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石欣灵 · 2020年09月27日

老师,麻烦讲解一下这道题的思路,答案贴不下,评论接着贴

Ivankiv offers another recommendation: “Our analysts believe both Australian and British long-term yields will decline more than long-term German yields over the coming year, with Australian long-term yields falling the most by a wide margin. The British yield curve is more steeply sloped than the Australian. Rather than remain invested in bunds, Kuaminika could invest in either British gilts or Australian government bonds and hedge the currency risk back to the euro with a rolling three-month foreign currency forward. There are, however, some issues to keep in mind:

  • Issue 1: The British gilt market is likely better for investment because its steeper yield curve provides larger benefits from ‘riding the curve.’
  • Issue 2: In order to properly account for the cost/benefit of eliminating currency exposure, hedge gains or losses should be measured relative to forward foreign exchange rates.
  • Issue 3: The rolling hedge will generate a profit (loss) if the spread between the short-term German yield and the short-term Australian or British yield increases (decreases) over time.”

Q. If all long-term rates fall as expected, which of Ivankiv’s issues regarding investment in the British gilt or Australian Treasury markets is least likely correct in the context of an inter-market trade?

  1. Issue 1
  2. Issue 2
  3. Issue 3


A is correct. Ivankiv is wrong regarding Issue 1. There is a stronger benefit from a larger relative decline in yields in the Australian market than the benefit from the steeper yield curve in the British market. Hedge gains and losses should be measured relative to forward rates, not anticipated spot rates. The rolling hedge is similar to borrowing short term in the Australian or British market and lending short term in the German market.

石欣灵 · 2020年09月27日

If the spread between short-term German and short-term Australian or British rates increases, earnings from lending will increase relative to costs from borrowing.

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发亮_品职助教 · 2020年09月28日

嗨,努力学习的PZer你好:


这道题的质量比较好,算比较难的题目了。每一个小问都可以对标到讲义的原句。


先看Issue 1:

The British gilt market is likely better for investment because its steeper yield curve provides larger benefits from ‘riding the curve.’

他说英国国债是更好的投资标的,因为收益率曲线更加陡峭,会收益率Riding the yield curve。这点错误。我们可以从两个角度来理解:

角度1:Riding the yield curve策略的大前提是Stable yield curve,也就是预期收益率曲线要保持不变。本题由于预期UK和Aus的长期利率都会下降,因此不是Stable yield curve,所以不可能做Riding the yield curve成功。因此Issue 1错误。

角度2:可以从影响Inter-market收益的因素分析。我们说,影响Inter-market收益最最最最决定性的因素是,两国利率之间的相对变化(Spread的变化),利率的变动对投资国外债券的影响远远大于Riding the yield curve和Carry trade带来的那点收益。

参考讲义合集P256下句:

Any significant spread changes will dominate the carry and riding the curve components of relative return and hence dominate the choice of markets.

即:Spread changes dominate the choice of markets。

本题中,由于预期Australian long-term yield会大幅下降,那我们直接买Aus长期债券即可,准备收获大幅的Capital gain。所以Issue 1的表述错误。


Issue 2的表述,完全就是讲义的原句,其实不用看本题的题干就能判断出来。参考讲义合集P263下局:

••Given a choice of assets, currency exposure decisions should be based on projected appreciation or depreciation relative to forward FX rates rather than on the basis of projected spot FX appreciation/depreciation alone.

也就是说,是否要Hedge,我们应该比较: projected appreciation or depreciation  VS forward FX rates

是否要Hedge,我们应该比较:预期的未来汇率升贬值与Forward带来的换汇收益,哪个方式带来的收益大,我们就选哪个方式,如果projected appreciation更大,我们就选择不Hedge,如果forward FX带来的收益更大,我们就选择Hedge;我们其实是以projected appreciation为标杆来判断是否利用Forawrd来Hedge:

所以Hedge benefits可以看成 = Hedged收益 -  projected appreciation or depreciation

所以Issue 2的表述:In order to properly account for the cost/benefit of eliminating currency exposure, hedge gains or losses should be measured relative to forward foreign exchange rates.

这个也没问题,他说比较Hedged gains or loss with forward foreign exchange,用Hedged return和预期未来的Exchange rate比较。

Issue 2这里写的forward foreign exchange其实是想表述预期的未来汇率变化(projected appreciation or depreciation),并非是Forward合约里面约定的汇率,所以这里的表述稍微有点问题,这道题可能这块有点瑕疵,但不影响本题对应的知识点理解。

比较是否Hedge,Hedge的好处时,一定是比较Hedged return和预期的汇率升贬值;而不是比较即期Spot exchange rate。 



Issue 3: The rolling hedge will generate a profit (loss) if the spread between the short-term German yield and the short-term Australian or British yield increases (decreases) over time.

Issue 3的表述也完全没有问题。

用Forward hedge汇率风险,如果合约是3个月合约,实际上相当于获得的是两国3个月利率之间的差。可以参考讲义P262原句:

•Rolling hedge will generate a profit (loss) if the spread between the three-month base currency rate and the three-month foreign currency rate increases (decreases) over time. Thus, the currency hedge introduces a bet on the spread at the short end of the curves.

也就是说,我们用Forward hedge带来的收益实际上是两国3个月的利息差。

这点可以用Forward收益来推导(基础班视频里面有推导),假设是3个月合约,Forward hedge带来的收益为(F代表Forward约定的汇率、S代表即期汇率,假设是把GBP Hedge成德国EUR):

(F - S) / S ≈   3个月EUR的利率 - 3个月GBP利率

所以Hedge的收益,完全是两国3个月利率的Spread,Hedge的目标货币在减号前面。

像本题,因为是都Hedge成德国EUR,所以Hedge的收益是:EUR - GBP or EUR - AUS

那可以看出来,德国3个月利率利率与AUS(GBP)3个月利率的Spread变大时,那Hedge带来的收益一定是变大的。相反,Spread变小时,Hedged的收益是变小的,因此Issue 3正确。


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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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