金融危机中相同到期期限的美国国债为何到期收益率不同?

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CeehwueXC   2018-9-24 01:26   17553   7
更新:我们老师并没有对这个case进行分析,我私下邮件问她,她也没有具体回复,只是让我参考同一节课的小组展示。
感谢每一个关注这个问题并提供了帮助的人。




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这是我们在一个hbs case中遇到的问题。
一个对冲基金经理在2008年11月观察到两张同样是2015年8月15日到期的债券收益率不同,一张是1985年8月15日发的票面利率为10.625%,收益率3.61%;另一张2005年8月15日发的票面利率4.25%,到期收益率3.26%。它们的一个基点的美元价值也不同,前者是0.0741,后者是0.0625。
信息如下图

这个收益率差在2008年3月的时候特别明显超出了流动性差异能解释的正常波动范围(见下图Exhibit2),那正是JP摩根收购Bear Stearns的时候。然后这个收益率之差不久后又消失了,直到6月又重新出现,之后这个差值一直扩大.在2008年9月雷曼破产的时候这个收益率差值达到了一个顶峰——10月7日时达到约35个基点。而联邦政府在10月3日出台了问题资产救助计划(Troubled Asset Relief Program).10月8日这个收益率只差又回落到零点附近。同一天联邦政府为AIG提供了378亿美元的贷款。所以这个收益率之差应该是和政府行动有关的,但如何解释呢,有没有办法稍微量化地解释?


但11月收益率差又上升到35个基点了。


由于新发行国债比旧国债流动性强引起的收益率差没有那么大,一般只有35个基点。
我们的问题是,这个利差是怎么来的,是不是由于它们久期不同造成的?但是息票利率高的那个久期小,应该投资者要求的收益率更低才对啊……
还有,怎么量化计算久期不同造成的收益率差?
下图是2008年11月3日的美国国债的收益率曲线
收益率曲线给的只是maturity和yield的关系啊,现在我们研究的是它们为何maturity相同但是yield不同,收益率曲线有什么用吗?还是说,我们根据这个case给的信息构造yield理论即期利率曲线,看它与现实中国债收益率曲线的差距,看看有没有套利机会?
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2#
匿名用户   | 2018-9-24 01:26:16 发帖IP地址来自
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3#
尉然  1级新秀 | 2018-9-24 01:26:17 发帖IP地址来自
Sorry I was at the library so I cannot type Chinese here.
I did some research on this question and would like to share my findings here.
(Update: Sorry I just found out that neither of the two bonds are really on the run at that time, but since one is relatively new and liquid. So maybe this explanation still works.)
This phenomenon is usually called "flight to liquidity". In normal time, both on/off the run treasury bonds can be used for financing in the Repo market rather interchangeably, although on the run bonds have a very little liquidity premium. While during crisis, people will strongly prefer on the run bonds due to the increasing macro uncertainty, which can be shown by the trading volume of these two bonds that day, as@Lenny Zhang has mentioned. Therefore magnify this liquidity premium significantly.

Actually similar phenomenon can also be observed during 1998 Ruble crisis, where the 30-yr T bond on the run premium rises from 4bps to 28bps.
The main reason for "10月8日这个收益率只差又回落到零点附近",I believe, is that the Fed lowered both discount rate and Fed Fund rate by 50bps the following day.
BTW,there are many papers talking about the on/off the run premium. Just google it.
But I still don't get the point of the last figure (The term structure one). Hope someone can shed some light on that.
After your prof talked about this, please do share some thoughts with us.
Many thanks!

Sources:personal.lse.ac.uk/vaya
Historical Changes of the Target Federal Funds and Discount Rates
rmi.nus.edu.sg/_files/e
merage.uci.edu/~jorion/
=====================================================
Updates:
Since@Lenny Zhang mentioned that the indicators of trading liquidity of the two bonds are not available. I tried to get some clues from the Fed's website. After reading the Press Release on Oct 08,2008 which is the date they lowered the interest rates and the testimony of Bernanke on Oct 20,2008 to U.S. House of representatives. I think the money market turmoil is the cause of this spread.
On Oct 20, Bernanke said "The financial turmoil intensified in recent weeks, as investors' confidence in banks and other financial institutions eroded and risk aversion heightened. Conditions in the interbank lending market have worsened, with term funding essentially unavailable. Withdrawals from prime money market mutual funds, which are important suppliers of credit to the commercial paper market, severely disrupted that market; and short-term credit, when available, has become much more costly for virtually all firms. "

Here is my interpretation. From his words we can infer that the money market credit was very tight at that time. Hence the demand for best collateral, namely on the run T-bonds, shot up. The Fed's following actions like TARP, lower rates and increase currency swap lines with foreign central banks ease this demand. That's why the spread went back a bit.

Unfortunately, I still can't explain it quantitatively. Discussions are more than welcomed !!
Sources:
FRB: 2008 Testimony
FRB: Press Release--FOMC statement: Federal Reserve and other central banks announce reductions in policy interest rates--October 8, 2008

Updates 06/12/2013:
@Lenny Zhang There is a field called "Estimated Traded Volume" and it is available for the two bonds. It surprised me that the volume for old bond is always higher than the relatively new one. I'm confused now. What do you think?
4#
CeehwueXC  1级新秀 | 2018-9-24 01:26:18 发帖IP地址来自
先自问自答一下。我现在的思路:
1.在这种金融危机的大环境下(流动性高度紧张,信用危机),美国政府会不会回购国债,或者出台政策,影响利率,进而影响国债收益率?如果市场的预期是美国政府会这么做的话,是不是构成这两个国债的收益率有差别的原因?
2.根据法博齐的《债券市场分析与战略》,定价一支债券时参考的必要收益率反应了
i.相对风险(Comparable Risk)
ii.可选(替代)投资(alternative or substitute investments)
会不会是因为两支国债所承担的其他风险(如再投资风险)不同导致人们对它们要求的收益率不同?例如,票面利率高的那支国债在金融危机下再投资风险更高?
3.是否应该用总收益率而不是到期收益率来考虑这两支债券,总收益率=[未来的现金流总和/债券购买价格]^(1/n)-1 n是付息的期数。
4.债券市场定价时的一价定律在这时失效了。本题中是怎样让一价定律失效了呢?

5.现在我们知道了那个10.625%票面利率的国债的一个基点的美元价值更大,也就是它的价格波动性更小,是否可以由此量化计算出由于波动性不同造成的人们对它们要求的到期收益率的差值?但是不是应该人们更喜欢价格波动性更小的债券,对它要求的收益率更低吗?

参考资料:维基百科中的一价定律zh.wikipedia.org/wiki/%

防范金融危机平息后美元与美国国债市场逆转风险

金融危机冲击下的中国国债利率期限结构分析
5#
tian  4级常客 | 2018-9-24 01:26:19 发帖IP地址来自
贡献我的五毛。我个人感觉应该是repo market出问题了,off the run low liquidity bond在repo market上在钱多的时候,可能repo跟on the run 差几个bps 甚至一样,所以这个按照roll down 两个券的长期价格差也就是这个repo差。但是在08年的时候,市场完全失灵,导致repo market只愿意拿最liquid的bond(也能理解,因为谁都不知道明天借钱的人会不会倒闭,而倒闭之后拿着的没有流动性的券,只怕就算90%discount也不一定会有人买,哪怕是ty),所以导致你拿这个off the run bond去repo,你可能要多花100-200 bps才能借到钱,那么这种情况下,这两个券差20-30bps,也没法arbitrage,因为你赌的其实是最后事情会好的,repo market会重新function,这两个券借钱的价格会converge。
6#
JimShuMayo  4级常客 | 2018-9-24 01:26:20 发帖IP地址来自
on-the-run vs off-the-run. I think mostly liquidity driven.
7#
Eric  3级会员 | 2018-9-24 01:26:21 发帖IP地址来自
同意 @Lenny Zhang@尉然 ,主要应该是flight to liquidity的问题。
另一个可能的原因是high coupon的债券re-invest的风险更大,所以在利率波动大的时候要求高yield来补偿。
8#
沧海  4级常客 | 2018-9-24 01:26:23 发帖IP地址来自
好像是这样的,比如美国政府发行了一张一年期价值100的国债,利息为2%,到期了就可以去兑换102美元,现在你100块买了,收益率就是2%,但是如果你急于用钱,90块买了,那么买家的收益率就是3%,大概是这样,毕竟非专业
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