A US-based corporation has decided to make an investment in Norwegian Kroner of NOK 500 Million (NOK = Norwegian Kroner) in 3 months. The company wishes to hedge changes in the the US dollar-NOK exchange rate using forward contracts on either the euro (EUR) or the Swiss Franc (CHF). The company makes the following estimates:
-If EUR forwards are used: The standard deviation of quarterly changes in the USD/NOK spot exchange rate is 0.005, the standard deviation of quarterly changes in the USD/EUR forward rate is 0.025, and the correlation between the changes is 0.90.
-If CHF forwards are used: The standard deviation of quarterly changes in the USD/NOK spot exchange rate is 0.005, the standard deviation of quarterly changes in the USD/CHF forward rate is 0.020, and the correlation between the changes is 0.80.
The current USD/NOK spot rate is 0.160 (i.e., USD 0.160 per NOK), the current 3-month USD/EUR forward rate is 1.36, and the current 3-month USD/CHF forward rate is 1.04.
If the company wishes to carry out a minimum-variance hedge, which currency should it use for this purpose?
A) CHF, because the forward exchange rate of near 1 makes it "more" like the USD.
B) EUR, because Norwegian trade with the eurozone countries far exceeds its trade with Switzerland.
C) EUR, because of the higher correlation of 0.90.
D) CHF, because of the lower correlation of 0.80.

Question

A US-based corporation has decided to make an investment in Norwegian Kroner of NOK 500 Million (NOK = Norwegian Kroner) in 3 months. The company wishes to hedge changes in the the US dollar-NOK exchange rate using forward contracts on either the euro (EUR) or the Swiss Franc (CHF). The company makes the following estimates: 
-If EUR forwards are used: The standard deviation of quarterly changes in the USD/NOK spot exchange rate is 0.005, the standard deviation of quarterly changes in the USD/EUR forward rate is 0.025, and the correlation between the changes is 0.90.
-If CHF forwards are used: The standard deviation of quarterly changes in the USD/NOK spot exchange rate is 0.005, the standard deviation of quarterly changes in the USD/CHF forward rate is 0.020, and the correlation between the changes is 0.80.
The current USD/NOK spot rate is 0.160 (i.e., USD 0.160 per NOK), the current 3-month USD/EUR forward rate is 1.36, and the current 3-month USD/CHF forward rate is 1.04.
If the company wishes to carry out a minimum-variance hedge, which currency should it use for this purpose?
A) CHF, because the forward exchange rate of near 1 makes it "more" like the USD.
B) EUR, because Norwegian trade with the eurozone countries far exceeds its trade with Switzerland.
C) EUR, because of the higher correlation of 0.90.
D) CHF, because of the lower correlation of 0.80.

Quizplus · Accepted Answer

The minimum-variance hedge would be most effective with the currency that has the highest correlation with the USD/NOK exchange rate changes. In this case, the EUR has a higher correlation (0.90) with USD/NOK changes than the CHF does (0.80), making it the better choice for minimizing variance in the hedge.

A US-Based Corporation Has Decided to Make an Investment in Norwegian