Friday, May 5, 2017

The Relationship Between Changes in Interest Rates and the Return on the S&P 500

The Relationship Between Changes in Interest Rates and the Return on the S&P 500

Question:  Is there a stable relationship between daily changes in the 10-year interest rate on U.S. government bonds and the daily return on the S&P 500?   How has the relationship between this interest rate and S&P 500 changed over time?  Discuss the implications of this research for the current investment environment.  

Data:  information on the 10-year government bond was found at yahoo finance.  
Quote for TNX:

The daily data for the 10-year bond rate went back to 1962.

I had to purchase the S&P data from MACROTRENDS



Methodology:   I studied the relationship between two variables – the dependent variable  Log(PSP500/LAG(SP500) and the independent variable Log(r10/lag(r10).   The dependent variable is a measure of the daily return on the S&0 500.   The independent variable is a measure of the daily change in the yield on the 10-year bond rate.

It is important to note that regression coefficients do not imply causality. Causation could run from the stock market to the bond market or from the bond market to the stock market.   Moreover, it is likely that many factors not considered here – supply shocks, Fed policy, the labor market, and inflationary expectations –  impact both variables and  the relationship between the bond market and the stock market.   

Results:  A separate regression was estimated for every year from 1962 to 2017.
The 56 estimated coefficients (one for each year) on the interest rate coefficient in the S&P 500 equation are presented below.



Estimated Impact of Change in Interest Rates
 on Return In S&P 500
Year
Estimated Coefficient
p-value
1962
0.194
0.213
1963
0.173
0.242
1964
0.155
0.243
1965
0.044
0.778
1966
0.025
0.736
1967
-0.149
0.006
1968
-0.191
0.010
1969
-0.331
0.000
1970
-0.423
0.000
1971
-0.147
0.010
1972
-0.205
0.077
1973
-0.108
0.502
1974
-0.736
0.004
1975
-0.342
0.001
1976
-0.195
0.070
1977
-0.258
0.001
1978
-0.876
0.000
1979
-0.300
0.000
1980
-0.154
0.001
1981
-0.194
0.001
1982
-0.514
0.000
1983
-0.552
0.000
1984
-0.446
0.000
1985
-0.160
0.003
1986
-0.351
0.000
1987
-0.602
0.000
1988
-0.712
0.000
1989
-0.349
0.000
1990
-0.543
0.000
1991
-0.495
0.000
1992
-0.126
0.000
1993
-0.181
0.000
1994
-0.403
0.000
1995
-0.270
0.000
1996
-0.431
0.000
1997
-0.475
0.000
1998
0.237
0.001
1999
-0.251
0.002
2000
0.158
0.187
2001
0.189
0.004
2002
0.543
0.000
2003
0.157
0.000
2004
0.013
0.706
2005
0.001
0.980
2006
0.065
0.218
2007
0.401
0.000
2008
0.339
0.000
2009
0.123
0.002
2010
0.257
0.000
2011
0.313
0.000
2012
0.189
0.000
2013
0.032
0.172
2014
0.214
0.000
2015
0.108
0.000
2016
0.121
0.000
2017
0.106
0.001


Observations on the Coefficient for the Interest Rate Variable:

During the 1962 to 1966 time period, the estimated coefficient of the interest rate variable was positive but insignificantly different from 0.

With the exception of one year (1998) the estimated coefficient was negative every year from the 1967 to 1999 time period.  The coefficients were often significantly different from 0.

Since 2000 the estimated impact of a change of interest rate on the S&P 500 has been positive.   The relationship was significant for most but not all years.


Discussion of a potential relationship between 10-year government bond rate and the S&P 500:

The relationship between changes in the daily 10-year interest rate and the S&P 500 seems to vary with macroeconomic conditions.   The impact of interest rates on the S&P 500 return appears positive in periods when inflationary expectations are low and negative when inflationary expectations are high. 

The tightening by the Federal Reserve Board in 1982 appears to correspond to a sharper negative relationship between the 10-year interest rate and the S&P 500.

The looser monetary policy since 2000 appears to correspond to a positive relationship between the 10-year interest rate and the S&P 500.

Potential Financial Implications:  

A positive relationship between interest rates and the S&P 500 has prevailed since 2000.  Aa a result, Investors with a mix of both bonds and stocks withstood the collapse of equities after 2007. 

 Currently, equities are back at their historic highs.   Some analysts argue that the positive relationship between interest rates and the stock market means diversification into government bonds could offset potential losses from a collapse in equities in 2017 or 2018.

I am skeptical that diversification into bonds provides investors with much financial protection    in the current financial environment.   The yield on the 10-year bond is currently around 2.3 percent.   The average 10-year yield in 2007 was around 4.6 percent so there was some room for interest rates to fall and bond prices to rise.

Interest rates are unlikely to fall much from their current levels even if the economy substantially weakened because they are already low.   Also, the relationship between interest rates and the stock market could turn negative.