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sliang · 2024年10月27日

fixed income

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ202112010200000104

问题如下：

In her market research, the manager learns that ASX 3-year and 10-year Treasury bond futures are the most liquid products for investors trading and hedging medium- to long-term Australian dollar (AUD) interest rates.

Although neither contract matches the exact characteristics of the cash bonds of her choice, which of the following additions to a barbell portfolio best positions her to gain under a bull flattening scenario?

选项：

A.

Purchase a 3-year Treasury bond future matching the money duration of the short-term (2-year) position.

B.

Sell a 3-year Treasury bond future matching the money duration of the short-term bond position.

C.

Purchase a 10-year Treasury bond future matching the money duration of the long-term bond position.

解释：

C is correct.

A bull flattening is a decrease in the yield spread between long and short-term maturities driven by lower long-term yields-to-maturity.

Both A and B involve changes in portfolio exposure to short-term rates, while C increases the portfolio exposure to long-term rates to benefit from a fall in long-term yields-to-maturity.



  1. 3个答案的后半段都写有“matching the money duration of。。。”，请问是什么意思呢？不明白为什么答案要加上后半段
  2. 这题可以long LT future，也可以short short term future。那为什B不对呢？


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发亮_品职助教 · 2024年10月28日

matching the money duration of..就是具体告诉新增的我们头寸是多大，便于我们分析。

原来的barbell portfolio是：

  • Barbell: Invest equally in 2-year and 9-year government bonds

即，50%的2-year, 50%的9-year

现在预测利率曲线发生bull flattening，于是要在barbell portfolio的基础上，再额外加上一个头寸，这个头寸就分别是A,B,C三个选项的情况。

题目说：additions to a barbell portfolio best positions...注意看，题目问的是additions to a barbell portfolio，即，在barbell的基础上加上一个头寸。

这样的话，【新头寸 + barbell】，就会形成一个新的组合。

现在说matching the money duration of...其实是在告诉我们加入的新头寸具体是多少。这样我们就能明白最终的组合是个啥样的组合。否则，如果加入的新头寸的money duration很小，那实际没有啥影响，最终影响还是最初的barbell portfolio，这种改变就没有意义。

像选项A说的，买入3-year t-bond futures，并且其money duration等于原barbell中2-year的Money duration：

Purchase a 3-year Treasury bond future matching the money duration of the short-term (2-year) position.

这说明，新头寸+原barbell，最终形成的是：

1/3 money duration在2-year，1/3 money duration在3-year，1/3 money duration在9-year。

由于2-year和3-year都是短期，这说明和原barbell相比，加入新头寸之后，组合有更多的权重在短期上。在发生bull flattening时，其实收益不高。

因为Bull flattening是长期利率下降幅度更大，更盈利的策略应该是给长期多增加一些duration。

选项B：

Sell a 3-year Treasury bond future matching the money duration of the short-term bond position.

选项B的话，sell 3-year t-bond futures，同时其money duration和原barbell里面的short-term bond position一致。

已知原barbell是long 2-year，现在是short 3-year t-bond futures，且两者money duration一致，则相当于最终short-term的money duration=0【2-year和3-year很近，近似定性分析】，而长期9-year的money duration没有改变。

在发生bull flattening时，长期、短期利率都下降（这是bull告诉我们的）

而长期利率下降幅度更多，短期利率下降相对少一点（这是flattening告诉我们的）（看相对改变的话，flattening就是长期相对下降，短期相对上升，在整体下降bull时，只是因为短期下降的幅度更少，长期下降的幅度更多，于是和长期相比，短期是相对上升的）

对于这种bull flattening，选项B的调整并没有额外增加多少收益。反而因为让short-term的duration变成了0，没有享受到短期利率下降带来的价格上升收益。

选项C的话：

Purchase a 10-year Treasury bond future matching the money duration of the long-term bond position.

买入10-year t-bond futures，且其money duration等于原barbell的长期money duration。

这说明选项C是直接增加了长期债券的money duration。在发生bull flattening时，可以直接获得长期债券价格上升的收益。

不考虑long-short策略，对于这种bull flattening，已知整体上利率是下降的，只不过长期利率下降幅度更多。

如果只是long策略，可以long short-term，可以long长期。

如果是long-short策略，必须要同时long一个期限，short一个期限。这时候就必须要看长短期利率之间的相对变化的。由于flattening是短期利率相对上升，长期利率相对下降（因为在bull flattening时，整体利率下降，但短期下降更少，和长期比，相对就是上升）。

于是，盈利的long-short策略必须是：long长期，short短期。

本题没有说是Long-short策略，在Bull flattening时，可以long短期也可以long长期。

这道题不是long-short策略，像A、C选项就是额外增加了long头寸。B选项是增加了short头寸。

选项B的问题是，增加了short头寸之后，短期没有盈利，而长期没变，没有额外盈利。

相比选项C是直接增加了长期头寸，原本的短期有盈利，长期增加duration后，盈利还更大。所以最优是C。

发亮_品职助教 · 2024年10月29日

不用客气！

气体密度计 · 2024年10月27日

因为是bull flattening，所以利率曲线下行，且长端下降幅度大于短端。所以这时候应该long而不是short。在bear 的时候利率上行才要short。所以B不对

气体密度计 · 2024年10月27日

money duration是组合的dollar amount对利率变化的敏感度，也就是当利率变化1bp的时候，组合变化了多少钱。因为题目给出用两个bond对冲AUD的利率波动引起的变化，所以要match money duration才能保证在利率变化的时候，组合变化的钱数和要对冲的AUD变化的钱数相等。比如利率变化1bp，要对冲的AUD上涨2块钱，那对冲的组合也要上涨2块钱。 因为题目里给出是bull flattening，也就是yield curve整体下行，而且长端下降幅度大于短端下降幅度。这时候long long term bond的获利最多。

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