Explanation

Empirical studies show that among the three principal components of yield curve movements, curvature typically explains the smallest proportion of total variance in interest rates.

Typical variance decomposition:

• Level factor: Explains approximately 80-90% of total variance
• Steepness factor: Explains approximately 8-15% of total variance
• Curvature factor: Explains approximately 1-5% of total variance

Why curvature has the smallest impact:

• Level shifts (parallel movements) dominate interest rate changes
• Steepness changes (slope changes) are more common than curvature changes
• Curvature changes (butterfly shifts) are relatively rare and have smaller magnitude

This pattern is consistent across different markets and time periods, making curvature the least significant factor in explaining interest rate variance.