老师您好，能解释一下解答中提到：收益率曲线非平行移动可能会改变 bond portfolio 的 cash flow yield 这句话吗？
问题如下图：
选项：
A. 
B. 
C. 
解释：
发亮_品职助教 · 2020年02月03日
嗨，爱思考的PZer你好：
Cash flow yield就是Bond portfolio的折现率，可以类比成债券的YTM。
对于单个债券，有明确的到期日，所以我们可以算一个YTM；
但是对于Bond portfolio，组合内部各个成份债券的到期日不一样，Portfolio没有一个统一、明确的到期日，所以他并没有一个“YTM”概念。
于是，我们可以把组合当成一个大的债券，期初购买组合的Price已知，组合内部的现金流已知（所有成份债券的现金流），现金流的发生时间已知，所以我们就可以像计算债券的YTM一样，计算出组合的折现率Cash flow yield，公式与YTM的公式一模一样。
所以组合的Cash flow yield，就是组合的折现率“YTM”，和债券的YTM本质是一个意思，都是分母折现率，并没有其他特殊的地方。
这样的话，可以类比理解，如果收益率曲线发生非平行移动，单个债券的价格有可能会变化，例如对于一支10年期的债券，收益率曲线非平行移动恰好是10年期的利率发生变化，那么10年期债券的价格变化，这样债券价格变、反求出来的折现率YTM就会变。
对于Portfolio，如果发生收益率曲线非平行移动，组合的价格Price可能会变化，因为非平行移动，可能会影响到成份债券的价格，进而影响到组合的Price，所以分子的现金流没变，Price变化，折现率Cash flow yield就可能会变：
-------------------------------就算太阳没有迎着我们而来，我们正在朝着它而去，加油！
NO.PZ2019103001000033 maximizing the cash flow yielof the bonportfolio. minimizing the fferenbetween liability ration anbonportfolio ration. A is correct. Minimizing the convexity of the bonportfolio minimizes the spersion of the bonportfolio. A non-parallel shift in the yielcurve mresult in changes in the bonportfolio’s cash flow yiel In summary, the characteristiof a bonportfolio structureto immunize a single liability are thit (1) hinitimarket value thequals or excee the present value of the liability, (2) ha portfolio Macaulration thmatches the liability’s e te, an(3) minimizes the portfolio convexity statisti为了降低Structurrisk（Non-parallel时，资产不匹配负债的风险），我们就要选择Convexity最小的债券但是这应该是在ration匹配的基础上再选convexity最小啊
NO.PZ2019103001000033 No.PZ2019103001000033 (选择题) 来源: 原版书 ug Kepler, the newly hirechief financiofficer for the City of Raor asks the puty financimanager, Hui Ng, to prepare analysis of the current investment portfolio anthe city’s current anfuture obligations. The city hmultiple liabilities of fferent amounts anmaturities relating to the pension fun infrastructure repairs, anvarious other obligations. Ng observes ththe current fixeincome portfolio is structureto matthe ration of ealiability. Previously, this structure causethe city to access a line of cret for temporary mismatches resulting from changes in the term structure of interest rates Kepler asks Ng for fferent strategies to manage the interest rate risk of the city’s fixeincome investment portfolio against one-time shifts in the yielcurve. Ng consirs two fferent strategies: Strategy 1: Immunization of the single liabilities using zero-coupon bon helto maturity Strategy 2: Immunization of the single liabilities using coupon-bearing bon while continuously matching ration. The effects of a non-parallel shift in the yielcurve on Strategy 2 creceby: 您的回答正确答案是: A A 正确minimizing the convexity of the bonportfolio. B maximizing the cash flow yielof the bonportfolio. C minimizing the fferenbetween liability ration anbonportfolio ration. A能选，为啥B不能选，根据convexity的公式，当CFY增加的时候convexity 减小，最大化CFY也可以是认为最小化convexity啊
NO.PZ2019103001000033 平行移动的话没有影响吗？对ration和凸度有没有影响？
请问题目中不是说针对multiple liabilities吗？那么为何是选择convexity最小的状况呢？
maximizing the cash flow yielof the bonportfolio. minimizing the fferenbetween liability ration anbonportfolio ration. A is correct. Minimizing the convexity of the bonportfolio minimizes the spersion of the bonportfolio. A non-parallel shift in the yielcurve mresult in changes in the bonportfolio’s cash flow yiel In summary, the characteristiof a bonportfolio structureto immunize a single liability are thit (1) hinitimarket value thequals or excee the present value of the liability, (2) ha portfolio Macaulration thmatches the liability’s e te, an(3) minimizes the portfolio convexity statisti对于yielcurve非平行移动，不是首先解决的是ration match，在ration match的情况下，再最小化convexity嘛？所以C为啥是错的？