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SHAO · 2024年07月12日

老师，请教下

  1. CFA II
  2. Fixed Income

NO.PZ2023040701000001

问题如下：

Bird is analyzing a newly issued, US Treasury bond with a five year maturity and a 7.00% coupon. The bond was issued at a price of 101.15. The bond’s yield to maturity at issuance was 6.72%. Bird is evaluating this bond for long term investors who intend to buy this bond and hold it to maturity. Her analysis is based on an expectation that the future path of interest rates follows that which is implied by the forward curve. Current spot rates and extrapolated one year forward rates are provided in Exhibit 1.

Based on the data provided in Exhibit 1 and assuming that Bird's interest rate expectation materializes, the realized return for the US Treasury bond if held to maturity would most likely be:

选项：

A.

less than the yield to maturity.

B.

equal to the yield to maturity.

C.

greater than the yield to maturity.

解释：

Correct Answer: C

The realized return would be greater than the yield to maturity “YTM” because the coupons would be reinvested at forward rates which increase and eventually exceed the YTM since the spot curve is upward sloping. The YTM can be a poor estimate of expected return if interest rates are volatile and if the yield curve is steeply sloped (up or down). YTM assumes that all reinvestment of coupons is made at the assumed rate, which is the YTM. The present value of the bond is 101.15. The future value of the bond assuming that all coupons are reinvested at the forward rates is 141.87. The annualized realized return is 7.0%, which is greater than the 6.72% yield to maturity.

老师，请问这道题是不是可以不用计算，只要forward rates每期都大于spot rates，就说明用forward rates计算得到的收益率要高于YTM

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品职答疑小助手雍 · 2024年07月12日

同学你好，是可以不用计算，不过对比上不太对，因为只要yield curve向上倾斜，forward rate一定比spot大。

这题要明白的是YTM的假设，它假设的是每期的coupon都已YTM做再投资，

但forward 的再投资利率假设是不同的，它假设以forward rate进行再投资，因为forward rate大于YTM，所以我们用forward rate进行再投资获得的realized return更高。

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