Trade-Weighted Index Adjusts for Relative Currency Depreciation Against Smaller Partner

Steps:

• Assume X's exchange rate with Y remains fixed at 100; Y's 20% depreciation against Z implies Z appreciates 20% against X.
• Bilateral index vs. Y stays at 100 (60% weight).
• Bilateral index vs. Z falls 20% to 80 (40% weight), as X weakens vs. Z.
• New index = (0.6 × 100) + (0.4 × 80) = 60 + 32 = 92.

Why C is correct:

• Matches the formula for trade-weighted index: weighted average of bilateral rates, where relative depreciation shifts the Z component by 20%.

Why the others are wrong:

• A: Assumes full 20% depreciation applied to entire index (100 × 0.8 × 0.6 + adjustment error).
• B: Approximates 0.6 × 100 + 0.4 × 85 or similar rounding error.
• D: Applies 20% appreciation to Y component instead (0.6 × 120 + 0.4 × 100 = 112, close but inverted assumption).

Final answer: C