Theory of Interest Rate Parity

1. Introduction

At present, the business world operates not only within the limits of a country but also transcends borders, so many companies have businesses abroad. Of course your objectives in international financial management are the same. You want to buy assets that are worth more than their cost, and you want to pay for them by issuing liabilities that are worth less than the money you get. It is in applying these criteria to international business that you face some additional problems.

The only peculiarity of international financial management is that you need to deal with more than one currency. Therefore, we will look at how international currency markets operate, why exchange rates vary, and what can be done to protect against this exchange rate risk.

The CFO should also remember that interest rates differ from country to country. For example, in the spring of 1990 the interest rate was 8% in the United States, 15% in Great Britain, and 40,000% in Brazil. We will discuss the reasons for these differences in interest rates, along with the implications for financial operations abroad. Should the parent company provide the money? Should you try to finance the operation locally? Or should you consider the world as your shell and go into debt wherever interest rates are lowest?

We will also discuss how international companies decide their capital investments. How do you choose the discount rate? How does the financing method affect the choice of the project? You'll find that the basic principles of capital budgeting are the same, but there are some pitfalls to watch out for.

2. The Foreign Exchange Market

Foreign Exchange Market

An American company that imports products from Switzerland buys Swiss francs, which it sells for dollars. The two companies make use of the foreign exchange market.

Except in a few European centers, the forex market does not have a central plaza. All business is conducted by telephone or telex. The main players are the largest commercial banks and central banks. Any company that wants to buy or sell foreign currency usually does so through a commercial bank.

The volume of business in the foreign exchange market is enormous. In London, nearly $ 200 billion change hands every day. The volume in New York and Tokyo is over 100 billion dollars a day.

In general, exchange rates in the United States are established in terms of the number of units of foreign currency needed to buy a dollar. So a rate of 1.3545 SFr / $ means that you can buy 1.3545 Swiss francs for $ 1. Or to put it another way, you need 1 / 1.3545 = 0.7383 dollars to buy a Swiss franc.

Table 34-1 reproduces a chart of exchange rates from the Wall Street Journal.

Unless otherwise stated, the table gives the price of a coin for immediate delivery. This is known as the spot exchange rate. You can check that the spot rate for the Swiss franc is 1.3545 SFr / $.

The term immediate delivery is relative; for a cash currency it is usual to buy against delivery within two days. For example, suppose you need 100,000 francs to pay for imports from Switzerland. On Monday he telephones his bank in New York and agrees to buy 100,000 francs at 1.3545 SFr / $. The bank does not give you a block of bills on the counter. Instead you instruct your Swiss correspondent bank to transfer

100,000 SFr on Wednesday to the account of the Swiss provider. The Bank debits your account 100,000 / 1.3445 = $ 73,828 either on Monday, or if you are a good customer on Wednesday.

In addition to a cash exchange market, there is a forward market. In the forward market you buy and sell the currency for future delivery, normally in 1.3 or 6 months, although in the main currencies banks are willing to buy or sell for up to ten years. If you know what you have to pay or receive in foreign currency at a future date, you can insure against losses by buying or selling forward. So if you need 100,000 francs in six months, you can enter into a six-month forward contract when the 100,000 francs is delivered.

If you look back at Table 34-1, you see that the six-month forward rate is set at 1.3618 SFr / $. If you buy Swiss francs for six-month delivery, you get more francs for your dollars than if you buy cash. In this case it is said that the franc is priced at a discount relative to the dollar, because forward francs are less expensive than cash francs. Expressed as an annual rate, the forward discount is:

2 x 1.3618 - 1.3545 x 100 = 1.07

1.3618

You can say that the dollar was selling at a 1.07% forward premium.

A forward purchase or sale is a tailor-made transaction between you and the bank. It can be done for any currency, for any amount, and any delivery date. There is also an organized currency market for future delivery known as the currency futures market. The futures markets are very homogeneous - there are only the main currencies, they are for specific amounts, and for a limited choice of delivery dates. The advantage of this homogenization is that it is a liquid market in futures currencies. A huge number of contracts are bought and sold on the future exchange market.

When you buy a forward or forward contract, you are committing to deliver the currency. As an alternative you can take an option to buy or sell a currency in the future at a price that is set today. Custom-made currency options can be purchased from the major banks, and the most homogeneous options are traded on exchange rate options.

Finally, you can agree with the bank that you will buy currencies in the future at whatever the spot rate is but subject to a maximum and minimum price. If the value of the currency rises suddenly, you buy at the upper limit, if it falls suddenly, you buy at the lower limit.

Some Basic Relationships

You cannot develop a consistent international financial policy until you understand the reasons for differences in exchange rates and interest rates. So let's consider the following four problems:

Problem 1: Why does the interest rate of the dollar (r $) differ from that of, for example, the Italian lira (rL)?

Problem 2: Why does the forward exchange rate (fL / $) differ from the spot exchange rate (SL / $)?

Problem 3: What determines the expected exchange rate between the dollar and the pound next year?

Problem 4: What is the relationship between the inflation rate in the United States (i $) and the Italian inflation rate (iL)?

3. Interest Rates And Exchange Rates

Practical case

You have 1 million dollars to invest for a year: What is better to make a loan in dollars or in lira? We are going to work on a numerical example.

Dollar loan: The one-year interest rate on dollar deposits 8.125 percent. Therefore at the end of the year you get 1,000,000 * 1.08125 = 1,081,250.

Loan in liras: The current exchange rate is 1,163 L / $. For a million dollars you can buy 1 * 1,163 = 1,163 million lira. The one-year lira deposit interest rate is 11.375 percent. So at the end of the year, he gets 1,163 * 1,11375 = 1,295 million lira. Of course you will not know what the exchange rate will be in a year. But it does not matter. You can set the price at which you will sell your lira today. The one-year term rate is 1,198 L / $. Therefore, by selling forward, you can ensure that you will get 1,295 / 1,198 = 1,081 or 1,081,000 dollars at the end of the year.

Therefore, the two investments offer almost the same rate of return. This is how it has to be, since both investments are risk free. If the domestic interest rate were different from the foreign rate, you would have a money maker.

When you make a loan in lira, you win because you get a higher interest rate. But he loses because he sells the lira for a lower price than he has to pay for them now.

The differential in interest rates is

(1 + r) / (1 + r)

And the difference between forward and spot exchange rates is

f / s

The interest rate parity theory says that the interest rate differential should equal the difference between the forward and spot interest rates.

The Term Premium And Variations In Spot Rates

Let us think about how the forward premium is related to changes in spot exchange rates. If people did not factor in risk, the forward exchange rate would depend only on what people expect the spot rate to be. For example, if the one-year forward rate of the lira is 1,198 L / $, it can only be because agents expect the one-year spot rate to be 1,198 L / $. If they expect it to be higher, no one would want to sell lira forward.

Therefore the theory of exchange rate expectations tells us that the percentage of the difference between the forward interest rate and the spot rate today is equal to the expected change in the spot rate:

In the derivation of the expectation theory we assume that traders do not care about risk. They do worry that the forward rate may be higher or lower than the expected spot rate. For example, suppose you have contracted to receive 100 million lire over three months. Your alternative is to sell the lira forward. In this case, you are setting the price at which you will sell the lira today. Since you avoid risk by selling lira forward, you may want to do so even if the forward price is slightly lower than the expected spot price.

Other companies may be in the opposite situation. They may have contracted to pay pounds in three months. They can wait until the end of the three months and buy lira then, but this leaves them open to the risk that the price of the lira may rise. It is safer for these companies to set the price today by buying lira forward. These companies may therefore wish to buy forward even if the forward price of the lira is slightly higher than the expected spot price.

Therefore some companies find it safer to sell lira forward while others find it safer to buy lira forward. If the first group predominates, the forward price of the lira is likely to be lower than the expected spot price. If the second group predominates, the forward price of the lira is likely to be higher than the expected spot price.

Changes In The Exchange Rate And The Inflation Rate

We now turn to the third side of our quadrilateral - the relationships between changes and the spot exchange rate and inflation rates. Suppose you realize that an ounce of silver can be bought at $ 8.50 in New York and will sell in Milan at 11,200 lira. He thinks that it may be a good deal, he decides to buy silver at $ 8.50 and send it on the first plane to Milan, where he sells it for 11,200 lire. So trading your 11,200 lira for 11,200 / 1,163 = $ 9.63 you have made a gross profit of $ 1.13 per ounce. Of course you have to pay transportation and insurance costs, but there should still be something left for you.

Money machines don't exist, not for long. As soon as others notice the disparity between the silver price in Milan and the price in New York, the price will be forced down in Milan and up in New York until profit opportunities disappear. The arbitration ensures that the dollar price of silver is almost the same in the two countries.

Of course, silver is a homogeneous product that is easy to transport, but to a certain extent you could expect that the same forces will comply to equalize domestic and foreign prices, among other goods, those goods that can be bought cheaper abroad will be imported and this will force falling prices of the domestic product. In the same way, those goods that can be bought cheaper in the United States will be exported and will force down the price of the foreign product. This is often called the Single Price Law or in a more general sense the Purchasing Power Parity in the same way that the price of goods in Pamplona should be almost the same as the prices of goods in Seville,the prices of goods in Italy when converted to dollars should be almost the same as the price in the United States.

The principle of the Single Price Law implies that any difference in the rate of inflation will be offset by a change in the exchange rate. For example, inflation is 5% in the United States and 1% in Italy in order to equalize the price of goods in dollars in the two countries, the price of the Italian lira should fall by (1.081) / (1.05) –1, or 3%. Therefore the law of one price suggests that in order to estimate changes in spot exchange rates, you need to estimate differences in the inflation rate.

Interest Rates And Inflation Rates

Now for the fourth leg! In the same way that water always flows downhill, capital always flows where returns are highest. In equilibrium, the expected real return on capital is the same in different countries.

But the bonds do not promise a fixed real return: they promise a fixed payment of money. So we have to think about how the money interest rate in each country is related to the real interest rates. An answer to this has been provided by Irving Fisher who argues that the interest rate on money will reflect expected inflation. In this case, the United States and Italy will offer the same expected real interest rate, and the difference in nominal interest rates will equal the expected difference in inflation rates.

In other words, the equilibrium of the capital market requires that the real interest rate be the same in any two countries. In Italy a real interest rate is 3 percent.

Is life that simple?

We have previously described four simple theories that link interest rates, forward rates, spot rates, and inflation rates. Note that the four theories are mutually consistent. This means that if any of the three is correct the fourth must also be correct. And conversely, if one is wrong at least one of the others must be wrong.

Of course no economic theory is going to provide an exact description of reality. We need to know to what extent those simple benchmarks predict actual behavior.

4. Theory of interest rate parity

Concept

The principle by which the currency exchange rate is increased reflects defects in the interest rates relative to the free risk instruments denominated in different currency alternatives. Currency forward rates and the structure of interest rates reflect these parity relationships. Currencies of countries with high interest rates, the market expects to depreciate over time and currencies of countries with low interest rates are expected to appreciate over time, reflecting, along with other elements, implicit differences in inflation.

These trends will be reflected in forward exchange rates as well as in the structure of interest rates. Any opportunity to make a profit from interest rate discrepancies will be arbitrage protecting currency risk.

If the parity in the interest rate is maintained, an investor will not be able to receive profits by borrowing from a country with low interest rates and lending in a country with high interest rates. For most of the major currencies, interest rate parity has not been maintained during the modern floating rate regime.

Condition

The theory of interest rate parity holds when the rate of return on dollar deposits is exactly equal to the expected rate of return on German deposits.

This condition is commonly simplified in many textbooks, removing the last term which is in this case the German interest. The logic behind this is that the last term does not change the value of the interest rate of return dramatically and is easier to assume by intuition. The approximate version of the IRP then is:

One must be careful anyway. The rough version would not be a good approximation when interest rates in a country are high. For example, in 1997, short-term interest rates in Russia were 60% for one year, in Turkey 75% per year. At these levels, the approximate rate cannot provide an accurate representation of rates of return.

Numerical Examples Using the Rate of Return Formula

Use the data presented below to calculate in which country it would have been better to obtain a producing asset of interest. These values were taken from the 8th. Edition of The Economist magazine:

Example 1: Consider the following data for interest rates and exchange rates in the United States and Germany.

i $ 5.45% per year

iDM 3.65% per year

e $ / DM96.6944 $ / DM

e $ / DM97.6369 $ / DM

We imagine that the decision will be made in 1996, with a view to 1997. Anyway, we calculate this after knowing what the exchange rate is. Therefore we use the 1997 rate for the expected exchange rate and the 1996 rate for the current rate. Then the ex - post (after the fact) rate of return on German deposits is given by:

A negative rate of return means that the investor would have lost money (in dollar terms) by purchasing the German Asset.

Since RoR $ = 5.45%> RoRDM = - 4.93% the investor looking for the highest rate of return should have deposited their money in the US account.

Example 2: Consider the attached data for interest rates and exchange rates for the United States and Japan.

i $ 5.45% per year

i ¥ 0.55% per year

E $ / ¥ 96 ¥ / $ 105

E $ / ¥ 97 116 ¥ / $

Imagine again that the decision is made in 1996 with a view to 1997. Anyway we calculate this after we know what the change is in 1997. So, we plug in the 1997 rate for the exchange rate and use the current 1996 rate.

Now, the ex-post rate of return on Japanese deposits is given by:

A negative rate of return means that the investor would have lost money (in dollar terms) having bought Japanese Assets.

So RoR $ = 5.45%> RoR ¥ = -8.97% the investor who was looking for a higher rate of return would have to have deposited their money in a US account.

Example 3: Consider the following data on interest rates and exchange rates in the United States and in Italy whose currency is the Lira.

i $ 5.45% per year

iL 10.31% per year

e $ / L96 1573 L / $

e $ / L97 1540 L / $

Again we imagine that the decision is made in 1996 with a view to 1997. Anyway we calculate this after knowing what the change is in 1997. So we insert the 1997 rate for the exchange rate and use the current 1996 rate.

Before calculating the rate of return, it is necessary to convert the equivalent Italian lira exchange rate instead of the dollar equivalent.

Now, the ex-post rate of return of Italian deposits is given by:

In this case, an investor would have made money (in dollar terms) by buying Italian Assets.

So now RoR $ = 5.45% <RoRL = 12.69% the investor looking for the highest rate of return should have deposited their money in the Italian account.

Asset Approach To Determine The Exchange Rate

The interest rate parity condition can be used to develop an exchange model for determining the exchange rate. Investor behavior, which generates interest parity, may explain why the exchange rate can rise and fall in response to market changes.

The first step is to reinterpret the calculation of the rate of return described above in more general terms. Instead of using the interest rate of a CD (certificate of deposit), the prevailing average interest rates will be interpreted.

Simultaneously, we imagine that the expected exchange rate is the expectations around various individual investors. The rates of return are then the expected average rates of return on a wide variety of assets across countries.

Next we imagine that investors exchange currencies in the international exchange market. Every day some investors arrive in a market ready to trade one currency for another while others do the same.

Consider the market for German Marks (DMs) in New York shown in the diagram. We measure the supply and demand of DMs around the horizontal axis and the price of DMs on the vertical axis. SDM stands for the Offer of DMs in exchange for dollars at all different prevailing exchange rates.

The offer is generally made by German investors who demand dollars to buy dollar-valued assets. In any case, the Dms Offer can

come from American investors who decide to exchange DMS currency in exchange for dollars, at different exchange rates that may prevail. The demand is generally for US investors who provide dollars to buy assets valued in DMs. Of course, the demand may also come from German investors who decide to convert previously acquired dollars.

Which implies that e $ / DM increases and RoRDM decreases. This means that German investors can supply DMs at a higher DM and that US investors would demand less DM with higher values.

The intersection of supply and demand specifies the equilibrium exchange rate, e $ / DM and the number of DMs, Qdm exchanged in the market.

The effect of changes in US interest rates on the spot exchange rate

Suppose that the Forex is in equilibrium SDM = DDM at the exchange rate e $ / DM. Now let the interest rate i $ grow. The increase in interest rates causes the rate of return on US Assets ROR $ to increase, which at the original rate of exchange causes the rate of return on US assets to exceed the rate of return on German assets ROR $> RORDM.

This elevates the supply of DM in the forex market, while German investors seek a higher average return on US assets. The demand for German DMs from German investors who choose to invest at home and not abroad will also decrease. Hence in terms of the graph, DDM is moving to the right while SDM is moving to the left.

The equilibrium rate of exchange grows at e2 $ / DM. This means that the increase in German interest rates produces an appreciation of the DM and a depreciation of the dollar. As the exchange rate rises, RORDM falls from

RORDM continues to fall until the ROR $ = RORDM interest parity condition again holds.

The effect of changes in the expected exchange rate on the spot exchange rate

Assume that the Forex market is initially in equilibrium, SDM = DDM, at the exchange rate e1 $ / DM. Now suppose that investors suddenly raise their future exchange rate to e2 $ / DM. This means that investors had expected the DM to appreciate, they now expect it to depreciate less. In the same way with investors who expected the dollar to depreciate, now they expect it to depreciate more. Also if they expected the DM to depreciate, now they expect it to depreciate less. Similarly, if they expected the dollar to appreciate, now they expect it to appreciate less.

This change can occur because new information appears. For example, the German Central Bank may release information that suggests an increase possibility, that the DM will rise in value in the future.

The increase in the expected exchange rate raises the rate of return on German Assets that exceed the rate of return on American Assets. This will increase the demand for DM in the international exchange market as US investors seek the highest average return on German Assets. The supply of DMs from German investors who decide to invest at home and not abroad will also decrease. So in terms of the graph, DDM is moving to the right while SDM is moving to the left. The equilibrium exchange rate will increase to e2 $ / DM. This means that the increase in the expected exchange rate e2 $ / DM, causes DM to appreciate and dollars to depreciate.

This case is one of self-fulfilling expectations. If investors suddenly think that the DM will appreciate more in the future, and if they act on that belief, then the DM will start to grow in the present, thus meeting their expectations.

As the exchange rate rises, RORDM falls to the interest parity condition, ROR $ = RORDM and remains.

5. Euro and forex markets

How are Forward FX rates calculated?

When a currency is bought or sold with a delivery beyond the delivery deadline, the appreciable exchange rate for the transaction is different from the agreed exchange rate.

This difference is exchanged in the Forex markets in the form of Swap (or Forward) points; Forex Market makers quote the number of Swap points that they will receive / pay when they buy or sell the base currency on a future date (forward)

Forward rates can also be obtained from the prevailing Spot rates, and the interest rates in the constituent currencies using the Theory of Interest Rate Parity. This theory does not give an opportunity for arbitrage of deposits in different currencies. In other words, investors should be indifferent to the choice of the exchange rate at which they hold their investments in the short term.

For example, consider an American investor who can invest in deposits in Dollars or in deposits in Yen by following the steps detailed below:

to. Convert funds from Dollars to Yen

b. Invest in Yen deposits

c. Lock in a forward rate to convert your deposits from Yen to Dollars

Since these two classes of investments have a similar risk, the Theory of the parity of the interest rates states that both must have the same return as well.

Using good logic we can work forward rates in terms of FX spot rate and Libor in two exchange rates.

Forward Rate = Spot Rate x (1 + itxdt) / (1 + ibxdb)

Where, It = Libor interest rate in exchange rate terms

Ib = Libor interest rate based on the exchange rate

Dt = Period of time based on the usual count of days in terms of the exchange rate

Db = Period of time based on the usual count of days based on the exchange rate

Premium And Discount Exchange Rates

The interest rate parity theory equation implies that the FX Forward rate is higher than the FX Spot rate when the exchange rate terms of interest rates are higher than the base of the currency exchange rate. interest rates and lower when interest rate exchange rate terms are lower than the exchange rate interest rates.

This means that the exchange rate that pays a higher interest rate depreciates over time, so any other interest that it pays is offset by a fall.

When the Forward rate is lower than the Spot rate, the base of the exchange rate is being valued to appreciate the overtime, and it is called "Exchange with a Prize". At the same time when the Forward rate is higher than the Spot rate, the base of the exchange rate is being valued to depreciate the overtime, and it is called "Discounted Exchange".

Bid And Offer At Forward Interest Rate

In practice, it is the market negotiator who is in charge of assigning the Bid-Offer margin for each transaction, involving a forward quota under construction for the client.

If there is a liquid FX swap market at a given exchange rate, Forwards are constructed with the combination of an FX swap and an FX spot in one transaction. The resulting bid-offer margin is the sum of the spot bid-offer and the points of the bid-offer swaps.

If FX swaps are not available in an exchange rate market, the market must build FX forwards based on XFX spot, a loan market and a deposit market. Again, the resulting bid-offer must take into account the bid-offer term in each of these transactions.

If the forward rate is calculated based on money markets, the bid-offer is considered wider if the rate is calculated using FX swaps, as the Libor-Libid spread is around 12.5 basis points, while the spread of Bid-offer swaps is only 1 to 2 basis points.

Example, A client asks his broker for a six-month Forward with direct purchase of SAR versus Dollars. This requirement effectively consists of:

to. A six-month loan for which the negotiator's charges are for six months Dollars-Libor

b. Conversion of Dollars to SAR, for which the negotiator is on the side of the offeror.

c. A six-month deposit in SAR, for which the negotiator pays six months EUR-Libid

Forward bid-offer margin includes bid-offer margin in the foreign exchange and money market.

How to Get Profits From Interest Hedging Arbitrage

An arbitration is an opportunity to make money without much risk. Hedging interest is a way to increase the term in case of inconsistency between the money markets, Euro and Forex. These markets are normally in equilibrium and when this equilibrium is broken there are opportunities for arbitrage.

The Euro exchange rate market is vast in offshore OTC markets, it is established in London, in which there are high rates for bank loans, which is why they lend to each other. In this market it is possible for traders to look at the cost of borrowing and income from borrowing money at any exchange rate.

The Forex market is also an OTC market, in which banks buy and sell exchange rates at future dates and spots. In this market it is possible for a trader to secure the exchange rate for others, both for the distribution of spot or forwards.

We apply the theory of interest rate parity to the relationship between the Euro and Forex market. In summary, it establishes that the exchange rates of forwards between various interest rates must be based on a spot rate and their respective interest rates in the market. A lower interest rate on an exchange rate is more appreciated than a higher one.

In other words, this theory says that forward rates must compensate for the difference between the interest rates that investors receive.

The lack of success of the Parity Theory.-

The theory gives us the relationship between the Euro and Forex exchange rates in the market. Here the FX Forward rates must compensate for the relative difference between the Interest rates (Libor) of various exchange rates.

These relationships are governed by news and market forces, which can drive this apparatus. These standards have given this theory a temporary lack of success.

In this situation it is possible for traders to have a greater profit by having a series of simultaneous deals in which they:

to. They buy one exchange rate with another

b. They lock in rates on both sides of the Euro exchange rate markets

c. And they ensure the rate at which the exchange rate purchase can be reserved

Closing deals abnormally with high Swap points.-

According to the theory, the swap points should compensate the interest rate for the spread between the constituted currencies.

Net income is approximately the difference between the points earned in swap and the differential interest rate paid over the arbitration period. The amount of the profit can be calculated by converting the value of deposits and loans at the end of the arbitration period, at the same exchange rate using the forward rate and finding the difference.

If the swap points are lower than those used by the interest rate differential, the arbitrage should, to. Pay swap points for the duration of the arbitrage

b. Borrow currency with low interest rates

c. Lending currency with high interest rates

Net income is the difference between deposits and loans at the end of the arbitration period.

Effect of the cost of executing the arbitration.-

The requirements in arbitrage coverage to perform separate transactions: FX swap, loan money market and deposit money market.

Each of these transactions creates a costly term for bid-offer spreads. FX swaps can have a cost that ranges from 0.02% to 0.1% and the spread between loans and deposits is around 0.125%, even maintaining the position, and avoiding risks, can increase costs.

The total cost of implementing arbitrage costs between 0.1% and 0.3%. A trader can exploit this arbitrage if the difference between the FX swap rates and interest are greater than their value.

In most cases the difference between the markets is small and growing. In this case only expert market negotiators and professionals can exploit and place these opportunities.