I supplemented this test with a more robust regression analysis that sought to explain these index’s returns (over Treasuries) using the market risk premium and monthly changes in the 10-year Treasury yield as explanatory variables. This approach controls for fluctuations in the market to present a clearer picture of how changing interest rates affect performance. Exhibit 2 shows the coefficients from these regres­sions. These indicate how sensitive each index is to the market and changing interest rates and the direction of those relationships. For example, an interest-rate coefficient of negative 1.1 would indicate that a 1% increase in monthly interest-rate changes corresponds to a 1.1% decrease in the index’s return.

The regression results corroborate the findings above. Both low-volatility indexes have a significant inverse relationship with interest-rate changes, while the high-beta index has a positive relationship with this variable. These interest-rate coefficients become a little smaller (in absolute terms) after adding small size, value, and momentum as additional variables in the regression, but they are still significant.