Question1.2 Which of the following statements about the yield to maturity (YTM) on a 6-year, 5% annual coupon bond is true?Select one alternative: None of the options is correct. The YTM is lower than the realised yield if the bond is held until maturity and interest rates decrease in the future. The YTM is greater than the realised compound yield if the bond is held until maturity and interest rates decrease in the future. The YTM is equal to the realised yield if the bond is held until maturity. The YTM is equal to the realised yield if the bond is held until maturity and interest rates increase in the future. ResetMaximum marks: 2.5 Flag question undefined

Question

BlackTom AI · Accepted Answer

Yield to maturity equals the single discount rate that equates a bond’s current price with the present value of its future coupon and principal payments; crucially, YTM implicitly assumes all coupon payments are reinvested at that same YTM (the reinvestment assumption). The realised (or realised compound) yield is the actual annual rate earned given the actual reinvestment rates experienced over the holding period.

Step-by-step reasoning:
1. Relevant concepts: a coupon bond’s cash flows (coupons each year and principal at maturity), YTM definition, and the reinvestment assumption for coupons. If actual reinvestment rates differ from YTM, the realised yield will differ from YTM.
2. If future market interest rates decrease after purchase, coupons received during the life of the bond must be reinvested at these lower rates. Because the YTM assumed reinvestment at the higher original rate, the actual compounded accumulation of coupons will be smaller than the accumulation assumed by YTM.
3. Numerical illustration (intermediate steps): assume face value 1000, coupon 5% → annual coupon 50, and the bond was originally priced at par so YTM = 5%. Suppose future reinvestment rate = 3% for coupons. Accumulated value at maturity (year 6) of coupons reinvested at 3%:
   - 50*(1.03)^5 = 57.9637
   - 50*(1.03)^4 = 56.2755
   - 50*(1.03)^3 = 54.6364
   - 50*(1.03)^2 = 53.0450
   - 50*(1.03)^1 = 51.5000
   - Final coupon + principal = 1050
   Sum FV ≈ 1323.4205. Solve 1000*(1 + r)^6 = 1323.4205 → (1 + r) = (1.3234205)^(1/6) ≈ 1.04786 → r ≈ 4.786% < 5%.
4. Why the correct answer is correct: Because coupons are reinvested at lower rates when interest rates fall, the realised compound yield (actual IRR) will be lower than the YTM that assumed reinvestment at the higher YTM. Thus the YTM is greater than the realised compound yield in this scenario.
5. Why other options are incorrect:
   - “YTM is lower than the realised yield if rates decrease”: opposite of true; lower reinvestment rates reduce realised yield.
   - “YTM equals realised yield if held to maturity”: true only if reinvestment rates equal YTM; not generally true.
   - “YTM equals realised yield if held and rates increase”: if rates increase, realised yield will be higher than YTM (not equal).
   - “None of the options is correct”: incorrect because one option is correct.
6. Conclusion: The correct option is: “The YTM is greater than the realised compound yield if the bond is held until maturity and interest rates decrease in the future.” This matches the provided answer.

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