exposure.

Question 67

An FI purchases a $9.982 million pool of commercial loans at par. The loans have an interest rate of 8 percent, a maturity of five years, and annual payments of principal and interest that will exactly amortize the loan at maturity. What is the duration of this asset?

A)4.12 years.
B)3.07 years.
C)2.50 years.
D)2.85 years.
E)5.00 years.

Question 68

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.
E)Cannot be determined.

Question 69

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

A)$28,572
B)$20,864
C)$15,000
D)$22,642
E)$71,428

Question 70

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.
E)dividing the value of duration by the curvature effect.

Question 71

Immunization of a portfolio implies that changes in _____ will not affect the value of the portfolio.

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

Question 72

Calculate the modified duration of a two-year corporate loan paying 6 percent interest annually. The $40,000,000 loan is 100 percent amortizing, and the current yield is 9 percent annually.

A)2 years.
B)1.91 years.
C)1.94 years.
D)1.49 years.
E)1.36 years.

Question 73

First Duration, a securities dealer, has a leverage-adjusted duration gap of 1.21 years, $60 million in assets, 7 percent equity to assets ratio, and market rates are 8 percent. What is the impact on the dealer's market value of equity per $100 of assets if the change in all interest rates is an increase of 0.5 percent [i.e., ΔR = 0.5 percent]

A)+$336,111.
B)-$0.605.
C)-$336,111.
D)+$0.605.
E)-$363,000.

Question 74

Consider a six-year maturity, $100,000 face value bond that pays a 5 percent fixed coupon annually. What is the price of the bond if market interest rates are 6 percent?

A)$95,082.68.
B)$95,769.55.
C)$95,023.00.
D)$100,000.00.
E)$96,557.87.

Question 75

Consider a six-year maturity, $100,000 face value bond that pays a 5 percent fixed coupon annually. What is the price of the bond if market interest rates are 4 percent?

A)$105,816.44.
B)$105,287.67.
C)$105,242.14.
D)$100,000.00.
E)$106,290.56.

Question 76

A $1,000 six-year Eurobond has an 8 percent coupon, is selling at par, and contracts to make annual payments of interest. The duration of this bond is 4.99 years. What will be the new price using the duration model if interest rates increase to 8.5 percent?

A)$23.10.
B)$976.90.
C)$977.23.
D)$1,023.10.
E)-$23.10.

Question 77

Which of the following statements is true?

A)The optimal duration gap is zero.
B)Duration gap measures the impact of 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.
E)The duration of equity is equal to the duration of assets minus the duration of liabilities.

Question 78

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.
E)When the leverage adjustment is incorporated.

Question 79

What is the duration of an 8 percent annual payment two-year note that currently sells at par?

A)2 years.
B)1.75 years.
C)1.93 years.
D)1.5 years.
E)1.97 years.

Question 80

Consider a one-year maturity, $100,000 face value bond that pays a 6 percent fixed coupon annually. If the bond is selling at par, what is the percentage price change for the bond if interest rates increase 50 basis points from 6 percent?

A)-0.1033 percent.
B)-0.4766 percent.
C)-0.4695 percent.
D)0.0000 percent.
E)-0.2907 percent.