Question at position 11 Which of the following are generally true of all bonds?All of the other options.A rise in interest rates is associated with a fall in bond prices, resulting in capital losses on bonds whose terms to maturity are longer than the holding periods.The only bond whose return equals the initial yield to maturity is one whose time to maturity is the same as the holding period.The longer a bond’s maturity, the greater the size of the price change associated with an interest rate change.

Question

BlackTom AI · Accepted Answer

Bond prices and yields move inversely, so a rise in interest rates lowers bond prices; price sensitivity increases with maturity; and yield-to-maturity (YTM) equals realized return only when the holding period equals the remaining time to maturity (assuming coupons are reinvested at the YTM).

1) Relevant knowledge points and concepts
- Inverse relationship: bond price = present value of future cash flows discounted at current yields; higher discount rate → lower present value.
- Price sensitivity: longer-maturity bonds have larger duration and thus larger percentage price changes for a given yield change.
- Yield-to-maturity definition: YTM is the internal rate of return if the bond is held to maturity (and coupons are reinvested at the YTM). If the bond is sold before maturity, realized return generally differs from initial YTM.

2) Step-by-step reasoning
- If market interest rates rise, new discount rates used to value a bond increase, reducing the present value of remaining payments → price falls. If the investor sells before maturity, that fall is a capital loss.
- The magnitude of the price change depends on time until those cash flows are received: more distant cash flows are discounted more heavily by a rate change, so longer maturities show larger price moves.
- YTM assumes holding to maturity; if the holding period < time to maturity, you must sell in the market at the new price, so realized return normally differs from initial YTM. Only when holding period equals time to maturity does realized return equal the originally quoted YTM.

3) Example calculation (intermediate steps)
Compare two zero-coupon bonds ($100 face): 1-year at 5% → price = 100/1.05 = 95.238. 10-year at 5% → price = 100/(1.05^10) = 61.391.
If yield rises to 6%: 1-year price = 100/1.06 = 94.340 (price change ≈ -0.898, −0.94%); 10-year price = 100/(1.06^10) = 55.84 (price change ≈ −5.551, −9.04%). This shows larger absolute and percentage change for the longer maturity.

4) Why the correct answer is correct
Each of the three listed statements is a standard, generally true property of bonds; therefore the choice “All of the other options.” correctly captures that all statements are true.

5) Why the single-option alternatives are not the best choice
Each individual option is true, but selecting only one would ignore the others. The best answer is the option that asserts all three are true.

6) Conclusion
All three component statements are generally true, so the correct answer is “All of the other options.” This matches the provided answer.

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