The yield to maturity on a bond is the interest rate you earn on your investment if interest rates do not change. If you actually sell the bond before it matures, your realized return is known as the holding period yield. Suppose that today you buy a coupon bond with 9 percent annual interest for $1,000. The bond has 12 years to maturity. Three years from now, the yield to maturity has declined to 7 percent and you decide to sell. What is your holding period yield?单项选择题
A
A. 8.84 percent
B
B. 9.49 percent
C
C. 10.96 percent
D
D. 12.83 percent

Question

The yield to maturity on a bond is the interest rate you earn on your investment if interest rates do not change. If you actually sell the bond before it matures, your realized return is known as the holding period yield. Suppose that today you buy a coupon bond with 9 percent annual interest for $1,000. The bond has 12 years to maturity. Three years from now, the yield to maturity has declined to 7 percent and you decide to sell. What is your holding period yield?单项选择题

A

A. 8.84 percent

B

B. 9.49 percent

C

C. 10.96 percent

D

D. 12.83 percent

BlackTom AI · Accepted Answer

Begin with the bond’s cash flows: annual coupon = 9% of $1,000 = $90. You pay P0 = $1,000 today and hold for 3 years, receiving three coupons. At t = 3 you sell; the new market yield (YTM) for the remaining life is 7%.

1. Relevant knowledge and concepts
- Price of a coupon bond = present value of remaining coupons plus present value of face value, discounted at the prevailing YTM.
- Holding-period total return = (price at sale + coupons received − price paid) / price paid.
- Annualized holding-period yield = (1 + total return)^(1/number of years) − 1.

2. Complete reasoning and computation
- You receive three coupons: 90 each year for 3 years → total coupons = 90 × 3 = $270.
- After 3 years there remain 9 years to maturity (12 − 3 = 9). The bond’s sale price at that time is the PV at the new YTM = 7% of the remaining 9 coupon payments plus face value:
  PVremaining = 90 × [1 − (1 + 0.07)^−9] / 0.07 + 1000 × (1 + 0.07)^−9.
- Compute the discount factor (1.07)^−9 ≈ 0.543865. Then the annuity factor = (1 − 0.543865)/0.07 ≈ 6.51622.
  So PV of coupons = 90 × 6.51622 ≈ 586.46. PV of principal = 1000 × 0.543865 ≈ 543.86.
  Thus the sale price P3 ≈ 586.46 + 543.86 = $1,130.33.
- Total proceeds at sale = P3 + coupons received = 1,130.33 + 270 = $1,400.33.
- Total holding-period return over 3 years = (1,400.33 − 1,000) / 1,000 = 0.40033 = 40.033%.
- Annualize the 3-year return: H = (1.40033)^(1/3) − 1 ≈ 0.1096 = 10.96% (annualized).

3. Why the correct answer is correct
- Discounting the remaining cash flows at the new market YTM (7%) gives the sale price at t = 3; combining that with the three coupons received produces a 3‑year total return of ~40.033%. Converting that cumulative return to an annual rate by taking the cube root yields an annual holding-period yield of about 10.96%.

4. Why the other options are incorrect
- A (8.84%) and B (9.49%) are too low; they understate either the capital gain from the fall in yields or the correct annualization of the three-year total return. D (12.83%) is too high; it corresponds to a different method (for example, treating the three coupon flows differently when computing an IRR) but not to the standard annualized holding-period yield as computed above.

Conclusion: Using the sale price at the new YTM of 7%, collecting three $90 coupons, and annualizing the cumulative 3‑year return gives a holding-period yield of approximately 10.96% — answer C.

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