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Tututu · 2024年10月13日

为什么不能用2.707%-1.84%

  1. CFA I
  2. Fixed Income

NO.PZ2023052301000030

问题如下：

An analyst is analyzing a three-year, 2.25% annual coupon bond issued by QWE Company. Currently, the bond’s yield-to-maturity is 2.707%. The three-year swap rate is 1.840%. The government spot rates are presented in the table.


If the price of the QWE bond is 98.70% of par, its Z-spread (in basis points) is closest to:

选项：

A.

80.

B.

82.

C.

87.

解释：

B is correct. To calculate the Z-spread, we must solve for Z in the following equation, given the spot rates and price of the bond:


The Solver add-in for Microsoft Excel finds Z = 0.0082, or 82 bps, by setting the price (sum of present values of cash flows) equal to 98.70 as the objective and Z as the change variable. Please refer to the candidate learning ecosystem online for a spreadsheet demonstrating the calculation.

A is incorrect because 80 bps is the value of the G-spread, not the Z-spread. The G-spread is calculated as the difference between the QWE bond yield and the yield of the government bond with the same maturity:

G-spread = 2.707% – 1.904% = 80 bps.

C is incorrect because 87 bps is the I-spread, not the Z-spread. The I-spread is calculated as a yield spread of a bond over the standard swap rate in the same currency and with the same tenor. The yield-to-maturity for the corporate bond is 2.707%, and the swap rate for the same maturity is 1.840%.

I-spread = 2.707% – 1.840% = 87 bps.

为什么不能用2.707%-1.84%

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1 个答案

吴昊_品职助教 · 2024年10月14日

嗨，爱思考的PZer你好：


1.840%是swap rate，所以2.707%-1.84%，这样算出来的是I-spread，而题目要我们求的是Z spread。 所以不能用2.707%-1.84%

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