CFA论坛 - Powered by Discuz! Board

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

(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

A)	borrow domestic currency and lend out foreign currency.

B)	arbitrage opportunities don't exist.

C)	borrow foreign currency and lend out domestic currency.

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.

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?

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.

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 + 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.

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.

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.

The spot rate for the dollar is 0.1432 $/ADF. Andorran and U.S. interest rates are 6.6% and 7.2%, respectively. If the 1-year forward rate is 0.1430 $/ADF, a U.S. investor could earn an arbitrage dollar profit per ADF of:

Let us first check if an arbitrage opportunity exists. Applying the interest rate parity theorem, we have:

Forward rate = 0.1432 × 1.072/1.066 = 0.1440 $/ADF > 0.1430 $/ADF (quoted forward rate)

This implies that an arbitrage opportunity exists. The inequality implies that ADF is mispriced (weak) in the forward market or is underpriced relative to the dollar. We should buy ADF in the forward market and sell the dollar in the spot market. This requires that we borrow in Andorra and convert the francs into dollars at the spot rate. Invest the proceeds in U.S. securities @ 7.2%, and simultaneously enter into a forward transaction where we sell the dollars for ADF @ 0.1430 $/ADF. Assuming that we borrow 1 ADF today and convert it into dollars, we will have 0.1432 dollars to invest at 7.2% for one year. After one year we will have 0.1432 × 1.072 = 0.1535 dollars. At that point, we will owe an Andorran bank 1 × 1.066 or 1.066 ADF, including interest. We will need to convert enough dollars at the forward rate to pay off this loan. At the forward contract rate, we will need to convert 1.066 × 0.1430 = 0.1524 dollars into ADF to pay off our obligation. This will leave us with an arbitrage profit of 0.1535 ? 0.1524 = 0.0011 dollars.

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

A)	borrow local currency and lend out foreign currency to earn arbitrage profits.

B)	borrow foreign currency and lend out local currency to earn arbitrage profits.

C)	you cannot determine if arbitrage opportunities exist with the data given.

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

A)	borrow local currency and lend out foreign currency to earn arbitrage profits.

B)	borrow foreign currency and lend out local currency to earn arbitrage profits.

C)	you cannot determine if arbitrage opportunities exist with the data given.

If (r_D ? r_F) < Forward premium, which is (Forward D/F) ? Spot(D/F) / Spot(D/F), then you would borrow domestic currency and lend out foreign currency. The domestic rate is low relative to the hedged foreign rate. You would borrow domestic currency units and convert them to foreign currency at the current spot rate, lend at the foreign currency interest rate, and simultaneously sell just enough foreign currency units forward to convert your foreign loan proceeds.

A)	flow in and out of the domestic country.

B)	flow into the domestic country.

C)	flow out of the domestic country.

A)	flow in and out of the domestic country.

B)	flow into the domestic country.

C)	flow out of the domestic country.

This equation is Interest Rate Parity rearranged! If the term on the left (1 + r_domestic), is less than the term on the right, it means that the domestic rate is low relative to the hedged foreign rate. Therefore, there is a profitable arbitrage from borrowing the domestic currency and lending at the foreign interest rate.

Because we lend in the foreign market, we say that the funds flow out of the domestic economy.

The interest rates in the U.S. and Great Britain are 7.23% and 6.94% respectively. The forward rate is 1.70$/? and the spot rate is 1.73$/?. Which currency would an investor borrow, if any, to make an arbitrage profit?

Use the following formula to determine if an arbitrage opportunity exists and which currency to borrow.

if 1 + r_D > [(1 + r_F)(Forward rate)] / Spot rate then borrow foreign.

1.0723 > [(1.0694)(1.70)] / 1.73

1.0723 > 1.81798 / 1.73

1.0723 > 1.0509, therefore borrow foreign (pounds).

Alternatively, the dollar is appreciating. [(1.73 ? 1.70) / 1.70] = 1.76% and the $U.S. interest rate is higher. Clearly, investing in $U.S. (and borrowing pounds) is the way to go.

The annual interest rate is 8.02% in Mexico and 7.45% in Canada. The spot peso-dollar exchange rate is 569.87 MXN/CAD, and the one-year forward rate is 526.78 MXN/CAD. If an arbitrage opportunity exists, how much would a person living in Mexico make borrowing 15,000,000 pesos or the equivalent in Canadian dollars?

Note that peso is at a forward premium (less pesos per CAD in the future) and that peso interest rate is higher. Therefore it is clear there are arbitrage profits from lending in pesos and borrowing CAD.

First convert to Canadian dollars to determine the amount of interest due at the end of the year. (15,000,000 MXN) × (CAD/569.87 MXN) = 26,321.79 CAD.

26,321.79 CAD × 0.0745 = 1,960.97 CAD interest due at the end of the year.

Lend out pesos 15,000,000 pesos × 1.0802 = 16,203,000 pesos received at the end of the year.

Convert to Canadian dollars (16,203,000 MXN) × (CAD/526.78 MXN) = 30,758.57 CAD.

Subtract the original loan amount and interest: 30,758.57 ? 26,321.79 (original loan) ? 1,960.97 (interest) = 2,475.81 CAD profit.

Convert the remainder back to pesos: (2,475.81 CAD) × (526.78 MXN/CAD) = 1,304,207.19 peso profit.

The annual interest rates in England and New Zealand are 6.54% and 7.03%, respectively. The one-year forward exchange rate between the British pound and the New Zealand dollar is 0.45 GBP/NZD and the spot rate is 0.41 GBP/NZD. If a person living in London can borrow 10,000 pounds or the equivalent amount in New Zealand dollars, how much arbitrage profit, if any, can he make?

Borrow 10,000 GBP at 6.54% = 654 GBP interest due at the end of the year.
Convert to NZD: (10,000 GBP) × (1 NZD/0.41 GBP) = 24,390 NZD.
Lend out NZD at 7.03% interest: (24,390 NZD) × (1.0703) = 26,104.88 NZD.
Convert back to GBP: (26,104.88 NZD) × (0.45 GBP/NZD) = 11,747.20 GBP.
11,747.20 GBP ? 10,000 GBP (original amount borrowed) ? 654 GBP interest = 1,093.20 GBP profit.

The forward rate between the Mexican peso and the U.S. dollar is 556.75 MXN/USD and the spot rate is 581.23 MXN/USD. The Mexican interest rate is 5.89%, and the U.S. rate is 5.75%. If a person lives in Mexico and can borrow $10,000 or the equivalent in pesos, how much can she make if currency arbitrage opportunities exist?

First determine if arbitrage opportunities exist by using the following equation:

if 1 + r_D > [(1 + r_F)(Forward rate)] / Spot rate, then borrow foreign (dollars).

1.0589 > [(1.0575)(556.75)] / 581.23

1.0589 > 588.763 / 581.23

1.0589 > 1.01296, therefore, borrow foreign (dollars).

Borrow $10,000 at 5.75%, interest = $575 due at the end of the year. Convert to pesos using the spot rate: ($10,000) × (581.23 MXN/USD) = 5,812,300 pesos.

Lend out at 5.89%: (5,812,300 pesos) × (1.0589) = 6,154,644.47 pesos. Convert to dollars: (6,154,644.47 MXN) × (USD/556.75 MXN) = $11,054.59. $11,054.59 ? $10,000 (original amount borrowed) ? $575 (interest) = $479.59 profit.

The spot rate between the Canadian dollar and the British pound is 1.265 CAD/? and the forward rate is 1.193 CAD/?. The interest rate in Canada and England are 6.13% and 6.01%, respectively. A person living in Toronto, Canada can borrow either Canadian dollars or pounds. If an arbitrage opportunity exists, which currency would they lend or borrow?

Use the following formula to determine if an arbitrage opportunity exists and which currency to borrow.

if 1 + r_D > [(1 + r_F)(Forward rate)] / Spot rate, then borrow foreign.

1.0613 > [(1.0601)(1.193)] / 1.265

1.0613 > 1.265 / 1.265

1.0613 > 1 therefore borrow foreign (British pound) and lend domestic (Canadian dollar).

If: 1 + r_D <	(1 +r_F)(forward rate)	funds will:
	spot rate

If: 1 + r_D <	(1 +r_F)(forward rate)	funds will:
	spot rate