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双 · 2023年04月30日

原理

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.

这个YTM是通过SPot rate 计算得到,而forward rate也是通过SPOT rate计算,最终realized return 比YTM要大的底层逻辑是什么?


1 个答案

pzqa31 · 2023年04月30日

嗨,从没放弃的小努力你好:


首先明确一些概念:

1.Spot rate是站在t=0时刻看到的投资不同期限的利率。

2.YTM是用债券的价格计算出来的如果持有至到期获得的年平均收益率,是spot rate的打包价,类似一系列spot rate的加权平均,并假设每期coupon的再投资利率也是YTM。

3.Forward rate是隐含在spot rate中的,是站在t=0时刻预测的,未来不同时间点的利率。

4.realized return是债券卖掉后的真实收益,可以提前把债券卖掉而不用持有到期。收益包括卖掉前获得的coupon、coupon再投资收益,还有capital gain


具体到这道题,realized return大于YTM的主要原因是再投资利率假设是不同的,一个假设以YTM进行再投资,另一个假设以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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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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