Hi there I've trying (unsuccessfully) to understand the solution which appears to be given in two limbs which I largely paraphrase: 1. From part (i)(b), the price of a bond with 5% coupons > $100. 5% > par yield (which we calculated as 4.14% in part (b)(i)). Hence the monetary amounts in the earlier years are relatively more than those in the par bond in (i)(b). 2. Since the GRY is an "average" of the interest rates, there will be more weight placed on the earlier interest rates. Since the interest rates are increasing, this means that the GRY will be lower than the par yield. My questions are: (a) When it says "monetary amounts in the earlier years are relatively more than those in the par bond in (i)(b)", are they comparing the par bond to a 5% coupon bond priced using the term structure or are they comparing the par bond to a 5% coupon bond priced using the GRY? (b) If the GRY weights the earlier interest rates more heavily and term structure starts at 3.85% and goes up to 4.15%, why is it relevant that the monetary amounts in the earlier years (of some 5% coupon bond) are relatively more than those in the par bond? Surely, the GRY would be between 3.85% and 4.15% and probably skewed towards 3.85% than 4.15%. Thanks for any help!
Firstly, I think this one of the hardest little questions in the course and I wouldn't lose too much sleep over it. But: (a) The comparison is simply between 5% and 4.14%. You could be valuing the bond at either GRY or term structure. (b) The GRY only weights the earlier rates more in this example because 5 > 4.14. Higher earlier coupons so more weight to the lower, earlier interest rates.
