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程卤蛋蛋 · 2025年01月12日

计算问题

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ202303270300006301

问题如下：

(1) The total expected return over the 1-year investment horizon for the Buy-and-Hold and Yield Curve Rolldown portfolios are closest to:

选项：

A.

2.515% for the Buy-and-Hold portfolio and 4.555% for the Yield Curve roll-down portfolio, respectively.

B.

2.42% for the Buy-and-Hold portfolio and 4.51% for the Yield Curve Rolldown portfolio, respectively.

C.

2.491% for the Buy-and-Hold portfolio and 3.59% for the Yield Curve Rolldown portfolio, respectively.

解释：

A is correct. Under a static yield curve assumption, expected returns are equal to rolldown return plus changes in currency over the investment horizon.

Since both strategies use zero-coupon bonds, the rolldown return is calculated from expected bond price changes from “rolling down” the THB yield curve, which is assumed to be static.

Buy and hold: 1.00% = (100.00-99.009)/99.009

Yield Curve Rolldown: 3.01% = (99.009-96.1169)/96.116

RFX is 1.5%. Expected returns are: Buy and Hold: E(R) = 2.515%, or (1.01 × 1.015)-1 Yield Curve Rolldown: E(R) = 4.555%, or (1.0301 × 1.015) - 1

请问这里的RFX就是TOTOAL RETUREN吗？不用再拿RFX加上ROLL DOWN或者持有到期的收益了吗？

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发亮_品职助教 · 2025年01月13日

请问这里的RFX就是TOTOAL RETUREN吗？


不是，RFX是外汇波动带来的收益。


这道题因为投资的是海外债券，所以先算了海外债券的收益率。


buy-and-hold的债券投资收益率是：（100-99.009）/99.009 =1.00%


roll down the yield curve strategy的收益是：coupon yield + price appreciation

但因为是拿零息债券做roll down strategy，所以没有coupon收益，只有债券的价差收益。所以roll down strategy的收益是：（99.009-96.1169）/96.1169=3.01%


以上两个都是海外债券的收益率，现在要考虑把他们换成本币，RFX告诉我们，货币升贬值带来的收益率是RFX=+1.50%


则把buy-and-hold的海外收益换回本币后的收益率为：

（1+1.0%）×（1+1.5%）-1 = 2.515%


把roll down strategy的海外收益换回本币收益后的收益率为：

（1+3.01%）×（1+1.5%）-1=4.555%


应用的公式是：

RDC = (1+RFX)×（1+RFC）-1


其中，RDC代表换回本国货币后的总收益率（total return），RFX是代表的是汇率的变动带来的收益率；RFC代表的是海外债券的收益率。


不用再拿RFX加上ROLL DOWN或者持有到期的收益了吗？


这道题用了精确的算法，即RDC = (1+RFX)×（1+RFC）-1。

这是利用乘法法则把海外债券的收益率换成了本币的收益率。


另外一种是近似的算法，就是加法。即海外债券的投资收益率加上汇率的升贬值。这道题因为已经用精确算法转换了汇率，所以就不用加法算近似值了。


近似算法是：RDC ≈ RFX + RFC，即海外债券的收益率+汇率升贬值，最终等于本国货币核算的收益率。


buy-and-hold是：1.0% + 1.5% ≈ 2.5%

roll down strategy是：3.01% + 1.5% ≈ 4.51%


考试的时候，精确算法（乘法）和近似算法（加法）都可以，不过可以优先考虑精确算法。

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