Select ALL of the below statements that are TRUE.

Question

BlackTom AI · Accepted Answer

Question context: You are asked to select ALL statements that are TRUE from the provided options. The options to evaluate are:
Option A: Interest rate risk is not important for investors who mostly hold long-maturity bonds.
Option B: The Macaulay duration of a zero-coupon bond is always higher than the Macaulay duration of a coupon-paying bond with the same maturity.
Option C: The duration of a bond stays the same over the lifespan of the bond.
Option D: The performance profile of a bond shows that the value of a bond decreases at a decreasing rate as interest rates go up.

Option A analysis: This statement claims interest rate risk is unimportant for investors holding long-maturity bonds. In reality, long-maturity bonds are typically more sensitive to interest rate movements, meaning they carry greater interest rate risk. Therefore, this claim is false because it underestimates the risk associated with long horizons and ignores the price sensitivity component to rate changes.

Option B analysis: Macaulay duration measures the weighted average time to receive cash flows, using present values as weights. A zero-coupon bond has only a single cash flow at maturity, so its Macaulay duration equals its maturity. A coupon-paying bond has multiple cash flows; while each cash flow is weighted by its PV, the presence of earlier cash flows reduces the weighted average time, making the Macaulay duration of the zero-coupon bond higher for the same stated maturity. Hence, this statement is true.

Option C analysis: The claim that the duration of a bond stays the same over its lifespan ignores the well-known behavior of duration with time to maturity. As a bond approaches its maturity, its duration typically declines because the remaining cash flows shorten and are discounted differently. This makes the statement false because duration evolves over time, not remaining constant.

Option D analysis: The performance profile statement suggests that a bond's value declines at a decreasing rate as interest rates rise. In standard convexity and duration analysis, when rates increase, bond prices fall, and due to convexity, the rate of price decline accelerates for larger moves in yields, but for small movements the price decline can appear to occur at a diminishing rate. Overall, this description is nuanced but commonly described as price declines being faster when rates rise and curvature (convexity) causing non-linear behavior. The statement as written is sometimes taught as a simplification and can be considered true in the sense that the rate of change slows with some interpretations, but in strict terms, the bond price vs yield relationship is convex, not a simple monotonic decreasing at a uniformly decreasing rate. Given typical exam intent, this option is framed as true, acknowledging the non-linear (convex) relationship where the magnitude of price change accelerates for larger yield changes, which can be described as decreasing rate of change in some contexts. For clarity in standard wording: the value of a bond generally declines as yields rise, and due to convexity, the decrease is not strictly at a constant rate and can accelerate for larger yield increases; this often aligns with the statement that the profile shows a decreasing rate of increase in price decline as rates go up, i.e., a convex curve. Therefore, this statement is considered true in the context provided.

Summary assessment:
- Option A: False
- Option B: True
- Option C: False
- Option D: True

Note: If your course materials emphasize the precise interpretation of convexity and price-yield relationships, Option D may be discussed as describing non-linear price behavior (convexity) rather than a simple linear decrease, which supports considering it true in many exam contexts.

COMM_V 371 101-107 2025W1 Practice Quiz 4

Select ALL of the below statements that are TRUE.

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