Explanation

This is a linear interpolation problem:

• 10-year spot rate: +10 basis points
• 20-year spot rate: +0 basis points (shock decreases linearly to zero)
• 14-year spot rate: We need to find the interpolated value

Calculation:

• Time interval: 10 years to 20 years = 10-year span
• Position of 14-year rate: 4 years from 10-year point (14 - 10 = 4)
• Total span: 10 years
• Fraction: 4/10 = 0.4
• Shock at 14 years: 10 bp × (1 - 0.4) = 10 bp × 0.6 = 6 basis points

Verification:

• At 10 years: 10 bp (100% of shock)
• At 14 years: 6 bp (60% of shock remaining)
• At 20 years: 0 bp (0% of shock remaining)

The shock decreases linearly from 10 bp at 10 years to 0 bp at 20 years, so at 14 years (which is 40% of the way from 10 to 20), the remaining shock is 60% of the original 10 bp, resulting in a 6 bp increase.