If a 5% coupon bond matures in one year and rates rise from 15% to 20%, the return is:

Question

BlackTom AI · Accepted Answer

For a one-year bond the price equals the present value of the coupon plus principal discounted at the prevailing yield, so the realized return when held to maturity equals the yield at which you bought the bond.

1. Relevant concepts
- Price of a coupon bond = (Coupon + Face) / (1 + current yield) when only one period remains.
- Holding-period (realized) return when you buy at the market yield and hold to maturity equals the initial yield-to-maturity (YTM).
- Coupon rate (5%) is not the same as the realized return when the bond is purchased at a discount or premium.

2. Step-by-step reasoning
- Assume face value = 100 (standard convention). Annual coupon = 5% × 100 = 5.
- Before rates rise, market yield = 15%. The fair price today = (Coupon + Principal) / (1 + 0.15) = (5 + 100) / 1.15.
- Compute purchase price: 105 / 1.15 = 91.3043478 (approx).

3. Intermediate calculations
- Purchase price = 91.3043478
- Cash received at maturity (one year later) = 5 (coupon) + 100 (principal) = 105
- Holding-period return = (105 − 91.3043478) / 91.3043478
- 105 / 91.3043478 = 1.15 → Return = 1.15 − 1 = 0.15 = 15%

4. Why the correct answer is correct
- You bought the bond at the market yield of 15%. Holding to maturity guarantees the promised 105 payment, so your realized return equals the initial yield (15%) regardless of interim interest-rate movements.

5. Why other options are incorrect
- a. 20%: Uses the new rate at maturity, but you already locked in price at 15%; future market rates after purchase do not change the cash flows you will receive at maturity.
- c. 5%: Equals the coupon rate, not the total return when bond is purchased at a discount; ignores capital gain.
- d. 10%: No basis here; not the coupon, purchase yield, or change in rates.

6. Conclusion
The correct return is 15%, matching answer b. 15%.

If a 5% coupon bond matures in one year and rates rise from 15% to 20%, the return is:Single choice

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