题目
Peter paid $93.40 to purchase a bond on June 1st, 2018; the bond pays a semi-annual coupon with a coupon rate of 3.0% per annum and matures in 10.0 years on June 1st, 2028. One year later, on June 1st, 2019, the bond's yield is unchanged; aka, unchanged yield assumption. Peter can reinvest his received coupons at a rate of 4.0% per annum. If Peter were to sell the bond on June 1st, 2019, which of the following is nearest to his gross realized return over the one year period since he purchased the bond?
选项
A.-1.09%
B.2.50%
C.3.84%
D.4.11%
答案
C
解析
3.84% (or more exactly 3.83718%) is the gross realized return, which includes one reinvested (at 4.0%) coupon.At the time of purchase, when the bond's price was $93.40, its yield was = RATE(10×2,100×0.030/2,-93.40,100)×2 ~= 3.80%. After one year, if the yield is unchanged, then we only need to re-price with a shorter maturity such that the price is PV(0.0380/2,9×2,100×0.030/2,100) = $93.954. Notice how the bond pulled to par. The gross realizes return includes the interim coupon compounded for six months at 4.0% and, therefore is given by[$93.954 ＋$1.50＋ $1.50×(1 0.040/2)－93.40]/93.40= 3.8372%. 3.84% (更精确些3.83718%)是已实现的总回报，其中包括一张再投资（利率为4.0%）的息票。在购买时，债券的价格为$93.4，他的YTM = RATE(10×2, 100×0.030/2, －93.40, 100)×2= 3.80%。一年后，如果利率不变，我只需要以较短的到期日重新定价，价格为PV(0.0380/2, 9×2, 100×0.030/2, 100)= $93.954。请注意债券如何拉到面值。 总实现回报包括以4.0％的比例计息六个月的中期息票率为4%，计算过程为[$93.954 ＋$1.50＋ $1.50×(1 0.040/2)－93.40]/93.40= 3.8372%.