Question 1

Interest Rate Parity (IRP)is best defined as

Accepted Answer

Interest Rate Parity (IRP) is primarily an arbitrage condition that must hold when international financial markets are in equilibrium. It assumes that the expected returns from hypothetical investments in two different currencies would be the same, and any deviation from this condition would provide an opportunity for arbitrage. Therefore, IRP represents the equilibrium relationship between the interest rates, exchange rate, and inflation rates of two different currencies. Options A and B are inaccurate as they do not entirely capture the concept of IRP.

Question 2

Suppose you observe a spot exchange rate of $1.0500/€.If interest rates are 5% APR in the U.S.and 3% APR in the euro zone,what is the no-arbitrage 1-year forward rate?

Accepted Answer

To calculate the no-arbitrage 1-year forward rate, we use the following formula:

(1 + rU.S) = (F/S) x (1 + rEuro)

where rU.S and rEuro are the respective interest rates, S is the spot exchange rate, and F is the forward exchange rate.

Plugging in the given values, we get:

(1 + 0.05) = (F/1.0500) x (1 + 0.03)

Solving for F, we get:

F = 1.0704

Since we want to find the euro-denominated forward rate, the answer is $1.0704/€.

Question 3

Covered Interest Arbitrage (CIA)activities will result in

Accepted Answer

Covered Interest Arbitrage (CIA) activities involve taking advantage of temporary differences in interest rates between different currencies to make profit through buying and selling of currency. This process helps to restore equilibrium prices quickly by narrowing the spread between the interest rates of the two currencies. Therefore, choice B is the best answer. CIA activities may also lead to a reduction in the volatility of international financial markets as arbitrageurs tend to exploit mispricing and restore market efficiency.

Question 4

Suppose that the one-year interest rate is 4.0 percent in Italy,the spot exchange rate is $1.60/€,and the one-year forward exchange rate is $1.58/€.What must the one-year interest rate be in the United States?

Accepted Answer

According to Interest rate parity (IRP), the forward exchange rate is calculated as follows:

Forward exchange rate = spot exchange rate x (1 + domestic interest rate) / (1 + foreign interest rate)

Given:
Spot exchange rate (S) = $1.60/€
Forward exchange rate (F) = $1.58/€
Domestic interest rate (id) = 4.0% (in Italy)
Foreign interest rate (if) = ?

Substituting the values in the formula, we get:

$1.58/€ = $1.60/€ x (1 + 0.04) / (1 + if)
1.58 / 1.60 = 1.04 / (1 + if)

Solving for foreign interest rate (if), we get:

if = 0.027 or 2.7%

Therefore, the one-year interest rate in the United States must be 2.7% to maintain interest rate parity. Hence, the correct answer is option B) 2.7%.

Question 5

Suppose that the one-year interest rate is 3.0 percent in Italy,the spot exchange rate is $1.20/€,and the one-year forward exchange rate is $1.18/€.What must the one-year interest rate be in the United States?

Accepted Answer

Using the interest rate parity formula: (1 + i_US) = (1 + i_Italy) * (Forward Rate / Spot Rate). Plugging in the values: (1 + i_US) = (1 + 0.03) * (1.18 / 1.20), we find i_US ≈ 0.012833 or 1.2833%.

Question 6

A currency dealer has good credit and can borrow either $1,000,000 or €800,000 for one year.The one-year interest rate in the U.S.is i_$ = 2% and in the euro zone the one-year interest rate is i_€ = 6%.The spot exchange rate is $1.25 = €1.00 and the one-year forward exchange rate is $1.20 = €1.00.Show how to realize a certain profit via covered interest arbitrage.

Accepted Answer

Option D provides two ways to generate profit. Firstly, borrowing €800,000 at i_€ = 6% and investing in the U.S. at i_$ = 2% for one year will yield a profit of $2,400 when the euro is converted back to dollars at a forward rate of $1.20 = €1.00. Additionally, one can borrow €800,000 at i_€ = 6%, invest in the U.S. at i_$ = 2% for one year, and convert back €850,000 into euro at the forward rate of $1.20 = €1.00 to make a profit of €2,000. Therefore, option D provides the best choice for covered interest arbitrage.

Question 7

Suppose that the one-year interest rate is 5.0 percent in the United States and 3.5 percent in Germany,and that the spot exchange rate is $1.12/€ and the one-year forward exchange rate,is $1.16/€.Assume that an arbitrageur can borrow up to $1,000,000.

Accepted Answer

To determine whether interest rate parity holds, we need to compare the expected returns from investing in each currency directly versus investing in the other currency through the forward markets.

In the US, investing $1,000,000 at 5.0% for one year would yield $1,050,000 at the end of the year.

In Germany, investing €892,857 (equivalent to $1,000,000/1.12) at 3.5% for one year would yield €924,107 at the end of the year, which could be exchanged for $1,075,610 at the spot rate of $1.16/€.

Thus, investing in the US directly would give a return of $50,000, while investing in Germany through the forward market would give a return of $75,610. This represents an arbitrage opportunity for the investor to borrow $1,000,000 at 5.0% in the US, exchange it for €892,857, invest it in Germany at 3.5%, and then exchange the proceeds at the one-year forward rate to receive $1,075,610, resulting in a risk-free profit of $25,610.

Therefore, choice B is correct as this is an example of an arbitrage opportunity where interest rate parity does not hold.

Question 8

Suppose that the annual interest rate is 5.0 percent in the United States and 3.5 percent in Germany,and that the spot exchange rate is $1.12/€ and the forward exchange rate,with one-year maturity,is $1.16/€.Assume that an arbitrager can borrow up to $1,000,000.If an astute trader finds an arbitrage,what is the net cash flow in one year?

Accepted Answer

The net cash flow from the arbitrage can be calculated by taking advantage of the difference in interest rates and the forward exchange rate. The trader can borrow dollars at 5.0 percent, convert to euros at the spot rate, invest at the German interest rate of 3.5 percent, and then convert back to dollars at the forward rate. The calculation is as follows:1. Borrow $1,000,000 at 5.0% interest rate.2. Convert $1,000,000 to euros at the spot rate of $1.12/€, which gives $1,000,000 / 1.12 = €892,857.14.3. Invest €892,857.14 at 3.5% interest rate in Germany, which results in €892,857.14 * 1.035 = €924,206.89 after one year.4. Convert €924,206.89 back to dollars at the forward rate of $1.16/€, which gives €924,206.89 * 1.16 = $1,072,079.99.5. Repay the original loan plus interest in dollars, which is $1,000,000 * 1.05 = $1,050,000.The net cash flow is $1,072,079.99 - $1,050,000 = $22,079.99. However, since the closest answer provided is $21,964.29, it appears there might have been a slight miscalculation in the final step or rounding differences in the calculation process. The correct process leads to a conclusion closest to option D, acknowledging a minor discrepancy in the final calculation.

Question 9

An arbitrage is best defined as

Accepted Answer

Arbitrage involves the simultaneous purchase and sale of the same or equivalent assets or commodities in different markets or in derivative forms to exploit price differences for guaranteed profits. This strategy is predicated on the certainty of profit due to existing price discrepancies, rather than on speculation or risk-taking.

Question 10

Suppose that the one-year interest rate is 5.0 percent in the United States; the spot exchange rate is $1.20/€; and the one-year forward exchange rate is $1.16/€.What must the one-year interest rate be in the euro zone to avoid arbitrage?

Accepted Answer

To avoid arbitrage, the interest rate parity condition should hold. That means the following equation must hold:

(1 + US interest rate) = (1 + euro interest rate) * (forward exchange rate / spot exchange rate)

Plugging in the given values:

(1 + 0.05) = (1 + euro interest rate) * (1.16/1.20)

Solving for the euro interest rate:

1.05 = (1 + euro interest rate) * 0.9667
1.05 / 0.9667 = (1 + euro interest rate)
euro interest rate = 1.0862 - 1 = 0.0862 = 8.62%

Therefore, the one-year interest rate in the euro zone must be 8.62% to avoid arbitrage. So, the correct answer is option C.

Question 11

A formal statement of IRP is

Accepted Answer

This formula is known as the Interest Rate Parity (IRP) theory, which states that the difference in interest rates between two countries is equal to the difference between the forward exchange rate and the spot exchange rate. Choice A represents this theory in its formal statement where F($/€) is the forward exchange rate, S($/€) is the spot exchange rate, i$ is the interest rate in the US, and i€ is the interest rate in the Eurozone.

Question 12

Suppose that the annual interest rate is 2.0 percent in the United States and 4 percent in Germany,and that the spot exchange rate is $1.60/€ and the forward exchange rate,with one-year maturity,is $1.58/€.Assume that an arbitrager can borrow up to $1,000,000 or €625,000.If an astute trader finds an arbitrage,what is the net cash flow in one year?

Accepted Answer

The answer of Suppose that the annual interest rate is...

Question 13

How high does the lending rate in the euro zone have to be before an arbitrageur would not consider borrowing dollars,trading for euro at the spot,investing in the euro zone and hedging with a short position in the forward contract? $$\begin{array} { r c c c c } 
& \text { Bid } & \text { Ask } & \text { Borrowing } & \text { Lending } \
\boldsymbol { s } _ { 0 } ( \$ / € ) & \$ 1.40 - € 1.00 & \$ 1.43 - € 1.00 & \text { i\$ } 4.20 \% \mathrm { APR } & 4.10 \% \mathrm { APR } \
F _ { 360( \$ / € ) } & \$ 1.44 - € 1.00 & \$ 1.49 - € 1.00 & \text { i€ } &
\end{array}$$

Accepted Answer

The arbitrage strategy involves borrowing dollars, converting them to euros at the spot rate, investing in the euro zone, and hedging the investment with a short position in the forward contract. The profit of the strategy is the difference between the euro zone interest rate and the dollar borrowing rate, minus the cost of the forward contract.

Let's calculate the profit of the strategy:
Profit = (Euro zone interest rate - Dollar borrowing rate) - (Forward rate - Spot rate)/Spot rate

We want to find the euro zone interest rate at which the profit becomes zero, i.e., when the cost of the forward contract equals the interest rate differential.

0 = (Euro zone interest rate - Dollar borrowing rate) - (Forward rate - Spot rate)/Spot rate

Euro zone interest rate = Dollar borrowing rate + (Forward rate - Spot rate)/Spot rate

Euro zone interest rate = 4.20% + (1.49 - 1.43)/1.43 = 4.20% + 0.042 = 4.242%

Therefore, the lending rate in the euro zone has to be at least 4.242% for the arbitrageur not to consider borrowing dollars and investing in the euro zone. The closest answer option is B) 3.48%, which is less than 4.242%, so it is not a high enough rate to deter the arbitrageur.

Question 14

Suppose that you are the treasurer of IBM with an extra U.S.$1,000,000 to invest for six months.You are considering the purchase of U.S.T-bills that yield 1.810 percent (that's a six month rate,not an annual rate by the way)and have a maturity of 26 weeks.The spot exchange rate is $1.00 = ¥100,and the six month forward rate is $1.00 = ¥110.The interest rate in Japan (on an investment of comparable risk)is 13 percent.What is your strategy?

Accepted Answer

Investing in Japan offers a higher interest rate (13%) compared to the U.S. T-bills (1.810%). By converting dollars to yen at the current spot rate and then hedging the investment with a short position in the forward contract, you lock in the exchange rate for converting yen back to dollars in six months, mitigating currency risk while benefiting from the higher interest rate.

Question 15

Suppose you observe a spot exchange rate of $2.00/£.If interest rates are 5 percent APR in the U.S.and 2 percent APR in the U.K.,what is the no-arbitrage 1-year forward rate?

Accepted Answer

To calculate the no-arbitrage forward rate, we need to use the Interest Rate Parity (IRP) equation:

F = S × (1 + r foreign ) / (1 + r domestic )

Where:
F = the no-arbitrage forward rate
S = the spot rate
r foreign = the foreign interest rate
r domestic = the domestic interest rate

Plugging in the given values, we get:

F = 2.00 × (1 + 0.02) / (1 + 0.05) = 2.0588

Since we want the forward rate for pounds per dollar, we take the reciprocal of 2.0588 and get:

1 / 2.0588 ≈ 0.4858

Therefore, the no-arbitrage 1-year forward rate is $2.0588/£.

Question 16

Suppose that you are the treasurer of IBM with an extra U.S.$1,000,000 to invest for six months.You are considering the purchase of U.S.T-bills that yield 1.810% (that's a six month rate,not an annual rate)and have a maturity of 26 weeks.The spot exchange rate is $1.00 = ¥100,and the six month forward rate is $1.00 = ¥110.What must the interest rate in Japan (on an investment of comparable risk)be before you are willing to consider investing there for six months?

Accepted Answer

To determine the interest rate in Japan that would make investing there attractive, we need to consider the covered interest arbitrage. The U.S. T-bills yield 1.810%, and the forward exchange rate implies a depreciation of the yen against the dollar. The correct answer, 1.991 percent, reflects the minimum yield in Japan that would make the investment there as attractive as the U.S. T-bills, considering the exchange rate movements and interest rates.

Question 17

An Italian currency dealer has good credit and can borrow €800,000 for one year.The one-year interest rate in the U.S.is i_$ = 2% and in the euro zone the one-year interest rate is i_€ = 6%.The spot exchange rate is $1.25 = €1.00 and the one-year forward exchange rate is $1.20 = €1.00.Show how to realize a certain euro-denominated profit via covered interest arbitrage.

Accepted Answer

Option C correctly outlines a covered interest arbitrage strategy that results in a certain profit. By borrowing €800,000 at 6%, converting it to dollars at the spot rate, investing at 2% in the U.S., and then converting back to euros at the forward rate, the dealer realizes a net profit of €2,000. This option correctly calculates the profit in euros, aligning with the initial borrowing and the final profit realization in the same currency.

Question 18

Suppose you observe a spot exchange rate of $1.0500/€.If interest rates are 3 percent APR in the U.S.and 5 percent APR in the euro zone,what is the no-arbitrage 1-year forward rate?

Accepted Answer

The answer of Suppose you observe a spot exchange rate...

Question 19

A U.S.-based currency dealer has good credit and can borrow $1,000,000 for one year.The one-year interest rate in the U.S.is i_$ = 2% and in the euro zone the one-year interest rate is i_€ = 6%.The spot exchange rate is $1.25 = €1.00 and the one-year forward exchange rate is $1.20 = €1.00.Show how to realize a certain dollar profit via covered interest arbitrage.

Accepted Answer

The answer of A U.S.-based currency dealer has good credit...

Question 20

When Interest Rate Parity (IRP)does not hold

Accepted Answer

When Interest Rate Parity (IRP) does not hold, there are opportunities for covered interest arbitrage. This means that an investor can borrow funds in a currency with a low interest rate, convert them into a currency with a higher interest rate, invest them in the higher interest rate country, and then convert the investment back into the low interest rate currency when the investment matures. This arbitrage opportunity would not exist if IRP were holding true. The other options, A and B, are not correct as high inflation is not always a factor in IRP not holding true and financial market equilibrium does not necessarily indicate whether IRP is holding true or not.

Quiz 6: International Parity Relationships and Forecasting Foreign Exchange Rates

Interest Rate Parity (IRP) is best defined as