题目
A $100 face value bond with 20 years to maturity pays a semi-annual coupon with a 4.0% coupon rate. If we compute effective duration and effective convexity, at a yield of 6.0%, with a shock of ten basis points (i.e., we re-price the bond at 5.90% and 6.10%), what is the estimate given by duration and convexity in PERCENTAGE terms if the yield DROPS by 100 basis points (1.0%)?
选项
A.+ 6.488%
B.+ 9.717%
C.+ 12.025%
D.+ 13.670%
答案
D
解析
At 5.9%, bond price = $77.8624At 6.0%, bond price = $76.8852At 6.1%, bond price = $75.9245(tip: don't re-key all the TVM inputs, only re-key the I/Y and re-compute the price)Effective duration = -1/P×(P[ 10 bps] - P[-10 bps])/(2×10 bps) = 12.6027.Effective convexity = 1/P×(P[ 10 bps] ＋P[-10 bps]-2×P[0])/(10 bps)^2 = 213.37.Estimated change in bond price (given -1.0% yield change) = -D×(-1.0%) 0.5×C×(-1.0%)^2 = 12.6027%＋1.067% = 13.6695%.This estimates a bond price of $87.3951 @ 5.0% yield, compared to an actual price of $87.4486.回报率 5.9%, bond price = $77.8624回报率6.0%, bond price = $76.8852回报率6.1%, bond price = $75.9245Effective duration = -1/P×(P[ 10 bps] - P[-10 bps])/(2×10 bps) = 12.6027.Effective convexity = 1/P×(P[ 10 bps] ＋P[-10 bps]-2×P[0])/(10 bps)^2 = 213.37.债券价格的估计变化（给出-1.0％的收益率变化）= -D×(-1.0%) 0.5×C×(-1.0%)^2 = 12.6027%＋1.067% = 13.6695%.估计债券价格为87.3951美元，收益率为5.0％，而实际价格为87.4486美元。