A copper wire manufacturer needs to hedge its physical copper price risk. Historical data reveals that the standard deviation of changes in spot copper prices is 9.00, the standard deviation of changes in copper futures prices is 10.00, and the correlation coefficient between spot and futures price changes is 0.90. What is the optimal Hedge Ratio, and how many metric tons (MT) must be hedged for a 100 MT physical exposure?

[ A ]Hedge Ratio is 1.00; exactly 100 MT must be hedged in the futures market.

[ B ]Hedge Ratio is 0.81 (0.90 * (9.00 / 10.00)); 81 MT of copper must be hedged in the futures market.[ CORRECT ]

[ C ]Hedge Ratio is 0.90; exactly 90 MT must be hedged in the futures market.

[ D ]Hedge Ratio is 1.23; 123 MT must be hedged in the futures market.

Takeaway

Option B is correct: Hedge Ratio is 0.81 (0.90 * (9.00 / 10.00)); 81 MT of copper must be hedged in the futures market.

Derivation

The optimal minimum-variance Hedge Ratio in commodity risk management is calculated as: Hedge Ratio (h*) = Correlation Coefficient (r) * [Standard Deviation of Spot Price Change (Sigma_S) / Standard Deviation of Futures Price Change (Sigma_F)]. Given: r = 0.90, Sigma_S = 9.00, Sigma_F = 10.00. Hedge Ratio = 0.90 * (9.00 / 10.00) = 0.90 * 0.90 = 0.81 (or 81%). For a 100 MT physical exposure: Quantity to be hedged = 100 MT * 0.81 = 81 MT. (Dividing by contract lot size yields the number of exchange contracts). This tests the mathematical formulation of the hedge ratio. The primary candidate error is assuming the hedge ratio equals the correlation coefficient alone (0.90).

Why the others fail

A — Hedge Ratio is 1.00; exactly 100 MT must be hedged in the futures market.

A hedge ratio of 1.00 assumes a naive 1:1 hedge, ignoring the volatility differential and correlation between spot and futures.

C — Hedge Ratio is 0.90; exactly 90 MT must be hedged in the futures market.

0.90 uses only the correlation coefficient (r) without multiplying by the ratio of standard deviations (9 / 10 = 0.90).

D — Hedge Ratio is 1.23; 123 MT must be hedged in the futures market.

1.23 is derived from erroneously inverting the standard deviation ratio (0.90 * (10 / 9) = 1.00) in the hedge formula.