*By Phillip Brzenk*

In a previous blog, we performed preliminary exploration of rising interest rate exposure of the S&P 500 Low Volatility Index. In this blog, we continue the analysis to see if there is a relationship between the magnitude of interest rate change and magnitude of active return of the low volatility index relative to the S&P 500. To do so, we run a regression line by plotting the historical monthly excess returns (y-axis) against the monthly interest rate changes (x-axis).

Looking at the trend line in Exhibit 1, there is a downward-sloping, negative relationship between the degree of interest rate movements and the excess return of the low volatility index relative to the S&P 500. The regression equation, also shown in the chart, confirms the negative relationship.

The regression equation has a slope coefficient of -3.07 and an r-squared value of 8.8%. The coefficient indicates that for every 1% change in interest rate, the excess return of the low volatility index is expected to change by -3.07 times. For example, if interest rates rise by 1%, the relative return is expected to be -3.07%. Conversely, if rates decline by 1%, the excess return is expected to be 3.07%.

The r-squared value is the trend line’s “goodness of fit” to the data; in essence, it is the explanatory power of interest rate movements on excess returns. We note that the r-squared value is relatively low; however, the coefficient to interest rates is statistically significant. **Ensuring that coefficients are statistically significant when it comes to factors that have low explanatory power, such as macroeconomic factors, on equity performance is especially critical.** In this case, the t-stat of the interest rate change coefficient is -5.61, which is significant at the 99^{th} percent confidence interval.

Combined with the findings in the first blog, we can conclude that, historically, the S&P 500 Low Volatility Index tends to be negatively affected by rising interest rates. In a subsequent blog, we will explore an alternative low volatility index strategy that is designed to reduce interest rate exposure while still preserving low volatility properties.

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