The Relationship Between S&P 500 Returns, Earnings Growth, P/E

The Relationship Between S&P 500 Returns, Earnings Growth, P/E Expansion, and Interest Rates

The S&P 500 increased from 2,789.80 on January 1, 2018 to 2,924.59 on October 1, 2018, a year-to-date return of 4.83%. As shown in the graph below, this return was fueled by a solid increase in earnings of 9.20% but was partially offset by a contraction of 4.37% in the P/E ratio.

While S&P 500 returns result from both P/E ratio expansion and increases in earnings, these factors have historically been negatively correlated. This means that the offsetting effect that we see above holds for monthly data over a longer period of time. In fact, the relationship for the period January 1970 through October 2018 as determined by linear regression is:

Monthly Increase in Earnings = 0.58% – 27.42% × (Monthly P/E Ratio Expansion)

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Based on this regression, a 2% decrease in the P/E Ratio will likely be accompanied by a 1.1% increase in earnings, yielding a negative 0.9% S&P 500 return.

Monthly P/E Monthly Increase Monthly S&P 500 Ratio Expansion in Earnings Return -2.0% 1.1% -0.9% -1.0% 0.9% -0.2% 0.0% 0.6% 0.6% 1.0% 0.3% 1.3% 2.0% 0.0% 2.0%

The graph below illustrates the historical relationship of monthly increases in earnings and monthly P/E Ratio expansion.

While we see an offsetting effect in monthly P/E ratio expansion and monthly increases in earnings, both factors have contributed to cumulative S&P 500 returns since January 1970. The index has increased 3,138.4% over this period, while earnings have expanded by 2,037.2% and the P/E ratio has increased by 51.5%.1 If we allocate the multiplicative component of the S&P 500 to earnings expansion and P/E ratio expansion, we find that 97.5% of the cumulative return in the S&P 500 since January 1970 has come from expansion in earnings, while 2.5% of the cumulative return is attributable to the growth in the P/E ratio. The chart below depicts the cumulative S&P 500 return.

1 3,138.4% = (1 + 2,037.2%) × (1 + 51.5%) - 1

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While S&P returns over long periods of time are attributable to earnings expansion, the variation in monthly returns is primarily explained by changes in the P/E ratio (approx. 62%). The chart below illustrates the relationship between monthly S&P 500 returns and the monthly percent change in the P/E ratio.

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Historical Distribution of the P/E Ratio

During the period January 1970 to October 2018, the S&P 500 P/E ratio averaged 19.5x. However, for the majority of the period, the P/E ratio was less than the 19.5x average. The P/E ratios had remained above the average for the last 48 months.

During the period January 1987 to October 2018, the P/E ratio averaged 23.5x and the median P/E ratio was 20.5x. In the last 15 years, the average P/E ratio has moved further upwards to 24.5x.

The S&P 500 P/E ratio as of October 1, 2018 was 23.9x, which is 22.6% higher than the historical average of 19.5x. At the same time, it was trading below the last 15 years average of 24.5x.

Interest Rates Compared to P/E Ratio

From our prior paper2 discussing S&P 500 returns, we know that the P/E ratio is theoretically a function of the long-term growth rate in earnings and the required rate of return. From January 1970 to October 2018, the Federal Funds Rate averaged 5.23%. At the same time, the S&P P/E ratio averaged 19.5x. From 1973 until the end of 1991, interest rates were almost always above the historical average. Most notably, in 1980 and 1981, the Federal Funds Rate rose to 20.00% on four occasions over the two-year period, the highest interest rate in United States history. However, the Federal Funds Rate has averaged 3.50% since 1986 and for the last 25 years, interest rates have remained below the historical average, plummeting to 0.15% in 2009. For the following seven years, the

2 https://www.valuescopeinc.com/resources/white-papers/the-sp-500-pe-ratio-a-historical-perspective/

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interest rate remained low and only began to increase in December of 2015 when the Federal Reserve determined that economic growth had stabilized. Due to low interest rates since the great recession, the Federal Funds Rate has averaged 1.34% in the last 15 years. It can be seen that the average interest rates have been falling for a long time and had only recently picked up. With some recent increases, as of October 2018, the Federal Funds Rate was 2.20%.

It can be observed that the relationship between the P/E ratio and Federal Funds Rate changed during this long period. It appears that the change happened somewhere near 1990. Before August 1987, the P/E ratio and Federal Funds Rate displayed the following logarithmic relationship:

P/E ratio = -6.173 ln (Fed Fund Rate) – 3.6381

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Alan Greenspan took over as Fed Chairman in August 1987. He supported an easy money policy and started reducing interest rates soon after. With a change in the Fed’s policy, the relationship between the P/E ratio and interest rates changed to a very weak linear relationship.

P/E ratio = 27.292 – 94.08 (Fed Funds Rate)

The outliers circled above occurred during recessionary periods. After removing the outliers, the relationship between the P/E Ratio and Federal Funds Rate remains weak, as shown in the chart below.

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Conclusion

Analysts estimate an 80.7% chance of at least one more increase in the Federal Funds Rate3 before the end of the year. While the prior relationship and financial theory would predict that increasing the Federal Funds Rate would lead to a decline in the P/E ratio through an increase in the required rate of return, our analysis shows that this relationship no longer holds. In future papers, we will investigate the determinants of the S&P 500 required rate of return by examining the implied equity cost of capital.

3 CME Group, FedWatch Tool, November 8, 2018

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Marty Hanan is the founder and President of ValueScope, Inc., a valuation and financial advisory firm that specializes in valuing assets and businesses and in helping business owners in business transactions and estate planning. Mr. Hanan is a Chartered Financial Analyst and has a B.S. Electrical Engineering from the University of Illinois and an MBA from Loyola University of Chicago.

The information presented here is not nor should it be treated as investment, financial, or tax advice and is not intended to be used to make investment decisions.

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APPENDICES

VALUESCOPE, Inc. Appendix A

S&P 500 PE Ratio; 1970 to Present 50x 25% 25% 100% Current PE 23.88 40x 20% 90% Percentile 82.3% 30x 15% 20% Current Value 80% 23.39 70% 20x 10% Min 6.8x 15% 60% 10x 5% 5% 7.9x 50% 25% 12.4x 0x 0% 10% 40% Median 17.8x 30% Mean 19.4x

5% 20%

Jan-1972 Jan-1974 Jan-1976 Jan-1978 Jan-1980 Jan-1982 Jan-1984 Jan-1986 Jan-1988 Jan-1990 Jan-1992 Jan-1994 Jan-1996 Jan-1998 Jan-2000 Jan-2002 Jan-2004 Jan-2006 Jan-2008 Jan-2010 Jan-2012 Jan-2014 Jan-2016 Jan-2018 Jan-1970 75% 22.6x 10% 95% 32.8x S&P 500 PE Ratio avg S&P 500 PE Ratio 0% 0% Max 123.7x

Fed Funds Rate 10-yr Treasury 5

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

100 105 110 115 120 125 60x 2,000 50x

40x 1,500

30x 1,000 20x 500 10x

0x 0

Aug-1972 Aug-1973 Aug-1974 Aug-1975 Aug-1976 Aug-1977 Aug-1978 Aug-1979 Aug-1980 Aug-1981 Aug-1982 Aug-1983 Aug-1984 Aug-1985 Aug-1986 Aug-1987 Aug-1988 Aug-1989 Aug-1990 Aug-1991 Aug-1992 Aug-1993 Aug-1994 Aug-1995 Aug-1996 Aug-1997 Aug-1998 Aug-1999 Aug-2000 Aug-2001 Aug-2002 Aug-2003 Aug-2004 Aug-2005 Aug-2006 Aug-2007 Aug-2008 Aug-2009 Aug-2010 Aug-2011 Aug-2012 Aug-2013 Aug-2014 Aug-2015 Aug-2016 Aug-2017 Aug-2018

S&P 500 PE Ratio avg S&P 500 PE Ratio S&P 500 Price

60x 16% 14% 50x 12% 40x 10% 30x 8% 6% 20x 4% 10x 2%

0x 0%

S&P 500 PE Ratio avg S&P 500 PE Ratio 10-yr Treasury Appendix B

S&P 500 PE Ratio, Fed Funds Rate and 10-yr Treasury; 1970 to Present Jerome William M. Martin Arthur F. Burns G. William Miller Paul Volcker Janet Yellen Alan Greenspan Ben Bernanke Powell 100x 90x 80x 70x 60x 50x 40x 30x 20x 10x

Jun-1975 Jun-1981 Jun-1987 Jun-1993 Jun-2009 Jun-2015 Jun-1971 Jun-1973 Jun-1977 Jun-1979 Jun-1983 Jun-1985 Jun-1989 Jun-1991 Jun-1995 Jun-1997 Jun-1999 Jun-2001 Jun-2003 Jun-2005 Jun-2007 Jun-2011 Jun-2013 Jun-2017

Oct-1980 Oct-1986 Oct-1992 Oct-1998 Oct-2004 Oct-2010 Oct-1970 Oct-1972 Oct-1974 Oct-1976 Oct-1978 Oct-1982 Oct-1984 Oct-1988 Oct-1990 Oct-1994 Oct-1996 Oct-2000 Oct-2002 Oct-2006 Oct-2008 Oct-2012 Oct-2014 Oct-2016 Oct-2018

Feb-1970 Feb-1976 Feb-1982 Feb-1998 Feb-2004 Feb-2010 Feb-2016 Feb-1972 Feb-1974 Feb-1978 Feb-1980 Feb-1984 Feb-1986 Feb-1988 Feb-1990 Feb-1992 Feb-1994 Feb-1996 Feb-2000 Feb-2002 Feb-2006 Feb-2008 Feb-2012 Feb-2014 Feb-2018

S&P 500 PE Ratio avg S&P 500 PE Ratio

Jerome William M. Martin Arthur F. Burns G. William Miller Paul Volcker Alan Greenspan Ben Bernanke Janet Yellen Powell 18% 16% 14% 12% 10% 8% 6% 4% 2%

Jun-1971 Jun-1977 Jun-1991 Jun-1997 Jun-2003 Jun-2009 Jun-2015 Jun-1973 Jun-1975 Jun-1979 Jun-1981 Jun-1983 Jun-1985 Jun-1987 Jun-1989 Jun-1993 Jun-1995 Jun-1999 Jun-2001 Jun-2005 Jun-2007 Jun-2011 Jun-2013 Jun-2017

Oct-1978 Oct-1984 Oct-1990 Oct-1996 Oct-2002 Oct-1970 Oct-1972 Oct-1974 Oct-1976 Oct-1980 Oct-1982 Oct-1986 Oct-1988 Oct-1992 Oct-1994 Oct-1998 Oct-2000 Oct-2004 Oct-2006 Oct-2008 Oct-2010 Oct-2012 Oct-2014 Oct-2016 Oct-2018

Feb-1972 Feb-1978 Feb-1984 Feb-1990 Feb-2010 Feb-2016 Feb-1970 Feb-1974 Feb-1976 Feb-1980 Feb-1982 Feb-1986 Feb-1988 Feb-1992 Feb-1994 Feb-1996 Feb-1998 Feb-2000 Feb-2002 Feb-2004 Feb-2006 Feb-2008 Feb-2012 Feb-2014 Feb-2018

10-yr Treasury avg 10-yr Treasury

Jerome William M. Martin Arthur F. Burns G. William Miller Paul Volcker Alan Greenspan Ben Bernanke Janet Yellen Powell 25%

20%

15%

10%

Fed Funds Rate avg Fed Funds Rate Appendix C

S&P 500 PE Ratio, Fed Funds Rate and 10-yr Treasury; 1970 to Present

80x 70x 60x 50x 40x 30x 20x 10x

1970 1975 1980 1983 1985 1988 1993 1998 2003 2008 2011 2013 2016 1971 1972 1973 1974 1976 1977 1978 1979 1981 1982 1984 1986 1987 1989 1990 1991 1992 1994 1995 1996 1997 1999 2000 2001 2002 2004 2005 2006 2007 2009 2010 2012 2014 2015 2017 2018

Recession S&P 500 PE Ratio avg S&P 500 PE Ratio

18% 16% 14% 12% 10% 8% 6% 4% 2%

1973 1975 1980 1982 1987 1989 1994 1996 2001 2003 2008 2010 2015 2017 1970 1971 1972 1974 1976 1977 1978 1979 1981 1983 1984 1985 1986 1988 1990 1991 1992 1993 1995 1997 1998 1999 2000 2002 2004 2005 2006 2007 2009 2011 2012 2013 2014 2016 2018

Recession 10-yr Treasury avg 10-yr Treasury

25%

20%

15%

10%

1974 1979 1981 1986 1991 1996 2001 2003 2008 2013 2018 1970 1971 1972 1973 1975 1976 1977 1978 1980 1982 1983 1984 1985 1987 1988 1989 1990 1992 1993 1994 1995 1997 1998 1999 2000 2002 2004 2005 2006 2007 2009 2010 2011 2012 2014 2015 2016 2017

Recession Fed Funds Rate avg Fed Funds Rate