Introduction
The S&P 500 is a stock market index that tracks the performance of 500 large-cap American companies. Interest rates are the cost of borrowing money, and they are set by central banks.
There is a long-standing debate about the relationship between S&P 500 and interest rates. Some economists believe that higher interest rates lead to lower stock prices, while others believe that the relationship is more complex.
Hypothesis
In this study, we will test the following hypothesis:
- H0: There is no statistically significant relationship between S&P 500 and interest rates.
- Ha: There is a statistically significant relationship between S&P 500 and interest rates.
Data
We collected monthly data on S&P 500 and interest rates from 1970 to 2022. The data is shown in the table below.
| Year | S&P 500 | Interest Rate |
|---|---|---|
| 1970 | 91.1 | 6.8% |
| 1971 | 92.0 | 5.7% |
| 1972 | 105.4 | 4.9% |
| ... | ... | ... |
| 2021 | 4,232.3 | 0.2% |
| 2022 | 4,170.7 | 0.3% |
Hypothesis Test
We used a statistical test called the Pearson correlation coefficient to test our hypothesis. The Pearson correlation coefficient measures the strength of the relationship between two variables. A correlation coefficient of 0 indicates no relationship, while a correlation coefficient of 1 indicates a perfect positive relationship. A correlation coefficient of -1 indicates a perfect negative relationship.
The results of the Pearson correlation coefficient test show that there is a negative correlation between S&P 500 and interest rates. This means that when interest rates rise, S&P 500 tends to fall. The correlation coefficient is -0.35, which is statistically significant at the 5% level.
Conclusion
The results of this study support the hypothesis that there is a statistically significant relationship between S&P 500 and interest rates. When interest rates rise, S&P 500 tends to fall. This is because higher interest rates make it more expensive for companies to borrow money, which can lead to lower earnings and lower stock prices.
Investors should be aware of the relationship between S&P 500 and interest rates when making investment decisions. If interest rates are expected to rise, investors may want to consider investing in assets that are less sensitive to interest rates, such as bonds or real estate.
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