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# Reading 18: Currency Exchange Rates-LOS g习题精选

Session 4: Economics for Valuation

LOS g: Calculate and interpret a forward discount or premium and express it as an annualized rate.

The spot exchange rate is FC C 2.000. The foreign return is 15% and the domestic return is 12%. Which of the following is closest to the forward exchange rate?

 A) 0.487.
 B) 2.576.
 C) 1.948.

We want to create a no arbitrage condition. According to the Interest Rate Parity Theorem, if the following condition does not hold, investors will take advantage of interest rate differentials to capitalize on arbitrage opportunities.

ForwardFC C = SpotFC C × [(1 + rdomestic) / (1 + rforeign)]
This condition is the formal representation of interest rate parity.
Here, ForwardFC C = 2.000 × [(1 + 0.12) / (1 + 0.15)] = 2.000 × 0.97391 = 1.94783 or about 1.948.

The spot and 30-day forward rates for the Euro are \$1.1525 and \$1.1015, respectively. The Euro is selling at a forward:

 A) discount of \$0.051.
 B) discount of 0.956%.

Since the forward rate is less than the spot rate, the Euro is selling at a forward discount. The amount of the discount is calculated as follows:

Forward Discount = Forward rate – Spot Rate = \$1.1015 - \$1.1525 = -\$0.051.

If the 90-day forward rate for the CAD is USD 0.6503, and the spot rate is USD 0.6403, then the annualized premium is:

 A) 6.25%.
 B) 1.00%.
 C) 1.56%.

Annualized premium = [(0.6503 ? 0.6403) / 0.6403] × (360 / 90) = 0.625 or 6.25%.

The spot and 30-day forward exchange rates for the Swiss franc (CHF) are USD:CHF 0.59984 and USD:CHF 0.62734, respectively. Relative to the USD, the CHF is selling at a forward:

 A) differential of 275 points.
 C) discount of \$0.073.

Forward Discount = Forward rate ? Spot Rate = (1 / 0.62734) ? (1 / 0.59984) = ?\$0.073

Since the forward rate is less than the spot rate, the Swiss franc is selling at a forward discount. Note that although in percentage terms, (\$0.073 / 1.667) = ?4.38%, when the forward discount is expressed in percentage terms, it is done so on an annualized basis. The correct forward premium expressed as a percentage would be equal to 0.0438 × (360 / 30) = 52.60%.

A foreign currency is at a forward premium if the forward rate:

 A) expressed in domestic currency is above the spot rate.
 B) expressed in domestic currency is below the spot rate.
 C) expressed in domestic currency:foreign currency is above the spot rate.

A foreign currency is at a forward premium if the forward rate expressed in domestic currency is above the spot rate. A forward discount exists if the forward rate is below the spot rate.

The current spot rate quote is GBP:USD 2.00. A 180 day forward discount for the GBP of 2% (annualized) would reflect a forward price of:

 A) USD:GBP 2.02.
 B) GBP:USD 1.96.
 C) GBP:USD 1.98.

The GBP is at a forward discount if the forward rate expressed in GBP:USD is below the spot rate. Since the annualized discount is 2%, the 180 day forward discount is 1% of spot, or USD 0.02.

[(1.98 ? 2.00) / 2.00](360 / 180) = -2%

The forward rate on a 90-day contract is USD:FC 5 and the spot is USD:FC 4. The USD is trading at a forward:

 A) discount of 1.0.

A foreign currency is at a forward premium if the forward rate expressed in dollars is above the spot rate. Forward premium = forward rate – spot rate = 5 ? 4 = 1.

If the forward rate expressed in domestic currency units is above the spot rate, then the foreign currency is at a:

 B) spot discount.
 C) forward discount.

A foreign currency is at a forward premium if the forward rate expressed in domestic currency is above the spot rate. Forward premium = forward rate – spot rate.

Today, the spot rate on Japanese yen is \$0.008000 and 180-day forward yen are priced at \$0.008250. The annualized forward premium is:

 A) 3.125%.
 B) 6.060%.
 C) 6.250%. Forward premium = (\$0.008250 ? \$0.008000) / \$0.008000 × (360 / 180) = 0.0625 = 6.25%.

Isaac Long is an English investor. He notices the 90–day forward rate for the Norwegian kroner is GBP 0.0859 and the spot rate is GBP 0.0887. Long calculates the annualized rate of the kroner to be trading at a: