Reading 18: Currency Exchange Rates-LOS h, (Part 2)习题精选 between, interest, following, 2010, face

土豆妮

Session 4: Economics: Economics for Valuation
Reading 18: Currency Exchange Rates

LOS h, (Part 2): Illustrate covered interest arbitrage

 

 

 

Given the following information:

• The forward rate between dollars and pounds is 1.66$/GBP.

• The current spot rate is 1.543 $/GBP.

• The UK interest rate is 5.77%.

• The interest rate in the United States is 5.976%.

Assume a U.S. investor can borrow pounds or dollars. What is the covered interest rate differential?

A) ?0.07814.

B) 0.6786.

C) 0.07661.

土豆妮

Given the following information:

• The forward rate between dollars and pounds is 1.66$/GBP.

• The current spot rate is 1.543 $/GBP.

• The UK interest rate is 5.77%.

• The interest rate in the United States is 5.976%.

Assume a U.S. investor can borrow pounds or dollars. What is the covered interest rate differential?

A) ?0.07814.

B) 0.6786.

C) 0.07661.

---

(1 + r_D) ? [(1 + r_F)(forward rate)] / spot rate

(1 + 0.05976) ? [(1 + 0.0577)(1.66)] / 1.543

1.05976 ? [(1.0577)(1.66)] / 1.543

1.05976 ? (1.75578 / 1.543)

1.05976 ? 1.13790 = ?0.07814

土豆妮

 

If (r_D ? r_F) > Forward premium, which is (Forward D/F) ? Spot(D/F) / Spot(D/F), then:

A) borrow domestic currency and lend out foreign currency.

B) arbitrage opportunities don't exist.

C) borrow foreign currency and lend out domestic currency.

土豆妮

 

If (r_D ? r_F) > Forward premium, which is (Forward D/F) ? Spot(D/F) / Spot(D/F), then:

A) borrow domestic currency and lend out foreign currency.

B) arbitrage opportunities don't exist.

C) borrow foreign currency and lend out domestic currency.

---

If (r_D ? r_F) > Forward premium, which is (Forward D/F) ? Spot(D/F) / Spot(D/F), then you would borrow foreign currency and lend out local currency. If the domestic rate is high relative to the hedged foreign rate, you would borrow foreign currency units and then sell them for domestic currency units at the spot rate, lend these domestic currency units at the domestic interest rate and simultaneously sell just enough domestic currency forward so that you can repay your foreign loan.

土豆妮

Suppose that the current interest rates in the U.S. and the European Union are 13.665% and 8.5000%, respectively. Also, the spot rate for the dollar is 1.1975 US$/euro, and the 1-year forward rate is 1.2545 US$/euro. If $100 is invested, what is the total arbitrage profit that a U.S. investor could earn?

A) $5.70000.

B) $23.06700.

C) No arbitrage profit can be made.

土豆妮

Suppose that the current interest rates in the U.S. and the European Union are 13.665% and 8.5000%, respectively. Also, the spot rate for the dollar is 1.1975 US$/euro, and the 1-year forward rate is 1.2545 US$/euro. If $100 is invested, what is the total arbitrage profit that a U.S. investor could earn?

A) $5.70000.

B) $23.06700.

C) No arbitrage profit can be made.

---

First determine if an arbitrage opportunity exists by:

(1 + r_D) = [(1 + r_F)(forward rate)] / spot rate = Covered Interest Differential

If the covered interest differential is > or < 0, then arbitrage opportunities exist.

(1 + 0.13665) = [(1 + 0.085)(1.2545) / 1.1975]

1.13665 = [(1.085)(1.2545) / 1.1975] =

1.13665 = 1.36113 / 1.1975 =

1.13665 = 1.13665 = 0, therefore no arbitrage profit can be made.

土豆妮

If 1 + the domestic interest rate < (1 + the foreign interest rate * the forward rate)/spot rate, an investor seeking arbitrage profits should borrow:

A) foreign, convert to domestic, lend out domestic, and convert back to foreign.

B) domestic, convert to foreign, borrow foreign, and convert back to domestic.

C) domestic, lend out foreign, and convert back to domestic.

土豆妮

If 1 + the domestic interest rate < (1 + the foreign interest rate * the forward rate)/spot rate, an investor seeking arbitrage profits should borrow:

A) foreign, convert to domestic, lend out domestic, and convert back to foreign.

B) domestic, convert to foreign, borrow foreign, and convert back to domestic.

C) domestic, lend out foreign, and convert back to domestic.

---

If 1 + r_D < (1 + r_F)(forward rate) / spot rate, then borrow domestic, lend out foreign, and convert back to domestic.

土豆妮

The forward rate between Swiss francs and U.S. dollars is 1.8 SF/$ and the current spot rate is 1.90 SF/$. The Swiss interest rate is 8.02% and the U.S. rate is 11.02%. Assume you can borrow francs or dollars and you live in Switzerland. If an arbitrage opportunity exists, how can you take advantage of it?

A) Borrow domestic currency.

B) Borrow foreign currency.

C) Lend foreign currency.

土豆妮

The forward rate between Swiss francs and U.S. dollars is 1.8 SF/$ and the current spot rate is 1.90 SF/$. The Swiss interest rate is 8.02% and the U.S. rate is 11.02%. Assume you can borrow francs or dollars and you live in Switzerland. If an arbitrage opportunity exists, how can you take advantage of it?

A) Borrow domestic currency.

B) Borrow foreign currency.

C) Lend foreign currency.

---

Borrow foreign if 1 + r_D> [(1 + r_F)(forward rate)] / spot rate

1 + 0.0802 > [(1 + 0.1102)(1.8)] / 1.9

1.0802 > 1.99836 / 1.9

1.0802 > 1.0518 therefore borrow foreign (dollars) and lend domestic (francs).

Alternatively, U.S. rate is 11.02 ? 8.02 = 3% higher and USD is at (1.8 ? 1.9) / 1.9 = 5.3% discount since USD will fall more than the extra 3% interest, better to lend francs.