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梦梦0708 · 2021年06月09日

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NO.PZ2019103001000038

问题如下:

Amy McLaughlin is a fixed-income portfolio manager at UK-based Delphi Investments. One year ago, given her expectations of a stable yield curve over the coming 12 months and noting that the yield curve was upward sloping, McLaughlin elected to position her portfolio solely in 20-year US Treasury bonds with a coupon rate of 4% and a price of 101.7593, with the expectation of selling the bonds in one year at a price of 109.0629. McLaughlin expected the US dollar to depreciate relative to the British pound by 1.50% during the year. McLaughlin chose the 20-year Treasury bonds because they were on the steepest part of the yield curve.

At the start of last year, the expected return on the portfolio strategy implemented by McLaughlin was closest to:

选项:

A.

9.61%.

B.

9.68%.

C.

12.61%.

解释:

A is correct.

The expected return on the strategy (riding the curve) is calculated as follows.

E(R)≈Yield income + Rolldown return +E(Change in price based on investor's views of yields and yield spreads) - E(Credit losses) + E(Currency gains or losses)

In this case, the E(Change in price based on investor’s views of yields and yield spreads) term is equal to zero because McLaughlin expects the yield curve to remain stable.

是不是说因为stable,所以就没有yield curve shift带来的return;其次,这个steep和stable并不矛盾,只要不shift,但是越倾斜,得到的roll down return就越高?

1 个答案

pzqa015 · 2021年06月10日

嗨,爱思考的PZer你好:


是不是说因为stable,所以就没有yield curve shift带来的return

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是的同学,你说的没错,E(change in price based on investor’s views of yields and yield spreads)是预期收益率曲线发生变化带来的持有债券收益的变化,也就是△P/P=-MD*△y,如果yield stable,那么△y=0,所以该部分expected return→△P/P=0。


其次,这个steep和stable并不矛盾,只要不shift,但是越倾斜,得到的roll down return就越高?

--------------


你说的没错,steep与stable并不矛盾,Steep与stable是对收益率曲线度量的两个维度,stable与flatten对应,stable与shift对应。

Steep说的是某个时点收益率曲线的形状,比如rst=1%, rlt=5%,stable说的是一段时间收益率曲线形状的变化,如果stable,那么一年后那个时点还是rst=1%, rlt=5%,如果shift,可能一年后那个时点,可能变为rst=1%, rlt=3%,但即使shift后,曲线可能仍然是steep的,如果一年后的那个时点,rst=1%, rlt=1%,那么此时收益率曲线的形状不再是steep,而是flattend的。


在收益率曲线形状不变的情况下,收益率曲线越倾斜,得到的roll down return越大。

举例:

假设两条收益率曲线,

第一条:r1=1%, r2=3%分别代表1年期利率与2年期利率。1只2年期0息债,现在的价格是P0=100/(1+3%)2=94.26,假设收益率曲线stable,1年后,这只债券的价格是P1=100/(1+1%)=99。Roll down return=(99-94.26)/94.26=5.03%

第二条:r1=1%, r2=5%,这条收益率曲线笔第一条更steep。那么2年期0息债的价格P0=100/(1+5%)2=90.70,1年后,这只债券的价格是100/(1+1%)=99,roll down return=(99-90.70)/90.70-1=9.15%。


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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