NO.PZ2020011303000208
问题如下：
The term structure is initially flat at 5%, and an investor buys a five-year bond with a face value of USD 100 and a coupon of 4% at a spread of ten basis points. At the end of six months the term structure is flat at 6% and the spread is zero. Carry out a P&L decomposition.
解释：
First we calculate the carry roll-down. The cash-carry is 2%. In this case, the assumption underlying the carry roll-down is that the term structure remains flat at 5%. (This is true for all three definitions of carry roll-down.) The initial price paid for the bond is
The price of the bond, if six months passes without rates changing or the spread changing, is
The carryroll-down is therefore: 2+95.626-95.199=2.427
This can alsobe calculated as 0.0255 × 95.199.
The value ofthe bond at the end of six months, assuming no spread change, is
After thespread change is considered, the value of the bond is
This leads tothe following table
The bond price in six months is 92.214 and the investor receives a coupon of 2.000 just before
92.214 + 2.000－95.199 = ﹣0.985
The P&L decomposition splits this into:
(a) A carry roll-down of 2.427,
(b) The impact of a term structure change of -3.782, and
(c) A spread change of 0.370.
﹣0.985 = 2.427－3.782 + 0.370
题目问：利率的期限结构最开始时flat的，利率是5%，投资者买了一个5年期的债券，面值是100USD，coupon rate是4%，spread是10bp。在6个月结束的时候，利率的期限结构依旧是flat的，利率是6%，spread是0，请carry out P&L的分解。
题目默认半年付息一次。
首先计算5年期，coupon rate是4%，半年付息一次，YTM是（5%+0.1%）=5.1%，的债券的价格：
PMT=4%*100/2=2，I/Y=5.1%/2=2.55，N=5*2=10，FV=100
利用金融计算器求出PV=95.199
6个月之后，债券变成期限为4.5年，YTM=6%，其他条件不变的债券，这个债券的价格为：
PMT=2，I/Y=6%/2=3，N=4.5*2=9，FV=100
金融计算器求出PV=92.214
需要将95.199到94.214的这-0.985进行分解，看是由什么带来的：
1.如果利率和spread都不变，半年后债券的价值算出来是95.626，再加上2的利息，获得的收益就是carry roll-down 也就是2.427。
2.然后在1的基础上：如果利率变成6%，spread仍然保留也就是折现率用6.1%，求出来4.5年期的债券价值是91.844，也就是term structure变化造成的收益就是91.844-95.626 =-3.782
3.然后再2的基础上：如果利率是6%，spread没了，也就是spreadchange带来的收益就是92.214-91.844=0.37。
-0.985被拆解成了三个产生原因2.427 - 3.782 +0.37
请问整道题怎么理解呢？。。。。
