READING 57 YIELD-BASED BOND DURATION MEASURES AND PROPERTIES Flashcards
(25 cards)
What does modified duration most directly measure?
A. The time it takes to recover the price of a bond through its cash flows
B. The percentage change in a bond’s price for a 1% change in yield
C. The convexity of the bond’s price-yield relationship
Correct Answer: B
Explanation:
B is correct: Modified duration estimates the % change in price of a bond for a 1% change in YTM, holding everything else constant.
A describes payback period, not duration.
C refers to convexity, not duration.
A bond has a Macaulay duration of 6 years and a YTM of 8% with annual payments. What is its modified duration?
A. 5.56
B. 6.48
C. 5.00
Correct Answer: A
Explanation:
A is correct: ModDur = MacDur / (1 + YTM) = 6 / (1 + 0.08) = 5.56
B incorrectly adds YTM instead of dividing.
C assumes MacDur equals ModDur, which is incorrect.
For a bond with semiannual coupons, MacDur = 7.2 and YTM = 6% compounded semiannually. What is the Modified Duration?
A. 6.92
B. 6.79
C. 6.99
Correct Answer: C
Explanation:
C is correct: The proper calculation gives 6.99.
A (6.92) and B (6.79) are incorrect and result from either rounding errors or wrong formulas (e.g., using annual YTM instead of periodic).
Modified duration is best described as:
A. A convex estimate of interest rate sensitivity
B. A linear approximation of price change for yield movements
C. A backward-looking measure of bond returns
Correct Answer: B
Explanation:
B is correct: ModDur is a linear estimate of price sensitivity to yield changes.
A refers to convexity.
C misrepresents duration as historical, not forward-looking.
Which of the following statements is most accurate about Macaulay and Modified Duration?
A. Modified duration is always higher than Macaulay duration
B. Macaulay duration is adjusted for interest rates to get modified duration
C. Macaulay duration reflects convexity effects more than modified duration
Correct Answer: B
Explanation:
B is correct: ModDur = MacDur / (1 + r). It adjusts MacDur to reflect price sensitivity.
A is false; ModDur is lower than MacDur.
C confuses duration with convexity.
Why is ΔYTM expressed as a decimal in the approximate ModDur formula?
A. To match bond market conventions
B. To convert bond prices to dollar terms
C. To scale the result to a 1% yield change
Correct Answer: C
Explanation:
C is correct: ΔYTM must be in decimal form (e.g., 0.005) to estimate ModDur per 1% yield change.
A is vague and not precise.
B is unrelated to the function of ΔYTM in the formula.
Given:
V– = 88.127
V+ = 85.092
V₀ = 86.59
ΔYTM = 0.005
What is the approximate ModDur?
A. 3.50
B. 1.75
C. 4.03
Correct Answer: A
Explanation:
A is correct: Approx ModDur = (88.127 - 85.092) / (2 × 86.59 × 0.005) = 3.50
B is the % price change, not the duration.
C is the MacDur (from the example), not the approximate ModDur.
If ModDur = 3.5, what is the approximate % change in bond price for a 0.5% increase in YTM?
A. −1.75%
B. +1.75%
C. −3.50%
Correct Answer: A
Explanation:
A is correct: %ΔPrice ≈ −ModDur × ΔYTM = −3.5 × 0.5% = −1.75%
B has the wrong direction (price drops, not increases).
C assumes a 1% YTM change.
Which of the following best describes a limitation of Modified Duration?
A. It fails to adjust for yield frequency
B. It overestimates price change for small yield movements
C. It becomes less accurate for large changes in YTM
Correct Answer: C
Explanation:
C is correct: ModDur assumes a straight line, so accuracy drops for large YTM changes.
A is incorrect—ModDur does adjust for frequency.
B is the opposite; it’s accurate for small changes.
Which of the following best describes the money duration of a bond?
A. The annual change in the bond’s market value.
B. The sensitivity of the bond’s value to a 1% change in YTM, expressed in currency terms.
C. The number of years it takes for a bond to recover its full price through coupon payments.
Correct Answer: B
Explanation:
Money duration = ModDur × Full price, representing how much a bond’s value (in currency) changes for a 1% YTM move.
A is incorrect because it refers to total return, not sensitivity.
C is incorrect; that’s more related to a payback concept, not duration.
Which bond will generally have higher modified duration, all else equal?
A. A 10-year bond with 3% coupon
B. A 10-year bond with 8% coupon
C. A 5-year bond with 3% coupon
Correct Answer: A
Explanation:
A is correct: Lower coupon → more sensitivity → higher duration.
B has a higher coupon → lower duration.
C has shorter maturity → lower duration.
Why does the approximate ModDur formula use both V+ and V–?
A. To adjust for coupon payments
B. To smooth the effect of price volatility
C. To average the price effects of upward and downward yield shifts
Correct Answer: C
Explanation:
C is correct: Using both V+ and V– ensures the estimate reflects symmetry around the current price.
A is irrelevant here.
B is vague and incorrect.
The price value of a basis point (PVBP) is best described as:
A. The change in a bond’s full price for a 1% change in yield.
B. The difference between a bond’s dirty and clean price.
C. The average price change for a 0.01% change in YTM, both up and down.
Correct Answer: C
Explanation:
PVBP = average of the bond’s price change when YTM rises and falls by one basis point (0.01%).
A is wrong; 1% change refers to money duration, not PVBP.
B refers to accrued interest, not PVBP.
Which factor most directly increases a bond’s money duration?
A. Higher coupon frequency
B. Lower ModDur
C. Higher bond price
Correct Answer: C
Explanation:
Money duration = ModDur × Full price → higher price increases it.
A does not directly increase money duration.
B would decrease, not increase, money duration.
All else equal, which bond is likely to have the highest interest rate risk?
A. A short-term, high-coupon bond
B. A long-term, zero-coupon bond
C. A short-term, floating-rate note
Correct Answer: B
Explanation:
Long maturity + no interim coupons = highest duration.
A and C offer early cash flows or rate resets, reducing risk.
Which of the following would cause a bond’s Macaulay duration to temporarily increase?
A. Passage of time between coupon payments
B. A drop in YTM
C. A coupon payment
Correct Answer: C
Explanation:
Duration falls as time passes but jumps up slightly right after a coupon, since time to next payment resets.
A is incorrect; duration usually decreases.
B increases price sensitivity, but not the MacDur jump.
Why does a floating-rate note (FRN) generally exhibit low interest rate risk?
A. Its price is fixed by the central bank.
B. Its coupons are reinvested at a fixed rate.
C. Its coupon adjusts with market interest rates.
Correct Answer: C
Explanation:
The reset feature means market rate changes don’t affect the bond’s value significantly.
A and B are unrelated to FRNs.
Which of the following best explains why zero-coupon bonds have higher interest rate risk than coupon bonds?
A. They are always issued at a premium.
B. They pay no interim cash flows.
C. They have lower convexity.
Correct Answer: B
Explanation:
No interim payments = entire value tied to final lump sum → highly sensitive to rate changes.
A is false.
C is incorrect; zeros often have higher convexity.
Which of the following best describes the relationship between YTM and interest rate risk?
A. Interest rate risk increases as YTM increases.
B. Interest rate risk decreases as YTM increases.
C. There is no relationship between the two.
Correct Answer: B
Explanation:
As YTM rises, duration falls → price is less sensitive.
A is incorrect—it’s the opposite.
C ignores the clear inverse link.
A bond’s price is more sensitive to changes in yield when:
A. The price-yield curve is flat.
B. The YTM is low.
C. The bond is callable.
Correct Answer: B
Explanation:
Lower YTM = steeper price-yield curve → greater price sensitivity.
A implies less sensitivity.
C adds complications but doesn’t answer the general case.
Which factor will decrease a bond’s price volatility?
A. Longer maturity
B. Lower coupon
C. Higher YTM
Correct Answer: C
Explanation:
Higher YTM compresses price sensitivity (flattens the price-yield curve).
A and B increase duration, raising price volatility.
Which of the following is true regarding PVBP?
A. It is the first derivative of the bond price with respect to yield.
B. It is constant across all bonds with the same YTM.
C. It varies based on bond characteristics like duration and price.
Correct Answer: C
Explanation:
PVBP depends on both duration and price.
A is conceptually similar but refers to duration.
B is false; PVBP differs even if YTM is the same.
What primarily determines the duration of a floating-rate note?
A. Time to maturity
B. Time to next coupon reset
C. Coupon size
Correct Answer: B
Explanation:
FRN duration is approximated by the time until its next rate reset.
A is for fixed bonds.
C has minimal effect on FRNs.
Why does higher coupon reduce interest rate risk?
A. It increases reinvestment risk.
B. It concentrates more value in earlier cash flows.
C. It increases the bond’s duration.
Correct Answer: B
Explanation:
Early cash flows reduce sensitivity to discount rate changes.
A is unrelated here.
C is false—duration falls with higher coupon.
