Recently, investors have been fearful of rising interest rates. Intuitive thinking says there should be an inverse relationship between changes in the 10-year treasury yield and the price changes of the S&P500. Putting intuitive thinking aside, what does the data actually show? To answer this question we charted the data in 3 ways in order to see what trends were displayed. The 3 charts include:

- Long-term Trends (S&P500 ROR vs. Delta 10-Year Treasury) – Chart 1
- Medium-term Trends (S&P500 ROR vs. Delta 10-Year Treasury) – Chart 2
- Monthly Trends (S&P500 ROR vs. Delta 10-Year Treasury) – Chart 3

First, let’s look at Chart 1. This chart depicts 1 period of long-term rising interest rates (1940 to 1982) and 1 period of long-term falling interest rates (1982 to 2009):

From this chart, it can be seen that from 1940 to 1982 the annual compounding rate for the 10-YR Treasury rate was bounded between +4.97% and +5.61% (average = +5.29%). The corresponding annual rate-of-return of the price appreciation for the S&P500 Index was bounded between +5.76% and +6.77% (average = +6.27%). From this chart, it can also be seen that from 1982 to 2009 the annual compounding rate for the 10-YR Teasury rate was bounded between -4.17% and -4.45% (average = -4.31%). The corresponding annual rate-of-return of the price appreciation for the S&P500 Index was bounded between +7.52% and +8.69% (average = +8.11%). Please note that this chart ignores the Dot-com bubble pricing. Taking the average trend information we get the following equation:

**Annual S&P500 ROR = 7.28% – 0.1917 x Annual Compounding Rate of the 10-YR Treasury Yield**

Though this equation does support the negative correlation assumption, the influence is relatively weak. The effect of interest rates on the long-term annualized S&P500 ROR was only +/-1%. On average, the S&P500 price appreciation should be negative when the 10-YR Treasury rate compounds faster than 38% per year.

**Examples:**

Initial yield = 2%

Max Yield by Year-end = 1.38 x 2% = 2.76%

Initial yield = 10%

Max Yield by Year-end = 1.38 x 10% = 13.8%

Second, let’s look at Chart 2. This chart depicts 20 periods of shorter-term rising interest rates and 20 periods of shorter-term falling interest rates between 1950 and 2017. The periods ranged in duration from 3 months to 4 years.

From this chart and the 40 data points, we get the following equation:

**Annual S&P500 ROR = 11.52% + 0.3805 x Annual Change in the 10-YR Treasury Yield, R ^{2} = 0.0017**

This equation actually supports a weak positive correlation between the annual S&P500 rate-of-return and the rate of change in the 10-Year Treasury yield. However, the low end of the ROR trend-line is 10.4% and the upper end of the trend-line is 12.8% (+/-1.2%).

Third, let’s look at Chart 3 which depicts approximately 1000 monthly data points form 1932 to 2018. The data points are plotted as Price change for the S&P500 vs. rate-of-change in the 10-Year Treasury.

From this chart and the approximately 1000 data points, we get the following equation:

**Monthly S&P500 ROR = 0.69% – 1.2723 x Monthly Change in the 10-YR Treasury Yield, R ^{2} = 0.0050**

This equation supports a weak negative correlation between the monthly S&P500 rate-of-return and the monthly rate of change in the 10-Year Treasury yield. The average 10YR Treasury yield during the 86-year analysis period was 5.05%. On average, the monthly S&P500 price appreciation should be negative when the 10-YR Treasury yield rises faster than 10.7% of the average yield per month (0.54% for the study period).

**Examples:**

Initial yield = 2.5%

Max Yield by Month-end = 1.107 x 2.5% = 2.77%

Initial yield = 10%

Max Yield by Month-end = 1.107 x 10% = 11.1%

**Conclusions: **

Long-term or large data set analyses of the S&P500 vs. 10-YR Treasury indicate the following:

- Over the long-term, there is a weak negative correlation between interest rate changes and the annual price appreciation of the S&P500 Index.
- Monthly compounding of the 10-YR Treasury yield rate by more than 10.7% may coincide with a downturn in the S&P500 Index.
- Annual compounding of the 10-YR Treasury yield rate by more than 38% may coincide with a downturn in the S&P500 Index.

**Footnotes:**

- The 10-YR Treasury yield rate rose by nearly 11% from Jan 1, 2018 (2.58%) and Feb 1, 2018 (2.86%).
- If the 10-YR Treasury yield rate rises to 3.01% before April 1, 2018, it will exceed an annual compounding of 38% from a low of 2.18% on April 1, 2017.