Final answer:
True, a bond's modified duration cannot exceed its Macaulay duration if the yield-to-maturity is positive, as modified duration is derived from Macaulay duration factoring in interest rate changes.
Step-by-step explanation:
The statement is true: A bond's modified duration cannot be larger than its Macaulay duration assuming a positive yield-to-maturity. Macaulay duration is a measure of the weighted average time before a bondholder receives the bond's cash flows. Modified duration, on the other hand, adjusts Macaulay duration to account for the change in the bond's price due to interest rate movements and is calculated by dividing the Macaulay duration by (1 + yield-to-maturity/n) where n is the number of compounding periods per year. Since the yield-to-maturity is assumed to be positive, the divisor is greater than 1, implying that the modified duration will always be less than or equal to the Macaulay duration.