Analysis of the relationship between inflation and the correlation between variable income and fixed income

The relationship between variable income (represented by the S&P 500) and fixed income (10 -year Treasury bonds) It has been subject to extensive studies in the financial field. This relationship may change depending on the inflation levelaffecting the strategy of diversification of investors. This study analyzes how the correlation between these two assets varies in different inflation environments and if inflation can predict said correlation. The period we have used is from 1928 to 2024.

To evaluate the relationship between inflation and the correlation between fixed and variable income, I have used a simple linear regression model.

Correlation = b₀ + b₁Inflation + e_t

Variable	Description
Correlation	Correlation coefficient between the profitability of the S&P 500 and the 10 -year Treasury Bonus in the T year. It is calculated with a 10 -year -old mobile window.
Inflation	Annual inflation rate in percentage (%), measured from the consumer price index in the T year.
Constant (b0)	Expected value of correlation when inflation is 0%.
Inflation coefficient (b1)	Indicates the change in the correlation between variable income and fixed income for every 1 additional percentage point in inflation.
Error (et)	Capture other factors not included in the model that affect the correlation.

Replacing the coefficients:

Correlation = −0.1686 + 0.0368*inflation + e_t

Variable	Coefficient	p-value
Constant (b0)	-0,1686	–
Inflation (b1)	0,0368	0,016
R-Cuadrado	0,067	–

The interpretation of the results of the variables of the model indicates that:

• Inflation coefficient (0.0368): For each percentage point of increase in inflation, the correlation between variable income and fixed income increases by 0.0368. This means that, as inflation rises, the relationship between both assets becomes less negative, becoming positive and very positive as it continues to increase.
• Constant (-0.1686): When inflation is 0%, the expected correlation is -0,1686, which suggests a slight investment of the movements of the two assets.
• R-Cuadrado (0.067): Inflation explains 6.7% of the variability in the correlation, which shows that there are other factors that influence.
• Statistical significance: he P-Value of 0.016 confirms that the relationship between inflation and correlation is statistically significant.

This simple model has its advantageshow to allow us to evaluate quantitatively the relationship between inflation and the correlation of financial assets. Also, I use almost 100 years datawhich guarantees some robustness in the results and the model is simple to interpret. However, the under r² Indicates that there are other factors -Comerate political, growth, etc. – that influence this correlation. In addition, the model Does not capture non -linear effects (In fact, in the graph we will see a quadratic trend to alleviate, in part, this deficiency) and does not take into account other variables that we know that affect, such as volatility.

The analysis shows that Inflation has a significant statistically impact on the relationship between variable income and fixed income. In environments of Low inflation, bonds and actions function as diversifying assets. However, From a threshold of 3% inflation, the correlation becomes positiveindicating that both assets can be jointly affected by the hardening of monetary policy.

_{Source: Carlos Arenas Laorga}

So, does inflation predict correlation?

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