Elements of internantional finance

Question 1

What is spot exchange rate and forward market for currency?
Is currency only for a medium of exchange?

Answer 1

The spot exchange rate is the current price to exchange one currency for another in the foreign exchange market. ( for this pack home currency is pounds and foreign currency is dollar),

The forward market is where participants agree to exchange currencies at a predetermined rate on a future date, using forward exchange rates.

No currency is a financial asset.

Question 2

We know that there is a lot of exchange rate risk for people and companies, hence entering into forward contracts hedge this risk, how do you denote this and spot exchange rate?

Answer 2

S is the spot exchange rate.

Question 3

What is the forward premium/discount?

Answer 3

Forward premium is the annualised percentage difference between the forward rate and the spot exchange rate. ( forward premium per day) .

Question 4

If the FP > 0 what does this mean. If the FP<0 what does it mean?

Answer 4

Question 5

How are forward contracts priced?

Answer 5

they priced to a similar principle of the absence of arbitrage.So if there is no arbitrage an investor cannot borrows money in a country with a lower interest rate and invest it in a country with a higher interest rate , while simultaneously covering the exchange rate risk with a forward contract. The net profit should be zero,

Question 6

Lets say
r is the interest rate in the home country (UK);
– r* is the interest rate in the foreign country (US).
And F is the one year forward price, no arbitrage pricing implies that the forward exchange rate = what? ( what is the overarching name given here?
In other words the one year forward rate)

Answer 6

f

Question 7

Suppose this is violated, how can we make arbitrage? but first of all what does this mean?

Answer 7

When F < S * (1+r)/(1+r*), the forward exchange rate is lower than the expected future spot exchange rate. This means that the cost of converting the foreign currency back to the home currency using the forward contract is less than what it should be according to CIP ( or f you were to exchange it at the expected future spot rate.).

Question 8

What is the arbitrage strategy now?

Answer 8

1) At t = 0 borrow $1 at the interest rate r*.
2) At t = 0 we convert the $1 into £S pounds using current spot exchange rate, then invest in UK bonds or bank account, in which we earn interest rate of r.
3) At t = 0 take long position in currency forward ( i.e commit to buy $ in one year at price $F) so we are hedging risk here because we borrowed in the uk.
4) At t = 1 we will get money from our UK investment and convert profit into $ at the forward price and repay your loan

Question 9

Lets say the inequality is the other way round, then how can we make aribitrage profit? Not sure this is correct btw?

Answer 9

1) Borrow a certain amount of money in the home currency (GBP) at the home interest rate (r).
2) Convert the borrowed amount into the foreign currency (USD) using the current spot exchange rate (S).
3) Invest the converted amount in the foreign country (US) at the foreign interest rate (r*).
4) Simultaneously enter into a forward contract to sell the foreign currency (USD) back to the home currency (GBP) at the specified forward exchange rate (F) at the end of the investment period.
5) After the investment period ends, repay the borrowed amount in the home currency (GBP) along with the interest (1+r).

Question 10

What is the CIP then investment horizon is not one year ( e.g. days? )

Answer 10

Question 11

How can we write the forward premium approxmiation for small rates?

Answer 11

So tells us FP is due to interest rate differential.

Question 12

What is the unbiased expectations hypothesis?

Answer 12

that the expected future spot exchange rate is equal to the current forward exchange rate. In other words, the market’s expectation of the future spot rate is reflected in the current forward rate ( remember these are determinant on supply and demand)

Question 13

Do the same for the other way round? Why is there no arbitrage opportunity here?

Answer 13

If Everyone is risk neutral, the market will push the forward rate down, until the left hand side and right hand side become equal.

There is no arbitrage as investors are risk neutral, they don’t care about the risks.

Question 14

What is the uncovered interest parity ( Hint it combines the CIP and UEH)? there are 2 ways we can write it?

Answer 14

the expected currency return = the interest rate differential between the 2 countries.

Question 15

Why doesn’t the unbiased expectations hypothesis? hold in the data?

Answer 15

Exchange rate risk arises from fluctuations in exchange rates when investing in foreign assets. If the forward rate inaccurately predicts the future spot rate, investors may face gains or losses, leading to a demanded risk premium. This risk premium causes deviations from the unbiased expectations hypothesis and may result in a non-zero estimate of ‘a’, representing the risk premium.
Hence when testing it a doesn’t equal 0 because ’a’ is the estimate of the risk premium.

Question 16

So far exchange rates have been determined in financial markets, but now we will see exchange rates will be developed in the market for goods and services ( so now we will be looking at the market for goods and services internally) first of all what is the law of one price for same goods but in different countries?

Answer 16

Law of One Price: If nothing prevents arbitrage in international goods markets e..g no shipping and transaction costs, then identical goods should sell for the same price (when evaluated in a common currency). ( also known as commodity price parity - similar commodities should be traded at similar prices)
If goods do not sell for the same price, then there is an arbitrage opportunity:
– Buy low; – Sell high.
e.g. bananas in the us should have the same price as bananas in the uk.

Question 17

What is the arbitrage strategy?

Answer 17

Question 18

If the law of one price holds then what is absolute Purchasing power parity?

Answer 18

Price in the home country = Price in foreign country x exchange rate. the exchange rate between two currencies should be equal to the ratio of the price levels in the respective countries.

Question 19

Let’s consider two countries, the US and the UK. The price of a specific product in the US (home country) is $50, and the price of the same product in the UK (foreign country) is £40. According to the absolute PPP theory what is the price? why does the ABSOLUTE PPP RARELY HOLD?

Answer 19

the exchange rate between USD and GBP should be:
St = Pt/Pt*

To find the exchange rate, we can plug in the values into the formula:

St= $50 / £40
St = $1.25/£1.
This implies that the exchange rate should be $1.25 per £1, making the cost of the product the same in both countries when expressed in a common currency.

However, it’s important to note that absolute PPP rarely holds in practice due to factors such as differences in product quality, transportation costs, taxes, tariffs, and other market frictions that can cause price discrepancies across countries.

Question 20

So we know that Absolute PPP can be violated, so actually there is a correction term of the exchange rate, now nothing related to this directly yet but what is the formula for the change in realised return, and change in domestic and foreign inflation from t to T? btw the change in R = 0, as we assume its constant. Also convert this equation using the answers you have derived for the changes?
Write the changes n the exchange as a function of prices?

Answer 20

Wchange in R = 0 as we assume the constant is 0

Question 21

Now write s in terms of inflation rate differential? known as relative PPP?

Answer 21

so it tells us that the change in exchange rates is approximately equal to the difference in inflation rate between the 2 countries. If a country has a higher inflation rate than another, its currency is expected to lose value compared to the other country’s currency.

Question 22

What are empirical finds of the relative PPP?

Answer 22

this relative PPP doesn’t perform well in empirically in short horizons ( 1 day to 5 years, exchange rates depend not only on goods market) but performs relatively well for long horizons ( 10-20 years, tendency of nominal exchange rates to move with inflation differentials towards PPP levels)

Question 23

What is real exchange rate?

Answer 23

the real exchange rate shows how much you can buy in one country using another country’s currency, considering both the exchange rate and the difference in prices between the two countries.

Inuition you could buy a number of R of Uk baskets for every foreign basket purchased?

Question 24

Let’s consider two countries: the United States (home country) and the United Kingdom (foreign country). Suppose we have the following data:

St (nominal exchange rate): $1.40 per £1
Pt (price level in the US): 110 (US Consumer Price Index)
Pt* (price level in the UK): 100 (UK Consumer Price Index). What is the real exchange rate.

Answer 24

Using the formula for the real exchange rate, we can calculate Rt as follows:

Rt = St x Pt* / Pt
Rt = ($1.40/£1) x (100 / 110)
Rt = $1.273/£1

Question 25

What is the fishers equation?

Answer 25

Where the nominal interest rate approximately is the expected real returns + expected rate of inflation.

Question 26

Investors do tend to look at real interest rates, so invest where real interest rates are higher, so in open economies where we have a few trading frictions then what?

Answer 26

the expected real rates across economies should be equal

Question 27

What is the difference between relative PPP and Absolute PPP?

Answer 27

Relative Purchasing Power Parity (PPP) is an economic theory that suggests the changes in exchange rates between two currencies are primarily driven by changes in their relative inflation rates. It is an extension of the Absolute PPP concept, which states that the exchange rate between two currencies should equal the ratio of the price levels in the two countries.

Question 28

What is the international fisher relation ( can be used to rearrange to find the one year interest rate)?

Answer 28

These are all one year time rates. ( forget Switzerland and uk ( the home country is Switzerland and foreign is uk)

Question 29

what is the Uncovered Interest Parity (UIP) in words?

Answer 29

Uncovered Interest Parity (UIP) simply states that the expected change in exchange rates between two currencies is equal to the difference in their interest rates. It implies that there should be no expected profit from investing in different currencies when considering the interest rate differences and expected exchange rate movements.

Question 30

What is another way to write relative PPP? if you wanna find out the exchange rate expected to be in one year?

Answer 30