Suppose you are holding a 5% coupon bond maturing in one year with a YTM of 15%. If rates rise from 15% to 20% during the year, your yearly return is:

Question

BlackTom AI · Accepted Answer

Purchase price = (coupon + principal) discounted at the initial YTM: P0 = 105 / 1.15 = 91.3043478.

1) Relevant knowledge points and concepts
- Yield-to-maturity (YTM) at purchase is the internal rate of return that equates the bond’s purchase price to the present value of its future cash flows.
- If you buy a bond and hold it to maturity (no default), your realized annual return equals the YTM at purchase regardless of interim market rate movements.
- Return over the year = (cash received at maturity / purchase price) − 1.

2) Step-by-step reasoning
- Face value assumed 100 (standard). Annual coupon = 5% of 100 = 5.
- The bond matures in one year, so at maturity you will receive 100 (principal) + 5 (coupon) = 105.
- You bought the bond when YTM = 15%, so the fair purchase price is the discounted value of the 105 receipt: P0 = 105/(1 + 0.15).

3) Calculations with intermediate steps
- Compute price: P0 = 105 / 1.15 = 91.3043478.
- Realized one-year return if held to maturity: Return = (105 / 91.3043478) − 1 = 1.15 − 1 = 0.15 = 15%.

4) Why the correct answer is correct
- The YTM at purchase (15%) already priced the bond so that receiving 105 in one year yields exactly 15% on your investment. Changes in market interest rates during the year do not change the cash you will receive at maturity, so if you hold the bond to maturity your realized return equals the original YTM.

5) Why other options are incorrect
- a. 20%: This would be a return only if you somehow received 20% on your invested amount; in fact a rise in rates to 20% would lower market price, not increase your realized return if you hold to maturity.
- b. 5%: This is just the coupon rate; it ignores the capital gain from buying below par (you paid ~91.30 and receive 105).
- d. 10%: No combination of the coupon and purchase price here yields 10%; the correct arithmetic gives 15%.

6) Conclusion confirming the answer
- The realized yearly return when holding to maturity is 15%, so the correct choice is c. 15%.

Suppose you are holding a 5% coupon bond maturing in one year with a YTM of 15%. If rates rise from 15% to 20% during the year, your yearly return is:Single choice

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