这题为什么用Par的算法啊…
问题如下图：
选项：
A. 
B. 
C. 
解释：
吴昊_品职助教 · 2019年12月31日
嗨，努力学习的PZer你好：
这道题没有牵涉到par rate。Smith买了一个四年期的债券并在两年后卖出，题目要我们求投资收益率，换句话说找到四年期债券的价格（初始购买金额），再找到两年后卖出的价格即可。同时，题目说用swap rate作为折现率yield。swap rate=spot rate+swap spread，分别可以算出两年期和四年期的swap rate。任何时候的债券价格都是未来现金流的折现求和。站在初始零时刻，四年期的零息债券价格为100/(1+0.0475)^4；同理，站在两年后，债券卖出的价格为100/(1+0.03)^2。从而通过两个价格求出收益率。
-------------------------------虽然现在很辛苦，但努力过的感觉真的很好，加油！
NO.PZ2018123101000027 问题如下 Smith gathers information on spot rates for on-the-run annual-coupon government securities answsprea, presentein Exhibit below.Smith buys a four-year, zero-coupon corporate bonanthen sell it after two years. Smith illustrates the returns from this strategy using the swrate a proxy for corporate yiel. Smith shoulshow a totreturn closest to: A.4.31%. B.5.42%. C.6.53%. C is correct.考点考察Ring the yielcurve策略解析由题干已知，Swrate来代替公司债的收益率；四年期的Swsprea差为0.70%，4年期的国债收益率Government spot rate 为4.05%，则4年期的swrate = 4.05% + 0.70% = 4.75%。因此，购买的4年期零息债券的价格为price=100(1+0.0475)4=83.058price=\frac{100}{{(1+0.0475)}^4}=83.058price=(1+0.0475)4100=83.058两年期的公司债收益率为2年期的Swrate, swrate = 2.70% +0.30% = 3%,4年期的零息债券持有2年后的卖出价格为price=100(1+0.0300)2=94.260price=\frac{100}{{(1+0.0300)}^2}=94.260price=(1+0.0300)2100=94.260则这笔投资的年化总收益为94.26083.058−1=0.0653=6.53%\sqrt{\frac{94.260}{83.058}}-1=0.0653=6.53\%83.05894.260−1=0.0653=6.53% 题目里面算出swrate，可以用它来折现？但是课上说swrate是一种prate？prate我理解就是每期现金流/pincipal的一个比率，应该是用来计算分子的？所以swrate到底是什么？为什么可以用来折现算价格？
NO.PZ2018123101000027 问题如下 Smith gathers information on spot rates for on-the-run annual-coupon government securities answsprea, presentein Exhibit below.Smith buys a four-year, zero-coupon corporate bonanthen sell it after two years. Smith illustrates the returns from this strategy using the swrate a proxy for corporate yiel. Smith shoulshow a totreturn closest to: A.4.31%. B.5.42%. C.6.53%. C is correct.考点考察Ring the yielcurve策略解析由题干已知，Swrate来代替公司债的收益率；四年期的Swsprea差为0.70%，4年期的国债收益率Government spot rate 为4.05%，则4年期的swrate = 4.05% + 0.70% = 4.75%。因此，购买的4年期零息债券的价格为price=100(1+0.0475)4=83.058price=\frac{100}{{(1+0.0475)}^4}=83.058price=(1+0.0475)4100=83.058两年期的公司债收益率为2年期的Swrate, swrate = 2.70% +0.30% = 3%,4年期的零息债券持有2年后的卖出价格为price=100(1+0.0300)2=94.260price=\frac{100}{{(1+0.0300)}^2}=94.260price=(1+0.0300)2100=94.260则这笔投资的年化总收益为94.26083.058−1=0.0653=6.53%\sqrt{\frac{94.260}{83.058}}-1=0.0653=6.53\%83.05894.260−1=0.0653=6.53% 关于持有两年后的价格计算，为什么不是用f（2,4）来折现，而是用S2来折现呢
NO.PZ2018123101000027 问题如下 Smith gathers information on spot rates for on-the-run annual-coupon government securities answsprea, presentein Exhibit below.Smith buys a four-year, zero-coupon corporate bonanthen sell it after two years. Smith illustrates the returns from this strategy using the swrate a proxy for corporate yiel. Smith shoulshow a totreturn closest to: A.4.31%. B.5.42%. C.6.53%. C is correct.考点考察Ring the yielcurve策略解析由题干已知，Swrate来代替公司债的收益率；四年期的Swsprea差为0.70%，4年期的国债收益率Government spot rate 为4.05%，则4年期的swrate = 4.05% + 0.70% = 4.75%。因此，购买的4年期零息债券的价格为price=100(1+0.0475)4=83.058price=\frac{100}{{(1+0.0475)}^4}=83.058price=(1+0.0475)4100=83.058两年期的公司债收益率为2年期的Swrate, swrate = 2.70% +0.30% = 3%,4年期的零息债券持有2年后的卖出价格为price=100(1+0.0300)2=94.260price=\frac{100}{{(1+0.0300)}^2}=94.260price=(1+0.0300)2100=94.260则这笔投资的年化总收益为94.26083.058−1=0.0653=6.53%\sqrt{\frac{94.260}{83.058}}-1=0.0653=6.53\%83.05894.260−1=0.0653=6.53% 相关公式可以写一下吗？
NO.PZ2018123101000027 问题如下 Smith gathers information on spot rates for on-the-run annual-coupon government securities answsprea, presentein Exhibit below.Smith buys a four-year, zero-coupon corporate bonanthen sell it after two years. Smith illustrates the returns from this strategy using the swrate a proxy for corporate yiel. Smith shoulshow a totreturn closest to: A.4.31%. B.5.42%. C.6.53%. C is correct.考点考察Ring the yielcurve策略解析由题干已知，Swrate来代替公司债的收益率；四年期的Swsprea差为0.70%，4年期的国债收益率Government spot rate 为4.05%，则4年期的swrate = 4.05% + 0.70% = 4.75%。因此，购买的4年期零息债券的价格为price=100(1+0.0475)4=83.058price=\frac{100}{{(1+0.0475)}^4}=83.058price=(1+0.0475)4100=83.058两年期的公司债收益率为2年期的Swrate, swrate = 2.70% +0.30% = 3%,4年期的零息债券持有2年后的卖出价格为price=100(1+0.0300)2=94.260price=\frac{100}{{(1+0.0300)}^2}=94.260price=(1+0.0300)2100=94.260则这笔投资的年化总收益为94.26083.058−1=0.0653=6.53%\sqrt{\frac{94.260}{83.058}}-1=0.0653=6.53\%83.05894.260−1=0.0653=6.53% 为什么2年后的卖出价格，不是用加上sprea的f(2,2)来折现100求得？
NO.PZ2018123101000027 问题如下 Smith gathers information on spot rates for on-the-run annual-coupon government securities answsprea, presentein Exhibit below.Smith buys a four-year, zero-coupon corporate bonanthen sell it after two years. Smith illustrates the returns from this strategy using the swrate a proxy for corporate yiel. Smith shoulshow a totreturn closest to: A.4.31%. B.5.42%. C.6.53%. C is correct.考点考察Ring the yielcurve策略解析由题干已知，Swrate来代替公司债的收益率；四年期的Swsprea差为0.70%，4年期的国债收益率Government spot rate 为4.05%，则4年期的swrate = 4.05% + 0.70% = 4.75%。因此，购买的4年期零息债券的价格为price=100(1+0.0475)4=83.058price=\frac{100}{{(1+0.0475)}^4}=83.058price=(1+0.0475)4100=83.058两年期的公司债收益率为2年期的Swrate, swrate = 2.70% +0.30% = 3%,4年期的零息债券持有2年后的卖出价格为price=100(1+0.0300)2=94.260price=\frac{100}{{(1+0.0300)}^2}=94.260price=(1+0.0300)2100=94.260则这笔投资的年化总收益为94.26083.058−1=0.0653=6.53%\sqrt{\frac{94.260}{83.058}}-1=0.0653=6.53\%83.05894.260−1=0.0653=6.53% 本题两个问题1.题目中没有说明spot rate曲线不变，是否应该增加此条件后题目才算严谨？2.求totreturn也要进行年化吗？什么情况下不需要年化呀？