Graham Capital:股票和债券的相关性——一个历史视角

Author：Jack Fan, Marci Mitchell

Time：2017-09

Abstract

The equity-bond correlation has been negative since the early2000s. A certain conventional wisdom has developed that this negativecorrelation is natural and enduring. However, when we take a much longerhistorical perspective and examine data going back to 1870s, we find that theequity-bond correlation is highly dynamic and has gone through prolongedperiods of positive correlation. As such, we should not dogmatically assumethat the equity-bond correlation will be negative going forward, especially inthe context of asset allocation and portfolio management.

Martin's Understanding:自2000年以来股票和债券的价格关系就呈现出负相关性。一种通常的观点认为这种负相关性不仅合理，还是长期持续的现象。然而，当我们从更长的历史周期去看待这个观点，我们会发现这种观点是站不住脚的。因此，我们不应该先入为主地认为这种负相关性是必然的，尤其是在资产的配置和组合管理上。

（注：Understanding不是翻译，而是本文编辑对原文的理解）

Keywords

Correlation; Stocks; Bonds; Beta

1.Introduction

Equity-bond correlation is immensely important for a multitudeof portfolio management tasks ranging from asset allocation to risk management.Despite a developing conventional wisdom over recent years that equity and bondprices are negatively correlated, the reality is far more dynamic. 

Over timeand across a variety of monetary policy regimes, equity-bond correlation isactually more likely to be positive than negative. Since the 1870s, equity-bondfive-year correlation has been negative in 635 months compared to 1,063 monthswhen it was positive. The modern regime of negative correlation really beganaround the late 90s. Since 2015, it has been slowly moving back towards zero.As a result, we should be wary of making hard assumptions about the magnitudeor direction of future equity-bond correlation

Martin's Understanding:尽管近些年人们逐渐认为股债之间确实是一种负相关关系，但从客观事实来看，这种关系要复杂得多。以过往的时间以及不断变化的货币政策机制来看，股债呈现正相关性的时间比呈现负相关性要长。从1870年以来，共有635个月出现负相关性，1063个月出现正相关性。当前关于股债的负相关性观点来源于上世纪90年代，但2015年-2017年，两者的协方差逐渐靠近0。因此，我们需要对这种先入为主的观点保持谨慎。

2. Economic Background

There is no generally accepted model for equity-bond correlationdespite the rich volume of literature on this topic in macroeconomics.Significantly, academic research has yet to even reach agreement on whetherbond and equity prices should move together or in opposite directions. 

For example, Shiller andBeltratti (1992) managed to find theoretical motivation forboth positive and negative correlations based on a discounted dividendsview of equities. Equity valuation is linked to bonds through the discountfactor. In the most basic configuration, equities should have positivecorrelation to interest rates. However, this is not observed (Leibowitz andKogelman, 1993). 

Baele (2010) tried to decompose thetime-series of the equity-bond correlation onto a set of macroeconomic factors.Interestingly, they found that fundamental factors such as inflation and outputgap do not generate the kind of time-variability that is observed in therealized equity-bond correlation. They did find, however, that additionalfactors, such as liquidity proxies, play an important role in mediating therelationship between equities and bonds. Taken together, these results suggestthat the equity-bond correlation is not the strict result of monetary policyregimes, but responsive to a wider set of market sentiments. 

Equity-bondcorrelation can be volatile, time varying, and not easily explained by anygiven set of fundamental factors. There is no exact set of known factors thatcan explain it or provide a basis for forecasting.

Martin's Understanding：在学术领域，股债之间的关系并没有出现一种被普遍接受的观点。比如，Shiller andBeltratti（1992）认为，要论证这种关系就需要基于股票的红利贴现过程，股票的估值通过贴现因子影响债券，在大多数情况下，股票的红利应该与利率呈正相关。Baele (2010)通过宏观因子划分不同时期的股债关系。无论如何，这些学术观点认为，股债关系并不纯粹是货币政策机制的结果，而是对市场的反应。总的来说，股债之间的关系并不那么单一，而是动态性的，复杂的。

3. A Historical Perspective

For our analysis, we use Shiller’s monthly data set1 for equityreturns and long term bond yields (see Figure 1 for S&P 500 levels and longyields since 1872). This data set is particularly remarkable for its longevity,stretching across multiple monetary policy regimes all back to the 1870s. Whilethe period that predates the Federal Reserve System may not be as relevant, wehope to use it as additional context for considering what equity-bondcorrelation may look like under a system completely different from the currentone.

Figure 1. S&P500 leveland long yields dating back to 1872.

Figure 1. S&P500 leveland long yields dating back to 1872.

We approximate the returns of a ten-year treasury bond from thebond yields. Treasury total returns is comprised of two components: pricechange and carry. The monthly price change we derive by multiplying change inyield level for that month by a hypothetical fixed duration of nine years. Forthe carry part, we use the prorated par yield of the previous month. Our approximation is not perfect as it ignores curve roll down at the very least.However, in our experience it is a reasonable method of estimating totalreturns for treasury bonds. 

We then compute the rolling one-year and five-yearcorrelations between equity and bond returns over this very long historicalperiod. The results are plotted in Figure 2. The averages of both one-year andfive-year correlations between equity and bonds are very close to zero (3% and7% respectively) over their entire history. However, equity-bond correlationcycles through periods of significant positives and negatives. This underlinesour view that we should not think of their nature as static, but rather as adynamic process that evolves over time. 

Equity-bond correlation appears to bevery volatile prior to the modern monetary policy system anchored by theFederal Reserve, fluctuating between positive and negative. There was a sharpdrop in correlation leading up to the Recession of 1913, which, perhaps as aresult of the Federal Reserve Act, seems to abruptly and rapidly reverse tobecome positive. 

Two major subsequent events seem to presage the relativestable periods in equity-bond correlation: in 1951 when the Federal ReserveSystem asserted its independence from the Treasury Department and when the U.S.dollar broke from the gold standard twenty years later. 

There does not seem tobe a stable relationship between recessions and correlation. The sign ofcorrelation between equity and bond changed twice over the course of the GreatDepression. Five-year correlations were positive in six out of the last tenrecessions as defined by NBER2 . The same is true if we look at one-yearcorrelations as well. 

During the initial periods of growth and inflationthrough the 1980s, correlation between equities and bonds was positive (over a5- year rolling window), peaking in 1997, but remaining positive until theearly 2000s. From then on, correlation turned negative. Campbell et al. (2014)suggests that this is a result of transition from being focused on bond risk inthe 1980s to output fluctuation and the persistence of monetary policy shocks.

The length and magnitude of the current negative correlation regime thatstarted in the 2000s has been unprecedented. June 2012 registered the lowestone-year correlation at -91% and March 2015 registered the lowest five-yearcorrelation at -68%. The highest one-year is 88% in September 1983 and 56% inDecember 1986 for five-year correlation. 

Since 2015, equity-bond correlationshave been rapidly rising. We could attempt to ascribe this to fundamentalfactors such as increases in inflation expectation and/or expectations for atighter monetary policy. However, we caution restraint in interpretation butnote that one should not be surprised if equity-bond correlation breaks intopositive territory for a sustained period of time

Martin's Understanding：作者通过使用Shiller的股票收益率和债券收益率的月度数据，假设了债券收益率约等于国债收益率。而国债的收益率可分为两个部分：价格变动和利息收入。通过作者计算，可以大致说明这种假设是成立的。同时，作者也计算了1871年以来，股票和债券价格在一年以及五年的滚动收益率的相关性。在整个时间序列里，股票和债券一年以及五年的滚动收益率的相关性接近0（事实上是3-7%的正相关）。然而，两者也出现了一些时期的明显正相关与明显负相关性。有两件事对此影响很大，分别是1951年美联储脱离美国财政部，以及1973年的布雷顿体系瓦解。此外，经济衰退与两者的相关性似乎并无直接的结论。从图中可以观察，股债的负相关在2000年以后变得更明显，特别是在2012年的6月以及2015年的3 月，两者的负相关性高达-91%以及-68%。2015年以后，股债之间的负相关性在上升，然而我们仍需要以谨慎的态度去应对这种复杂的，动态的过程。

4. Conclusions

Equity-bond correlation is not a static number. It can be bothpositive and negative. The observed correlation is the result of rich anddynamic interaction between a multitude of macroeconomic factors. There is noeconomic theory or empirical model that fully captures this dynamism. 

Our longhistorical analysis of equity-bond correlations going back over 140 years showsthat equity-bond correlation has gone through many regimes. The most recentperiod of negative correlations began in the ‘90s. Prior to that, equity-bondcorrelation was positive for over 40 years. 

As the current period of negativecorrelation seems to be closing in towards zero, we should not be constrainedby any preconceived notion about what this correlation ought to be. As historycan readily demonstrate, equity-bond correlation can be positive for quite sometime.

Martin's Understanding：股债的相关性关系并不是一个可以很容易就能解决的问题，从1870-2017年的数据表明，两者的关系经历了各种社会形态，制度的变化，但却不能呈现出一个确定的规律和结论。然而，当前一年期的股债相关性在逐渐靠近0，根据过往的历史波动，也许未来一段时间股债的相关性会慢慢重回正相关的关系。

References

L. Baele. The determinants of stock and bond return comovements.Review of Financial Studies, 23(6):2374–2428, June 2010.

J. Y. Campbell, C. Pflueger, and L. M. Viceira. Monetary policydrivers of bond and equity risks. NBER Working Papers 20070, National Bureau ofEconomic Research, Inc, Apr 2014. 

M.Leibowitz and S. Kogelman. Resolving the equity durationparadox. Financial Analysts Journal, 49(1):51–64, 1993. 

R. Shiller. IrrationalExuberance. Broadway Books. Currency/Doubleday, 2005.

R. Shiller and A. E. Beltratti. Stock prices and bond yields:Can their comovements be explained in terms of present value models? Journal ofMonetary Economics, 30(1):25–46, 1992.