READING 59 CURVE-BASED AND EMPIRICAL FIXED-INCOME RISK MEASURES

Question 1

Which of the following best describes a callable bond?
A. A bond that gives the investor the right to sell it back to the issuer before maturity
B. A bond that combines an option-free bond and a short call option position
C. A bond with fixed cash flows and no embedded options

Answer 1

Correct Answer: B
Explanation:

Callable bonds give the issuer the right to redeem the bond early, equivalent to holding a short call option.

Option A describes a putable bond, not a callable bond.

Option C describes an option-free bond.

Question 2

What embedded option is present in a putable bond?
A. The issuer’s right to redeem the bond early
B. The investor’s right to sell the bond back to the issuer before maturity
C. The borrower’s right to prepay mortgage loans

Answer 2

Correct Answer: B
Explanation:

A putable bond grants the investor the right to sell the bond back early (long put option).

Option A describes a callable bond.

Option C relates to mortgage-backed securities (MBS), not putable bonds.

Question 3

Why do bonds with embedded options not have a single well-defined yield?
A. Their cash flows and timing are uncertain due to option exercise possibilities
B. Their coupon payments are fixed and guaranteed until maturity
C. They always trade at par value

Answer 3

Correct Answer: A
Explanation:

The possibility of early redemption changes cash flow timing, affecting yields.

Option B applies to option-free bonds.

Option C is not true for bonds with embedded options.

Question 4

Effective duration measures:
A. Sensitivity of a bond’s price to changes in its own yield to maturity (YTM)
B. Sensitivity of a bond’s price to changes in the benchmark yield curve, assuming spreads remain constant
C. The bond’s credit spread over government bonds

Answer 4

Correct Answer: B
Explanation:

Effective duration isolates price sensitivity to benchmark curve shifts, holding spreads constant.

Option A describes modified duration.

Option C is a credit risk measure, not duration.

Question 5

What is the main difference between modified duration and effective duration?
A. Modified duration applies only to callable bonds, effective duration applies to all bonds
B. Modified duration uses changes in bond YTM, effective duration uses changes in benchmark yield curve
C. Modified duration accounts for credit spreads, effective duration ignores them

Answer 5

Correct Answer: B
Explanation:

Modified duration uses bond YTM changes; effective duration uses benchmark curve changes to reflect embedded options.

Option A is incorrect; modified duration applies mainly to option-free bonds.

Option C is incorrect; neither explicitly accounts for credit spread changes.

Question 6

Why does effective duration separate the effects of benchmark yield changes from credit and liquidity spreads?
A. To isolate price sensitivity only due to changes in benchmark rates
B. To ignore any changes in bond prices due to interest rates
C. To measure credit risk exposure

Answer 6

Correct Answer: A
Explanation:

Effective duration isolates sensitivity to benchmark yield curve changes, assuming spreads are constant.

Option B is false because it focuses on interest rate sensitivity.

Option C refers to credit risk, not duration.

Question 7

Which bond type can exhibit negative convexity?
A. Option-free bond
B. Callable bond
C. Putable bond

Answer 7

Correct Answer: B
Explanation:

Callable bonds can have negative convexity because the call option caps price appreciation at low yields.

Option-free bonds always have positive convexity.

Putable bonds also have positive convexity.

Question 8

What happens to the price of a callable bond when yields fall significantly?
A. The price rises without limit
B. The price rise is limited due to the call option being more valuable
C. The price decreases

Answer 8

Correct Answer: B
Explanation:

The issuer is more likely to call the bond, capping price gains.

Option A is true for option-free bonds.

Option C is opposite of typical yield-price relationship.

Question 9

At high yields, how does the duration of a putable bond compare to that of an equivalent option-free bond?
A. It is longer
B. It is shorter
C. They are equal

Answer 9

Correct Answer: B
Explanation:

At high yields, the put option becomes more valuable, reducing duration since bondholders can sell back early.

Option A is incorrect; duration decreases.

Option C ignores the put option impact.

Question 10

Why can modified duration and effective duration differ slightly for an option-free bond?
A. Because credit spreads are volatile
B. Due to nonparallel shifts in the government spot rate curve affecting yields differently
C. Because option-free bonds have embedded options

Answer 10

Correct Answer: B
Explanation:

Nonparallel shifts in spot rates cause slight differences in yield changes and thus duration measures.

Option A applies more to credit risky bonds.

Option C is false; option-free bonds have no embedded options.

Question 11

What is the role of the government spot curve in calculating effective duration?
A. It remains constant when the benchmark curve shifts
B. It shifts nonparallelly, affecting the bond’s yields
C. It is ignored in the calculation

Answer 11

Correct Answer: B
Explanation:

Spot rates shift nonparallelly, influencing yields and effective duration calculations.

Option A is incorrect; spot curve changes with benchmark.

Option C is incorrect; spot rates are essential in pricing.

Question 12

Effective convexity differs from traditional convexity in that it:
A. Measures price sensitivity only to changes in the bond’s YTM
B. Measures price sensitivity to changes in the benchmark yield curve for bonds with embedded options
C. Is always positive

Answer 12

Correct Answer: B
Explanation:

Effective convexity accounts for embedded options and benchmark curve changes.

Option A describes traditional convexity.

Option C is incorrect because callable bonds can have negative convexity.

Question 13

Which statement best describes the yield of a callable bond?
A. It is constant over the life of the bond
B. It depends on whether the call option is exercised
C. It is the same as the yield of an option-free bond

Answer 13

Correct Answer: B
Explanation:

Yield changes depending on call exercise timing.

Option A is false; yield varies with option exercise.

Option C ignores embedded options.

Question 14

Mortgage-backed securities (MBSs) are similar to which bond type?
A. Putable bonds
B. Callable bonds
C. Option-free bonds

Answer 14

Correct Answer: B
Explanation:

Borrowers can prepay loans early, similar to issuer’s call option.

Option A is incorrect; MBSs are not putable bonds.

Option C ignores embedded options.

Question 15

When calculating price sensitivity for bonds with embedded options, which yield change is used?
A. Change in the bond’s own YTM
B. Change in the benchmark government yield curve
C. Change in credit spread

Answer 15

Correct Answer: B
Explanation:

Effective duration uses benchmark yield curve shifts.

Option A applies to option-free bonds.

Option C is not considered in effective duration.

Question 16

Which factor does NOT influence whether the embedded option in a bond is exercised?
A. Level of credit spreads
B. Level of government benchmark yields
C. Bondholder’s age

Answer 16

Correct Answer: C
Explanation:

Credit spreads and benchmark yields impact option exercise; bondholder’s age does not.

Option A and B are relevant factors.

Question 17

What happens to the price-yield curve of a callable bond at low yields?
A. It becomes flatter due to limited price appreciation
B. It becomes steeper due to greater price increases
C. It is identical to an option-free bond

Answer 17

Correct Answer: A
Explanation:

Call option caps price gains causing flattening (negative convexity).

Option B is incorrect; price gains are limited.

Option C ignores embedded option effect.

Question 18

A putable bond’s price is less sensitive to yield increases at high yields because:
A. The issuer will call the bond
B. The investor can put the bond back, limiting price declines
C. The bond has no embedded options

Answer 18

Correct Answer: B
Explanation:

The put option limits downside risk to the investor.

Option A describes callable bonds.

Option C is false; putable bonds have embedded options.

Question 19

Which duration measure would you use to analyze interest rate risk for a mortgage-backed security?
A. Modified duration
B. Effective duration
C. Macaulay duration

Answer 19

Correct Answer: B
Explanation:

MBSs have embedded options, so effective duration is appropriate.

Option A is for option-free bonds.

Option C is a weighted average time measure, less used for interest rate risk.

Question 20

When benchmark yields shift nonparallelly, what happens to the risky bond’s yield?
A. It shifts exactly by the same amount
B. It shifts slightly differently due to different spot rate weights
C. It remains unchanged

Answer 20

Correct Answer: B
Explanation:

Different spot rates change by different amounts, causing yield deviations.

Option A assumes parallel shifts.

Option C is incorrect.

Question 21

Which of the following is true about effective duration?
A. It assumes credit spreads change significantly when benchmark yields change
B. It assumes credit spreads remain constant during benchmark yield changes
C. It ignores benchmark yield curve shifts

Answer 21

Correct Answer: B
Explanation:

Effective duration assumes spreads remain constant.

Option A is false.

Option C is false; benchmark curve changes are fundamental.

Question 22

Why does a callable bond have less duration than an option-free bond at low yields?
A. Because the call option limits the bond’s price gain potential
B. Because the bond’s coupon is higher
C. Because the bond’s maturity is longer

Answer 22

Correct Answer: A
Explanation:

Call option caps upside price movement, reducing duration.

Option B and C do not explain duration differences caused by options.

Question 23

How does effective convexity behave for a putable bond?
A. It is always negative
B. It is always positive
C. It fluctuates between positive and negative

Answer 23

Correct Answer: B
Explanation:

Putable bonds exhibit positive convexity due to downside protection.

Option A is incorrect.

Option C is incorrect.

Question 24

What is the effect of credit spread changes on effective duration?
A. Effective duration measures sensitivity assuming constant credit spreads
B. Effective duration captures credit spread changes fully
C. Effective duration ignores benchmark yield curve changes

Answer 24

Correct Answer: A
Explanation:

Effective duration isolates benchmark yield sensitivity assuming spreads constant.

Option B is false.

Option C is false.

Question 25

Which type of bond’s price is likely to decrease less during rising yields due to its embedded option? A. Option-free bond B. Putable bond C. Callable bond

Answer 25

Correct Answer: B Explanation: The put option limits downside price drops. Option A has no embedded options. Option C can have greater price declines due to call risk.

Question 26

Which embedded option tends to make a bond’s convexity negative? A. Put option B. Call option C. No embedded option

Answer 26

Correct Answer: B Explanation: Call options cause negative convexity. Put options cause positive convexity. No embedded option means positive convexity.

Question 27

What does a nonparallel shift in the spot rate curve imply for bond yield changes? A. All spot rates change by the same amount B. Spot rates change by different amounts, affecting bond yield calculations C. The yield curve becomes flat

Answer 27

Correct Answer: B Explanation: Different maturities’ spot rates change unevenly. Option A describes parallel shifts. Option C is unrelated.

Question 28

Why might effective duration and convexity not provide better price estimates for bonds with embedded options? A. Because option exercise depends on factors beyond benchmark yield level B. Because they ignore the impact of benchmark curve shifts C. Because they are only valid for option-free bonds

Answer 28

Correct Answer: A Explanation: Factors like credit spreads and principal outstanding affect option exercise. Option B is false; they account for benchmark shifts. Option C is false.

Question 29

What assumption is made when calculating effective duration? A. Credit spreads and liquidity conditions remain constant B. Credit spreads change proportionally with benchmark yields C. The bond has no embedded options

Answer 29

Correct Answer: A Explanation: Effective duration assumes all else equal except benchmark curve shifts. Option B is false. Option C is false.

Question 30

In the context of embedded options, why is analyzing interest rate risk based on benchmark curve shifts preferred over bond YTM changes? A. Because YTM changes ignore option exercise probabilities B. Because benchmark shifts are easier to measure C. Because YTM never changes

Answer 30

Correct Answer: A Explanation: YTM changes reflect uncertain cash flows due to options; benchmark shifts isolate pure interest rate risk. Option B is not the primary reason. Option C is false.

Question 31

Which of the following best describes the concept of key rate duration? A. The sensitivity of a bond’s price to changes in interest rates across the entire yield curve. B. The sensitivity of a bond’s price to a change in the benchmark yield at a specific maturity, holding other yields constant. C. The change in a bond's price relative to a change in its credit spread.

Answer 31

Correct Answer: B Explanation: B is correct: Key rate duration measures the price sensitivity to a yield change at a specific maturity, assuming other parts of the curve remain unchanged. A is incorrect: That describes effective duration, which assumes parallel shifts in the curve. C is incorrect: This refers more to credit spread duration, not key rate duration.

Question 32

Key rate duration is especially useful for analyzing: A. Interest rate risk under parallel shifts in the yield curve. B. The reinvestment risk of callable bonds. C. Shaping risk caused by nonparallel shifts in the yield curve.

Answer 32

Correct Answer: C Explanation: C is correct: Key rate duration helps assess shaping risk, or the impact of nonparallel yield curve movements. A is incorrect: That’s what effective duration is designed for. B is incorrect: Reinvestment risk relates more to callable/putable bonds, not key rate analysis.

Question 33

Which of the following best explains why the sum of a bond’s key rate durations equals its effective duration? A. Because effective duration averages the price response across all maturities. B. Because each key rate duration represents the bond’s full sensitivity to any interest rate change. C. Because key rate durations isolate the price sensitivity at each maturity point on the curve.

Answer 33

Correct Answer: C Explanation: C is correct: Each key rate duration shows sensitivity to a specific maturity’s yield; adding them gives total sensitivity (i.e., effective duration). A is incorrect: Effective duration doesn’t average—it reflects total price sensitivity. B is incorrect: No single key rate shows full sensitivity; each is only partial.

Question 34

A limitation of using effective duration for a bond with embedded options is that: A. It is not appropriate for callable or putable bonds. B. It does not capture the impact of nonparallel yield curve shifts. C. It always overestimates a bond's sensitivity to interest rates.

Answer 34

Correct Answer: B Explanation: B is correct: Effective duration assumes parallel shifts, so it fails to capture nonparallel changes. A is incorrect: Effective duration can be used for bonds with options, but its limitations must be recognized. C is incorrect: Effective duration does not always overestimate—it depends on the shape of the curve and bond type.

Question 35

What does shaping risk refer to? A. The risk of a bond's duration changing due to credit rating downgrade. B. The risk associated with changes in the slope or curvature of the yield curve. C. The reinvestment risk associated with steepening of the yield curve.

Answer 35

Correct Answer: B Explanation: B is correct: Shaping risk is about nonparallel shifts, like twists in the yield curve. A is incorrect: That’s related to credit risk, not yield curve shape. C is incorrect: Reinvestment risk and shaping risk are separate concepts.

Question 36

Empirical duration is most appropriate for: A. Portfolios with primarily government bonds. B. Bonds with stable credit spreads. C. Corporate bonds where credit spreads vary with market conditions.

Answer 36

Correct Answer: C Explanation: C is correct: Empirical duration captures real market behavior, including spread movements in corporate bonds. A is incorrect: Government bond portfolios are better suited to analytical duration. B is incorrect: If spreads are stable, analytical duration is sufficient.

Question 37

The primary difference between analytical and empirical duration is: A. Analytical duration is calculated using regression, while empirical is based on bond math. B. Analytical duration assumes stable credit spreads, empirical does not. C. Analytical duration includes credit risk, empirical does not.

Answer 37

Correct Answer: B Explanation: B is correct: Analytical duration assumes unchanging credit spreads; empirical duration reflects actual spread behavior. A is incorrect: It's the reverse—empirical uses regression (historical data). C is incorrect: Analytical duration excludes credit risk; empirical may capture it through observed data.

Question 38

During a flight to quality, empirical duration would likely be: A. Higher than analytical duration. B. Lower than analytical duration. C. Equal to analytical duration.

Answer 38

Correct Answer: B Explanation: B is correct: Corporate bond prices may not rise much (or may fall), making empirical duration lower than theoretical. A is incorrect: That would mean bond prices were more sensitive than expected, which isn’t the case here. C is incorrect: They would only be equal if spreads didn’t change, which they do during flight to quality.

Question 39

Key rate duration is especially useful in identifying: A. Convexity errors. B. Which segment of the yield curve a bond is most sensitive to. C. The reinvestment income of a bond portfolio.

Answer 39

Correct Answer: B Explanation: B is correct: It isolates maturity-specific price sensitivities. A is incorrect: That’s related to convexity analysis. C is incorrect: Reinvestment income is unrelated to key rate duration.

Question 40

Why is empirical duration preferred in volatile credit markets? A. It relies on future projections of spread movements. B. It models the yield curve mathematically. C. It reflects actual correlations between yield and spread changes.

Answer 40

Correct Answer: C Explanation: C is correct: Empirical duration is based on historical behavior, including correlations between yield and credit spread. A is incorrect: Empirical duration is based on past, not forecasted spreads. B is incorrect: That describes analytical duration.

Question 41

Which of the following assumptions underlies analytical duration? A. Bond yields are normally distributed. B. Interest rate and credit spread changes are independent. C. Yield curves always shift in a steepening pattern.

Answer 41

Correct Answer: B Explanation: B is correct: Analytical duration assumes that credit spreads don’t change with interest rates. A is incorrect: That’s a statistical assumption not tied to this duration concept. C is incorrect: Shifts can be flattening, steepening, or parallel.

Question 42

Which statement about empirical duration is most accurate? A. It is a forward-looking estimate based on spread modeling. B. It estimates price sensitivity based on actual past price and yield changes. C. It assumes yield curve shifts are parallel.

Answer 42

Correct Answer: B Explanation: B is correct: Empirical duration is based on past price-yield relationships. A is incorrect: It’s not forward-looking—it’s based on historical data. C is incorrect: That’s an assumption of effective/analytical duration.

Question 43

In a diversified bond portfolio, which duration type would most accurately reflect real-world price behavior under shifting credit conditions? A. Analytical B. Modified C. Empirical

Answer 43

Correct Answer: C Explanation: C is correct: Empirical duration captures actual changes, including credit spread impact. A is incorrect: Analytical duration assumes unchanging spreads. B is incorrect: Modified duration also assumes parallel shifts and no spread impact.

Question 44

Which of the following best explains why modified duration and effective duration may differ for an option-free bond in a non-flat yield curve environment? A. Modified duration incorporates changes in credit spreads, while effective duration does not. B. A shift in the par curve leads to a nonparallel shift in the spot curve, altering bond yields. C. Modified duration is calculated using convexity, whereas effective duration is not.

Answer 44

Correct Answer: B Explanation: Correct: A change in the government par yield curve leads to an uneven (nonparallel) shift in the spot curve, and since spot rates determine bond cash flow discounting, the bond's effective duration reflects these uneven shifts — causing a slight divergence from modified duration. A is incorrect: Modified duration does not account for credit spread changes; both measures assume spreads are constant. C is incorrect: Both modified and effective duration can be combined with convexity, but that's not the core distinction between them.

Question 45

In the context of duration, which of the following best describes a key limitation of effective duration when applied to bonds with embedded options? A. It cannot be used in nonparallel yield curve shifts. B. It ignores the impact of credit spreads and other option-exercise factors. C. It assumes a flat yield curve.

Answer 45

Correct Answer: B Explanation: Correct: Effective duration assumes that changes in price are only driven by changes in benchmark interest rates, but for bonds with embedded options, other factors like credit spreads, prepayment behavior, and callability also matter. A is incorrect: Effective duration is specifically useful for nonparallel yield shifts. C is incorrect: While yield curve shape affects the result, effective duration does not assume a flat curve; in fact, it accommodates shifting curves.

Question 46

Which of the following most accurately describes how bond yields are derived in the context of the spot curve? A. Bond yields are equal to the spot rate corresponding to the bond’s maturity. B. Bond yields are a weighted average of relevant spot rates across maturities. C. Bond yields are calculated independently of spot rates using the par curve.

Answer 46

Correct Answer: B Explanation: Correct: Bond yields are the internal rate of return of a bond’s cash flows, which are discounted using spot rates of different maturities. The final yield is a weighted average of these spot rates. A is incorrect: Only zero-coupon bonds use a single spot rate equal to their maturity. C is incorrect: While the par curve can be used to approximate yields, it's ultimately constructed from spot rates, not the other way around.

Question 47

Why might effective duration and convexity not provide significantly better estimates of price changes for bonds with embedded options, even for small changes in yield? A. Yield changes affect bonds with embedded options linearly. B. Option-exercise decisions are influenced by more than just benchmark interest rates. C. The effective duration does not account for the time value of money.

Answer 47

Correct Answer: B Explanation: Correct: In bonds with embedded options, price behavior depends not just on benchmark yields but also on option-exercise considerations like credit spreads or outstanding principal. These factors may cause the bond to react differently than duration/convexity models suggest. A is incorrect: Bond price responses — especially for options — are not linear with respect to yield changes. C is incorrect: Duration inherently reflects discounted cash flows, so it does consider the time value of money.