Work It Out, Chapter 13, Question 1

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
This problem will ask you to consider a Dutch investor with 1,000 euros to place in a bank deposit in either the Netherlands or Great Britain. The (one-year) interest rate on bank deposits is 1 percent in Britain and 5 percent in the Netherlands. The (one-year) forward euro–pound exchange rate is 1.65 euros per pound and the spot rate is 1.5 euros per pound. Answer the following questions, using the exact equations for uncovered interest parity (UIP) and covered interest parity (CIP) as necessary. We begin by setting up the problem. The Dutch investor has 1 thousand euros, so the deposit amount equals 1 thousand euros.

(Description)
The following text is written: Deposit equals 1000 euros.

(Speaker)
The Great Britain interest rate is 1 percent.

(Description)
The following text is written below the previous one: I subscript the pound sign (Great Britain) equals 1 percent.

(Speaker)
The Netherlands interest rate is 5 percent.

(Description)
The following text is written below the previous one: I subscript the euro sign (Netherlands) equals 5 percent (Citizens of Netherlands are also known as a Ducth).

(Speaker)
The forward euro–pound exchange rate is 1.65.

(Description)
The following text is written below the previous one: F subscript the euro sign over the pound sign equals 1.65.

(Speaker)
The spot euro–pound exchange rate is 1.5.

(Description)
The following text is written below the previous one: E subscript the euro sign over the pound sign equals 1.5.

(Speaker)
Be careful and use the correct symbols. Question (a) will ask for the euro-denominated return on Dutch deposits for this investor. We start by identifying the correct formula for the euro return on euro deposits and writing it down.

(Description)
The following relation is written: euro return on euro deposit equals deposit multiplied by the sum of 1 and i subscript the euro sign.

(Speaker)
Then, using the information we already identified when we set up the problem, we plug in the correct values. The answer is a thousand 50 euro.

(Description)
The previous relation changes into the following one: euro return on euro deposit equals 1000 euro multiplied by the sum of 1 and 0.05 equals 1050 euro.

Work It Out, Chapter 13, Question 2

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (b) will ask for the euro-denominated return on British deposits for this investor. We start by identifying the correct formula for the euro return on British deposits and writing it down.

(Description)
The following relation is written: euro return on euro deposit equals deposit multiplied by the sum of 1 and i subscript the euro sign multiplied by F subscript the euro sign over the pound sign divided by E subscript the euro sign over the pound sign.

(Speaker)
Then, using the information we already identified when we set up the problem, we plug in the correct values. The answer is 1 thousand 111 euro.

(Description)
The previous relation transforms into the following one: euro return on euro deposit equals 1000 euro multiplied by the sum of 1 and 0.01 multiplied by 1.11 equals 1111 euro.

Work It Out, Chapter 13, Question 3

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (c) will ask you to decide if the answers to Questions (a) and (b) suggest any arbitrage opportunity and to explain why or why not. It also will ask if the answers to Questions (a) and (b) suggest that the forward exchange rate market is in equilibrium. There is a clear arbitrage opportunity. Comparing the values of the euro return on euro investment with the value of the euro returns on British investments, we conclude that investing the 1 thousand euro in Great Britain will bring 1 thousand 111 minus 1 thousand and 50 equals 61 more euros than investing in the Netherlands.

(Description)
The following relation is written: 1050 euro - 1111 euro equals negative 61.

(Speaker)
Since there is an opportunity for arbitrage, the market is not in equilibrium. Investors will move their money from the Netherlands to Great Britain until the interest rates in the Netherlands and Great Britain equalize and CIP will hold.

Work It Out, Chapter 13, Question 4

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (d) will ask for the equilibrium forward rate (according to CIP) If the spot rate is 1.5 euros per pound, and interest rates are as stated previously. We start by identifying the correct equilibrium forward rate formula and writing it down.

(Description)
The following relation is written: F subscript the euro sign over the pound sign equals E subscript the euro sign over the pound sign multiplied by the sum of 1 and i subscript the euro sign divided by the sum of 1 and i subscript the pound sign.

(Speaker)
Then, using the information we already identified when we set up the problem, we plug in the correct values. The answer is 1.56.

(Description)
The previous relation transforms into the following one: F subscript the euro sign over the pound sign equals 1.5 multiplied by the sum of 1 and 0.05 divided by the sum of 1 and 0.01 equals 1.5 multiplied by 1.05 over 1.01 equals 1.56.

Work It Out, Chapter 13, Question 5

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (e) will ask you to compute the forward premium on the British pound for the Dutch investor (where exchange rates are in euros per pound), to identify the sign of the forward premium, and to explain why investors require this premium/discount in equilibrium. Hint: assume the forward rate takes the value given by your answer to (d). We start by identifying the correct equilibrium forward rate formula and writing it down.

(Description)
The following relation is written: forward premium equals the fraction with F subscript the euro sign over the pound sign in the numerator, and E subscript the euro sign over the dollar sign in the denominator, minus 1.

(Speaker)
Then, using the information we already identified when we set up the problem, we plug in the correct values. The answer is 0.04 or 4 percent.

(Description)
The previous relation transforms into the following one: forward premium equals 1.56 over 1.5 minus 1 equals 1.04 minus 1 equals 0.04 or 4 percent.

(Speaker)
The value is positive. A positive forward premium implies that investors expect the euro to depreciate relative to the British pound. Therefore, when establishing forward contracts, the forward rate is higher than the current spot rate.

Work It Out, Chapter 13, Question 6

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (f) asks you compute the expected depreciation of the euro (against the pound) over one year, assuming UIP holds. We know from UIP that Forward premium equals Expected rate of depreciation.

(Description)
The following relation is written: forward premium equals expected rate of depreciation.

(Speaker)
The expected rate of depreciation equals the forward premium value computed for question (e) and is 0.04 or 4 percent.

(Description)
The previous relation transforms into the following one: 0.04 equals 4 percent equals expected rate of depreciation.

Work It Out, Chapter 13, Question 7

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (g) asks you compute the expected euro–pound exchange rate one year ahead while considering the answer to question (f). We can demonstrate that the expected exchange rate one year ahead equals the forward exchange rate.

(Description)
The following relations are written: The fraction with F subscript the euro sign over the pound sign in the numerator, and E subscript the euro sign over the pound sign in the denominator, minus 1 equals the fraction with F superscript e subscript the euro sign over the pound sign in the numerator, and E subscript the euro sign over the pound sign in the denominator, minus 1. The fraction with F subscript the euro sign over the pound sign in the numerator, and E subscript the euro sign over the pound sign in the denominator, equals the fraction with F superscript e subscript the euro sign over the pound sign in the numerator, and E subscript the euro sign over the pound sign in the denominator, minus 1 plus one. The fraction with F subscript the euro sign over the pound sign in the numerator, and E subscript the euro sign over the pound sign in the denominator, equals the fraction with F superscript e subscript the euro sign over the pound sign in the numerator, and E subscript the euro sign over the pound sign in the denominator.

(Speaker)
Start with the formula showing that that the forward premium equals the expected rate of depreciation. Observing that the ones will cancel, it follows that the ratio between the forward rate and the spot rate equals the ratio between the expected rate and the spot rate. However, since the denominators are equal, it follows that the numerators are also equal. The expected exchange rate equals the forward exchange rate computed for question (d) and is 1.56.

(Description)
The following relation is written below the previous ones: F superscript e subscript the euro sign over the pound sign equals E subscript the euro sign over the pound sign equals 1.56 (computed at question d).