今年国债收益率「国债收益率多少」

译者 王为

BY ploutos from seekingalpha.com

Summary

要点

An AArated Austrian century bond has returned 65% in 2019, better than 99% of the S&P 500 components.

评级为 AA 的奥地利百年国债2019年以来的回报率达到65%，高于99%的标准普尔500指数成分股的股价升幅；

This article uses the tremendous performance of this bond to discuss the concepts of duration and convexity.

本文将借该国债的惊人回报表现来谈谈债券的久期和凸性这两个概念；

Rate duration and positive convexity can be important contributors to portfolios in times of market uncertainty.

在市场动荡时期，债券利率的久期和正凸性可成为投资组合收益的重要来源。

One of the most interesting stories in capital markets in 2019 is the performance of a government bond from Austria. With a population of 8.7 million people, Austria would be the 12th largest U.S. state, nestled between New Jersey and Virginia population-wise. Why is the performance of a government bond from that sovereign so important to global capital markets?

在2019年的资本市场上最有意思的一件事就是奥地利百年国债的回报表现。奥地利有870万人口，如果奥地利是美国的一个州的话，其人口将排名第十二，位于新泽西州和维吉尼亚州之间。为什么对全球资本市场来说这样一个国家的这样一只国债的回报表现会如此重要？

On September 12th, 2017, the Austrian government issued a century bond with a 2.1% coupon maturing in 2117. Some bond market participants hailed it as a great victory for the Austrian government. They locked in what was viewed as low cost funding for the next 100 years. For context, at the time of the issuance it had been just 103 years since the assassination of Archduke Franz Ferdinand of Austria-Hungary had spurred the outbreak of World War I. A century is a long time in the history of a country, and the Treasury of Austria was believed to be appropriately forward thinking.

2017年9月12日，奥地利政府发行了一只将于2117年到期的票息为2.1%的世纪国债，当时一些市场人士欢呼这是奥地利政府的一个巨大的成功，因为可以将未来一百年的政府借债成本锁定在低利率。需要指出的是，2017年正是奥匈帝国大公弗朗茨·斐迪南遇刺引爆第一次世界大战103年后。从一个国家的历史角度来看一个世纪是很长的时间，当时奥地利财政部被认为是相当的深谋远虑。

In 2019, the issuance of that century debt is already looking like an expensive mistake. On August 7th, 2019 - less than two years after the bond was issued - the bond was trading at 191% of par. The bond was priced at 116.5% of par to start the year. At 191% of par, it has had unrealized capital appreciation of 64%. Add in the just over 1% coupon return through the point in the year, and the bond had returned a whopping 65%. The Austrian government could lock in a century of financing for less than half the cost today.

到了2019年，这只百年国债的发行看上去已经像是个代价不菲的失误。在发行不到两年后的2019年8月7日，这只债券的市场价为面值的 191% ，而今年年初的市场价为面值的116.5%，今年以来该券未实现的资本增值率为64%（即 191% / 116.5%-1=63.95%），再加上该券今年截至到目前为止的票息收益刚刚大于1%（该券票息为2.1%，2019年年初至8月7日已经过半，大概为0.6年，因此该券今年的票息收益应=2.1%*0.6=1.26%），因此该券年初至今的总回报高达65%（即63.95% 1.26%=65.21%）。如果是按照现在的利率水平发行同样期限的国债，奥地利政府锁定未来一百年政府借债的成本将不到两年前的一半。

Bond prices move inversely to interest rates. As yields on European sovereign bonds have fallen, the Austrian bond has moved higher in value. This particular bond is one of the longest duration instruments in financial markets. Below is its exponential-looking price graph over the past two years.

债券价格与利率的涨跌方向相反。当欧洲国家的国债收益率出现下跌，奥地利国债的价格将上涨。这支特殊的债券是金融市场上久期最长的投资工具之一，以下是其在过去两年间呈指数上涨的价格走势图。

Source: Bloomberg

图表来源：彭博资讯

Duration has a dual meaning in finance. It is both the weighted average timing of the bonds"s cash flows - the periods at which bonds pay their promised principal and interest - and also a measure of interest rate sensitivity. The very low coupon on the Austrian bond, and its very long-dated, one-hundred year maturity mean that the bond has a very long duration. Ultimately, investors will receive 310 euros (2.1% * 100 years of coupon and their 100 euros back in 100-years). They will not get half of that 310 euros of compensation until 2090. Duration is the weighted average timing of cash flows, and those cash flows are very back end weighted with a low coupon, ultra long bond.

在金融学上久期有两个含义，一是对一只债券各期现金流的产生时间进行加权平均后的结果，即该债券偿还全部本息所需要的时间；二是用于衡量利率的敏感性。低票息以及长达百年的存续期间意味着这只奥地利国债的久期极长。投资者最终将收到310欧元(每年2.1%的票息 * 100年 100年后到期时收到的100欧元本金)，但在2090年之前投资者收回的资金还不到310欧元的50%（2090年-2019年=71年*每年2.1%的票息 =149.1欧元，而310欧元*50%=155欧元），低票息、超长期债券的现金流具有越临近到期日久期权重越大的特点。

At issuance, the Austrian century bond had a duration of 42 years. For a 100bp move higher (lower) in interest rates, the bond would move lower (higher) by 42% as a function of the duration. As the market yield of the security has moved lower - the yield is now 0.79% versus 2.1% at issuance - the duration has extended to 57 years.

在刚发行的时候，这只奥地利国债的久期为42年，如果收益率上升100个基点，作为久期函数的债券价格将下行42%。随着该券的二级市场收益率下跌，如今为0.79%，而刚发行时为2.1%，该券的久期已经增加到57年。

The change in duration as the market yield changes is a function of the bond"s convexity. Convexity is a function of the non-linear nature of the relationship between yield and a bond"s price. If you remember your high school calculus, you can think of duration as the first derivative of the price/yield function, and convexity as the second derivative. Too confusing? A bond with positive convexitywill have more upside for a given move in interest rates than downside. Mortgage-backed securities tend to have negative convexity when they trade at premiums to par. That is because the underlying home borrowers are more likely to prepay the mortgage (e.g. refinance) as interest rates fall. Negatively convex bonds have more downside than upside. The Austrian century bond has no prepay option, and very positive convexity to complement its very long duration.

久期是会发生变化的，因为市场收益率会随着债券凸性的变化而波动，而凸性是债券收益率和债券价格之间所固有的非线性关系的产物。还记得初中学的微积分吗，可以将债券的久期看成债券价格和债券收益率之间函数关系的一阶导数，而凸性则是二阶导数。听上去很复杂吧？如果一只债券的凸性为正的，当利率波动幅度是固定的情况下，对债券价格的涨跌进行对比可见，该券价格的升幅将超过降幅，也就是易涨不易跌。当一只按揭抵押债券的交易价格超过面值时，其凸性往往是负的，这是因为该按揭抵押债券背后的房屋买主即按揭贷款的贷款人在利率水平下行的市场行情中更有可能提前偿还贷款。负凸性的债券易涨不易跌，也就是在债券收益率涨跌幅度一致的情况下，债券价格的降幅比升幅要大。奥地利百年国债没有提前偿还的条款，该券非常长的久期会导致该券的正凸性非常高。

The Austrian government bond is one of the longest and most positively convex financial instruments, and it has done phenomenally well as rates have rallied. Only 1% of S&P 500 constituents - Chipotle (CMG), Advanced Micro Devices (AMD), MarketAxess (MKTX), Ball (BLL), and Tyson (TSN) - have returned more than the 65% performance from this Austrian century bond in 2019.

奥地利百年国债是久期最长、凸性最高的金融工具之一，在利率水平下行的情况下其价格的涨幅将极其可观。在标准普尔500指数的成分股当中，2019年只有1%公司的股价涨幅超过这只奥地利百年国债65%的综合回报率。

I was certainly not banging the table to buy a 98-year government bond with a 2.1% coupon at 116% of par at the beginning of the year, and am not extolling the value of this security now. I am trying to highlight how bond duration and convexity works. Closer to home, the iShares 20Year Treasury Bond ETF (TLT) has a year-to-date total return of 19.4%, newly surpassing the 16.3% total return of the S&P 500.

我完全没有强烈推荐各位去买一只98年后才到期、票息为2.1%、2019年年初价为面值116.5%的债券的意思，也不是夸赞该券眼前的高价，我的目的是强调一下债券的久期和凸性是如何发挥作用的。话说回来，安硕20年以上期限美国国债交易所交易基金TLT2019年年初至今的累计回报率为19.4%，最近刚刚超过标准普尔500指数年初至今16.3%的累计回报率。

Source: Bloomberg

As the yields on government bonds falls, durations extend. This increase in interest rate sensitivity can work for and against investors dependent on their interest rate call and positioning. While the 30-year Treasury is approaching all-time low yields, its coupon is still higher than what the coupon on the Austrian century bond was two years ago. At a 2.15% yield, the 30-year Treasury has 64.5 points of upside if it were to equal the zero yield on German 30-year government bonds. (At a zero yield, the current price of a par coupon 30-year bond would be equal to all its future cash flows - 2.15*30 100). This article is not to argue whether the zero interest rates plaguing the rest of the developed world are likely to find their way to the shores of the United States, but it is meant to illustrate that returns can be found in surprising places when long duration, positively convex investments experience an interest rate rally. Given the traditional negative correlation between flight-to-quality Treasury bonds and riskier assets, these securities can provide important portfolio construction options in an uncertain market environment, which is partly why we have seen long government bonds bid up in value recently.

如果国债的收益率出现下行，其久期将增加，至于利率敏感性的提升带来的是利还是弊要看投资者的立场和仓位情况。虽然30年期美国国债的收益率正在创下历史新低，其票息仍高于奥地利百年国债两年前发生时的水平。以当前2.15%的收益率水平来计算，如果30年期美国国债的收益率跌至同期限德国国债收益率当前0%的水平，30年期美国国债的价格将还有64.5%的上涨空间。（如果债券的收益率为0%，票息为2.15%的30年期新发债券当前的价值=该券未来30年全部现金流，即100 2.15*30=164.50）。本文讨论的不是困扰其他发达国家的零利率是否会波及到美国，而是告诉各位，在长久期、正凸性的债券遇到收益率下行时，高回报可能会出其不意地冒出来。考虑到作为避险资产的美国国债和高风险的资产之间传统上一直存在的负相关关系，此类债券可成为不确定的市场环境中构筑投资组合的重要选项，这就是为什么近期各国长期限国债的价格在市场追捧下走高的原因之一了。