One of the difficult aspects of international investment activities is the fact that the value of assets is expressed in different currencies. How to compare a 5% rate of return in German marks with a 10% rate of return

“Formally, we measure the correlation of an asset with the total market portfolio, i.e.

With a portfolio made up of all financial assets available on the market.

18 The CAPM defines a general relationship, known as the market equilibrium line, that relates equilibrium levels of an asset's expected return to its risk characteristics. When an asset is positively correlated with the total portfolio of financial assets traded on financial markets, its equilibrium level of return will be higher than that of an asset with a negative correlation. According to the theory, what matters in determining the equilibrium level of expected return is not the riskiness of the asset considered in isolation (measured, for example, by dispersion), but its riskiness compared to other assets, measured by covariance with the total portfolio of assets traded in financial markets.

level of profitability in dollars? We have already discussed this problem briefly in other chapters. Here we deepen our analysis of this important issue.

In ch. 10 we introduced the concept of international interest arbitrage. We have shown that, under conditions of complete certainty, the return on $1 invested in foreign bonds should be equal to the return on $1 invested in domestic bonds if the returns are denominated in the same currency. For the arbitration condition to be satisfied, we assumed the absence of barriers to international trade in financial assets and complete certainty about the future. We now introduce a more realistic but model-complicating assumption of exchange rate uncertainty to understand how the interest rate arbitrage condition, equation (10.5), will change. However, we ignore other types of risk, such as the risk of non-payment or the political risk of expropriation of property by a foreign government.

Suppose the US Treasury pays annual interest /. This means that $1 invested today produces a return of $1 + $0 in a year. We call the value 1 + /" gross income (in dollars), and the value / - net income. Now consider a German bond issued by the Bundesbank whose face value is expressed in German marks, yielding income /*. We will consider the United States as a “own” country and therefore express the income from the German bond in dollars in order to compare it with /". The fact is that the income from the bond expressed in dollars Bundesbank depends both on /* and on the dynamics of the exchange rate during the year. Let us denote by E the exchange rate in dollars for one German mark in the current period, and by E+1 the corresponding exchange rate of the next period. For example, at the beginning of February 1991. E was close to 0.68, i.e. 1 mark could buy approximately $0.68.

Let us now consider the purchase of a German bond in the current period. For 1 dollar you can buy 1/E bonds with a par value of 1 him. brand. At the end of the year, each bond will earn (1 + /*) in German marks, and thus the total income will be (1 + 1*) / E in German.

Mark. The dollar value at the end of the year will be E+1 (1 + 1*)/E. Thus, the gross dollar receipts from domestic and foreign assets will be, respectively:

internal asset: (1 + /);

foreign asset: *"4 --

The problem is that in the current period there is no certainty about the value of E+y. If the exchange rate is floating or subject to devaluation, then we can only estimate (“guess”) what the exchange rate will be at the end of the next period.

In the general case, in the current period we have only the expected value?¦+, which we denote by En and determine at the beginning of the investment period. Then the expected return on the foreign bond is E%x (1 + r*)/E. The actual income, when uncertainty disappears, is equal to E+1 (1 + 1*)/E. Since the expected (E+1) and actual (?+1) exchange rates usually differ, the expected and actual incomes also differ from each other.

Chapter 20. Financial markets 423

Uncovered interest arbitrage

If investors only care about expected returns and don't worry about risk, i.e. are risk neutral, and if all investors have the same expectations, then all assets should have the same expected return. Otherwise, no investor will invest in assets with an expected return below average. Therefore, market equilibrium leads to uncovered interest arbitrage (uncovered because investors are not protected from exchange rate risk):

(1 + /) - E^1 + GC (20.8)

Note that equation (20.8) is the same as expression (10.5). There, however, we did not take risk considerations into account. To account for these considerations here, we replace the actual value of the exchange rate (E+1) with its expected value (E^).

Expression (20.8) can also be presented in a more familiar and intuitive form. Allowing for a slight approximation, we can write equation (20.8) as follows19:

/ . + ^+1--"/. (20.9)

Equation (20.9) says that the domestic interest rate is equal to the foreign interest rate plus the expected rate of depreciation of the currency. This property highlights one important characteristic of foreign investment. The purchase of a foreign asset is an investment not only in a security that pays a given interest rate (C), but also in a foreign currency, the return on which depends on the fall (or rise) in the exchange rate. For example, if the annual interest rate in the United States is 9, and in Germany - 6, then the German asset has a higher yield in dollars if the dollar has decreased by more than 3% over the year.

In general, however, investors also care about risk, which means that the conditions for uncovered interest arbitrage must be modified

" Equation (20.8) can be rewritten in the form:

Since (E^- E)/E and Γ are, as a rule, small numbers, their product is close to 0 and therefore may not be taken into account. If we make such an approximation, then equality (20.9) is satisfied.

How good is the approximation of equation (20.9) to expression (20.8)? Suppose that E = 0.60, a?¦", = 0.63 (i.e., the dollar exchange rate is expected to fall by 5% over the year). If Г = 0.06, then? "+| ( 1 + \")/E - = 1.113; on the other hand, 1+/" + (E"+( - E)/E= 1.110. The approximation is indeed good if both the foreign interest rate and the expected rate of depreciation of the currency are small. But it is hardly applicable in relation to countries subject to high inflation (and therefore a rapid rate of currency depreciation), since in this case the value of [(?"+1 - E)/E\\" will not be close to zero.

Part V. Special Issues in Macroeconomics

ffect. In reality, because the risk of investing in a domestic asset is different from the risk of investing in a foreign currency asset, there may be a positive or negative risk premium for investing in a domestic asset. In this case, the modified equation will be:

where Rg is the risk premium. If Рг > 0, equation (20.10) means that investors require a higher expected return on a domestic asset compared to a foreign one.

What is the source of the so-called “currency risk” Rg! As in the CAPM model, the size of Pg will depend not only on currency fluctuations and how unexpected they are, but also on the covariance of exchange rate fluctuations and the return on other financial assets. It can be said, for example, that the US dollar tends to appreciate unexpectedly when world oil prices rise unpredictably. In this case, holding dollars rather than German marks will protect investors from the risk of rising oil prices and the corresponding fall in the profitability of certain types of assets of industrial companies. Such a correlation could help determine Pr. In practice, it is difficult to detect a consistent relationship between changes in exchange rates and other types of risk, so economists have not yet succeeded in determining the magnitude and sources of the risk premium of the type Pr.

Covered interest arbitrage

In the example we just discussed, the investor chooses between holding a domestic or foreign asset for one year and then converting the foreign currency in which it is denominated at the exchange rate at the relevant point in time. In reality, there are other choices. If an investor buys a bond denominated in German marks today, he knows that in the future he will receive a certain number of marks to exchange for dollars (namely the quantity 1 + /*). But instead of waiting a whole year for the appropriate exchange rate to become known, he can enter into a contract today to sell that quantity of Deutsche Marks in a year's time at the price specified in the contract. Thus, the investor uses a forward contract, which is an agreement to buy or sell a commodity (or currency) at a certain future point in time at a price set today20.

By using a forward contract, an investor can eliminate all risk associated with exchange rate movements. Instead of buying a foreign bond and waiting for a year to see what E+1 will be, the investor sells the foreign currency proceeds in advance at a fixed price called the "forward price", which is denoted by Thus, the investor knows that at the end of the year he will receive (1 .+ /*)/? German

Formally, we must distinguish between two types of contracts involving foreign

strange currencies: futures contracts, which are traded on open futures exchanges, and forward contracts, which are bought and sold commercial banks. Essentially, however, they have the same purpose. In the text we will use one term - "forward contract" - to refer to this type of transaction.

Chapter 20. Financial markets 425

marks and will sell them, as he agreed today, for ^(1 + i*)/E dollars. The transaction will not be completed before this future date, but its terms are established today.

Thus, the purchase of a German bond in combination with the forward sale of the yield on that bond produces a gross dollar return equal to U + i")/E, without any exchange rate risk. Using technical terms, we say that the investor covers his position in German marks, selling them under a forward contract, so that he is no longer exposed to exchange rate fluctuations. Since buying assets denominated in German marks, combined with a forward sale, has the same return as buying dollar assets directly (since neither transaction is used). does not contain currency risk), then we obtain a market equilibrium condition called covered interest arbitrage:

(1 + i) - ]. (20.11)

Equation (20.11) can be approximated similarly to equation (20.8) by the expression

/ =. + (P~EE) ¦ (20.12)

Equation (20.12) says that the domestic interest rate is equal to the foreign interest rate plus the forward discount (E - E)/E. Note that the forward discount can be either positive or negative. If E > E, then the dollar is said to be selling at a forward discount; in this case, the dollar interest rate should be higher than the German one. In the opposite case, if E If we combine equations (20.10) and (20.12), we get a very important relationship:

R-E^+ERg. (20.13)

This equation states that the forward exchange rate is equal to the next period's expected exchange rate plus the product of the current exchange rate and the percentage risk premium associated with investing in a domestic asset instead of a foreign one. If all agents are risk neutral, i.e. Рг = 0, then the forward exchange rate reflects market expectations regarding the exchange rate of the next period. However, if investors are risk averse, meaning there is a risk premium for holding a domestic asset instead of a foreign one, then the forward exchange rate will not equal the expected exchange rate.

If we consider an investor who wants to increase the initial amount of money he has over time, using the possibilities of deposits in various currencies, then we should discuss the possibilities of the so-called interest rate arbitrage.

Consider an investor who has investment capital in dollars. He has two options: either deposit them in dollars, or convert the dollars into euros at the spot rate, deposit the resulting amount into a deposit in euros, and then convert the entire amount into dollars at the current forward rate.

It can be shown that the use of forward purchase of dollars (forward sale of euros) is beneficial to our investor (located initially in the $ zone) if the inequality for the forward rate is satisfied:

,

where can be either less or greater than zero, depending on the relationship between the quantities and .

Question for independent work . Find the value using the data in the “Pure Arbitrage” section. Show that when .

For an investor with initial investment capital in euros, the situation is the opposite: it is profitable for him to use a forward sale of $ if

If a bank acts as a financial investor, earning money from a client deposit placed with it in euros, then it can choose in which currency it is more profitable to issue loans. It is not difficult to show (without taking into account the required reserve fund) that it will be more profitable for a bank to issue a loan in $, then selling dollars under a forward contract, if

.

If the bank deposit used is in $, then it will be profitable for the bank to issue a loan in €, then buying dollars under a forward contract, if

.

Resume. Among the four types of investors considered who want to make money on interest rate arbitrage, there will always be pairs of investors with opposing interests to buy and sell euros under a forward contract if the forward rates lie in the interval:

It is not difficult to show that , and therefore this interval lies in the zone of impossibility of pure arbitrage.

Research Question. Consider the possibilities of interest rate arbitrage when using risk-free government bonds before the maturity date. This is, of course, a less flexible instrument since the repayment terms are fixed.

Figures 1 and 2 show the location of the areas of interest of various participants in the euro-dollar forward market for two possible relationships between the values ​​and .

Let us pay attention to the area of ​​intersection of interests of various market participants in the vicinity, when the cost of forward contracts is in a small vicinity of the value. It can be assumed that transactions of those market participants who adhere to a risk-free strategy will take place in the vicinity of this price.

Test questions for the section “Pure and interest arbitrage”

1. An American exporter will receive in n months the amount of euros for his goods. Having this security in the future, the exporter wants to get the maximum dollar loan for these n months, for which he is going to pay with the amount received from exports. Discuss two risk-free strategies:

1) Take a loan in dollars from a bank for n months and enter into a forward contract to buy dollars for euros with a maturity of n months.

2) Take a loan in euros from a bank for n months and convert this amount into dollars at the spot rate.

2. The European exporter will receive in n months the amount of dollars for his goods. Having this security in the future, the exporter wants to receive a maximum loan in euros for these n months, for which he is going to pay with the amount received from exports. Discuss two risk-free strategies:

1) Take a loan in euros from a bank for n months and enter into a forward contract to buy euros for dollars with a maturity of n months.

2) Take a loan in dollars from a bank for n months and convert this amount into euros at the spot rate.

When is a forward contract strategy beneficial?

3. When is it beneficial for a European importer to use a forward purchase and sale transaction of $, if he, having today a certain amount in euros, must pay a sum of dollars for the goods in n months?

4. When is it beneficial for an American importer to use a forward purchase and sale transaction for $, if he, having a certain amount in dollars today, must pay in euros for the goods in n months?

5. In what range of values ​​are there pairs of economic participants described in the previous 4 situations that have opposing interests regarding the forward purchase and sale of $, which can lead to the satisfaction of their interests?

6. Table 1 below shows spot and forward prices in dollars for the pound sterling, the German mark, the Swiss franc, the Canadian dollar, the Japanese yen, and interest rates as of Thursday December 23, 1993. The US interest rate was 3. 19%.

Table 1

	lb.	brand	franc	Canadian dollar	yen
Spot price	1,5040	0,5900	0,6976	0,7544	0,008942
Forward price
with delivery in 30 days	1,5010	0,5883	0,6968	0,7540	0,008960
with delivery in 60 days	1,4987	0,5869	0,6963	0,7436	0,008976
with delivery in 90 days	1,4964	0,5859	0,6959	0,7434	0,008992
Money market interest rates (% per annum)	5,32	6,08	4,13	3,79	1,06

Based on these data, fill in three lines in tables 2 and 3. (It is wise to use the computing capabilities of Excel for this). In Table 2, fill in the values ​​for the equilibrium forward rate of each currency for three terms: 30, 60, 90 days.

Table 2

	lb.	brand	franc	Canada Doll	yen
Spot price	1,5040	0,5900	0,6976	0,7544	0,008942
Forward price eq
with delivery in 30 days
with delivery in 60 days
with delivery in 90 days
	5,32	6,08	4,13	3,79	1,06

And in Table 3, fill in similar lines for the value.

Table 3

	lb.	brand	franc	Canada Doll	yen
Spot price	1,5040	0,5900	0,6976	0,7544	0,008942
Ln (Ford price/Ford price eq)
with delivery in 30 days
with delivery in 60 days
with delivery in 90 days
Money Market Interest Rates (%)	5,32	6,08	4,13	3,79	1,06

Estimate the deviation from zero relative to money market interest rates for the relevant currency. It is convenient to do this in a separate table.

7. Mitsubishi Motors (Japan) signed an agreement to supply Mitsubishi (USA) with 200 cars for a total amount of 2640*10^6 yen. The amount must be paid within three months.

The following data is presented:

Spot rate 110.10 Ұ /$

Forward rate for 90 days in the USA 110.45 Ұ /$

Interest rate (per annum) for 90 days in the USA 3.25%

Interest rate (per annum) for 90 days in Japan 4.50%

90 day call option (right to buy yen

for a fixed price – strike price,

paid with a premium - the price of the option)

Strike price 110.00 Ұ /$

Option price 0.5% of the amount

Expected spot rate in 90 days 110.11 Ұ /$

What would you suggest that the financial manager of Mitsubishi (USA) do to ensure the necessary payments in yen?

• - A bill, on the bill amount of which...

  Dictionary of business terms

• - INTEREST ARBITRATION Transactions in foreign exchange between financial centers, taking advantage of differences in interest rates in the two centers and differences in forward and cash exchange rates...

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  Librarian's terminological dictionary on socio-economic topics

• - English interest arbitrage arbitration, carried out in the form of placing the purchased currency on a foreign currency deposit with the subsequent sale of the currency after the end of the deposit period...

  Dictionary of business terms

• - agreement on the maximum rate on floating rate bonds...

  Dictionary of business terms

• - Foreign exchange transactions between financial centers, taking advantage of differences in interest rates between the two centers and differences in forward and spot exchange rates...

  Dictionary of business terms

• - a transaction with the aim of making a profit due to the difference in interest rates for different currencies. Used by arbitrageurs, as a rule, to regulate the currency structure of their short-term assets and liabilities...

  Financial Dictionary

• - in the USA - arbitrage, in which dollar funds are invested in instruments denominated in foreign currency, and the currency risk arising as a result of this operation is hedged through exchange...

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• - a transaction that combines foreign exchange and deposit operations, aimed at regulating banks and firms the currency structure of their short-term assets and liabilities in order to make a profit from the difference in...

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• - an agreement on the maximum rate on bonds with a floating interest rate, traded as an independent security...

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• - INTEREST, interest, interest. 1. adj. to percentage, expressed as a percentage. Percentage. Interest remuneration. 2. Interest-bearing. Interest-bearing papers...

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• - interest expressed as a percentage; interest-bearing; n-th securities - securities, debt obligations that bring a certain interest on the capital invested in them...
• - calculated from one hundred, expressed as a percentage; interest-bearing; interest-bearing securities - securities, debt obligations that bring a certain interest on the capital given for them...

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"Interest Arbitrage" in books

Interest rate risk

From the book Let's profit from the crisis of capitalism... or Where to invest money correctly author Khotimsky Dmitry

Interest rate risk Loss of money due to growth interest rates called interest rate risk. Let's say you put money in a bank deposit at 5% per annum. And a month later, panic begins in the financial markets. Banks offer 10% for a similar type of deposit.

Chapter 33. How to defeat the “percentage virus”?

From the book On Interest: Loan, Judicial, Reckless. “Monetary civilization” and the modern crisis author Katasonov Valentin Yurievich

Chapter 33. How to defeat the “percentage virus”? Abolition of interest: “soft” and “hard” options Throughout the book we talked about the “monetary revolution”. About how moneylenders took over the monetary system, seized economic and political power in society, to what

108. Interest arbitrage

From the book Market securities. Cheat sheets author Kanovskaya Maria Borisovna

108. Interest arbitrage Currency arbitrage is often associated with operations in the loan capital market. The owner of any currency can place it on the loan capital market in another currency at a more favorable interest rate. Interest arbitrage is based on the use

86. Interest arbitrage

From the book Banking Law. Cheat sheets author Kanovskaya Maria Borisovna

86. Interest arbitrage Currency arbitrage is often associated with operations in the loan capital market. The owner of any currency can place it on the loan capital market in another currency at a more favorable interest rate. Interest arbitrage is based on the use

83. Interest arbitrage

From the book Banking. Cheat sheets author Kanovskaya Maria Borisovna

83. Interest arbitrage Currency arbitrage is often associated with operations in the loan capital market. The owner of any currency can place it on the loan capital market in another currency at a more favorable interest rate. Interest arbitrage is based on the use

33. Loan interest (interest income) and interest rate.

From the book Money. Credit. Banks: lecture notes author Shevchuk Denis Alexandrovich

33. Loan interest (interest income) and interest rate. Loan % (interest income) is the lender’s monetary reward for providing a loan. Is the loan price (fee) that a borrower owes to a lender for a loan. Characterizes the distribution of income and risks,

Arbitration

From the book by Warren Buffett. How to turn 5 dollars into 50 billion. The strategy and tactics of a great investor author Hagstrom Robert J

Arbitration Arbitration, in its simplest form, involves the purchase of securities in one market and their simultaneous sale in another market. The purpose of such an operation is to make a profit on price discrepancies. For example, if a company's stock is trading at $20 per share

B. Arbitration

From the book Essays on Investments, Corporate Finance and Company Management by Buffett Warren

B. Arbitrage As an alternative to holding short-term cash equivalents, our subsidiaries insurance companies are engaged in arbitration operations. Of course, we prefer large long-term investments, but often we have more money than good ones

Arbitration

From the book The Practice of Human Resource Management author Armstrong Michael

Arbitration Arbitration is the process of resolving conflicts through an independent third party. The parties agree in advance to accept the arbitrator's decision as an instrument for the final resolution of the dispute. Sometimes there is a reluctance to resort to this method because

Interest-bearing loan between Jews and Christians

From the book Middle Ages and Money. Essay on Historical Anthropology by Le Goff Jacques

Interest-bearing loan between Jews and Christians Without delving deeply into the issue of peasant debts, which is difficult to study in detail, we note that, for example, in the Eastern Pyrenees in the 13th century. The creditors of many peasants were Jews. In fact, the increase in demand for money created

Arbitration

From the book Encyclopedia of Lawyer author Author unknown

Arbitration ARBITRATION is a method of resolving economic and labor disputes, which consists of submitting them to an arbitration tribunal elected (appointed) by the parties, as well as one of the names of the latter. See also Treteysky

Arbitration

From the book Great Soviet Encyclopedia (AR) by the author TSB

Instead of a conclusion. HOW TO DEFEAT THE “PERCENT VIRUS”?

From the book World Cabal: Jewish Robbery author Katasonov Valentin Yurievich

Instead of a conclusion. HOW TO DEFEAT THE “PERCENT VIRUS”? ...the organization of a modern state is based on money... Everything may be bad, but monetary system is good, and the state will prosper. Everything is fine, but the monetary system is bad, and the state will go bankrupt and end up in

Chapter 33 HOW TO DEFEAT THE “PERCENT VIRUS”?

From the book About interest on loans, jurisdictional, and reckless. Reader modern problems"monetary civilization". author Katasonov Valentin Yurievich

Chapter 33 HOW TO DEFEAT THE “PERCENT VIRUS”? Abolition of interest: “soft” and “hard” options Throughout the book, we talked about the “monetary revolution.” About how moneylenders took over the monetary system, seized economic and political power in society, to what

Instead of a conclusion How to defeat the “percentage virus”?

From the book World Cabal. Robbery... author Katasonov Valentin Yurievich

Instead of a conclusion How to defeat the “percentage virus”? ... the organization of a modern state is based on money... Everything may be bad, but the monetary system is good, and the state will prosper. Everything is fine, but the monetary system is bad, and the state will go bankrupt and end up in

Arbitration

Arbitrage is an activity aimed at generating income by reselling securities or currencies at more favorable prices on the same market, but in some future period, or on other markets.

Arbitrage and related activities involve both knowledge of price differences and the ability to anticipate price movements, transaction volumes, possible profits and risks. Arbitrage is primarily concerned with international forward financial transactions, including foreign exchange rates, short-term interest and securities prices.

The maximum profit from arbitrage trades varies depending on the risk involved.

Interest arbitrage in money markets is the movement of resources from one currency to another in order to improve lending or borrowing conditions.

In fact, interest rate arbitrage comes down to choosing a country or currency with the most favorable loan interest rate. Time bank deposits or government bonds may be used as financial instruments for interest rate arbitrage. The movement of resources from one currency to another involves the presence of currency risk, and such currency transfers fall under the category of uncovered interest arbitrage.

If currency speculation turns out to be justified, then the risk associated with combining interest rate arbitrage with an open currency position makes it possible to obtain additional profits, which enhances the winnings obtained through interest rate arbitrage itself. So, if we place the first currency on deposit for a period T, we get

And if you use uncovered interest arbitrage, then

Here St is the rate of the second currency relative to the first Vt(1)=St Vt(2) at time t, Vt(1) is the current value of the first currency, ri, i=1.2 is the interest rate for the i-th currency. The total gain is obtained when ST>S0 and r2>r1.

Currency risk is associated with random values ​​of the ST exchange rate. Profits/losses received by the arbitrageur at the end of the financial transaction are calculated using the formula

Equivalent arbitrage is the buying or selling of combinations of options and cash positions where a price difference arises between theoretically equivalent combinations in practice.

For example, the combination of a long cash position and a put option creates a buy option, and the combination of a short cash position and a call option creates a put option. Indeed, for S0=K we have
S0-ST+(ST-K)+=(K-ST)+.

Equivalent arbitrage ensures that option prices match the cash price of the underlying asset, and also maintains equilibrium prices for buy and put options. For any t, the price parity formula must hold for European-style call and put options on the same underlying asset with the same strike price:

When parity is violated, an arbitrage situation arises.

The simplest arbitrage strategy with futures is intermarket arbitrage, which can involve either only futures contracts or simultaneous transactions in the futures and forward markets. About 30% of open positions in FT-SE 100 share index futures on the London Futures Exchange are used for arbitrage. A number of financial institutions that are members of the futures exchanges in Chicago and London use their personnel only to perform intermarket arbitrage in interest rate futures contracts based on three-month time deposits on the one hand and US Treasury bonds or cash time deposits on the other hand.

In December 1981, the Chicago Futures Exchange introduced a futures contract based on a three-month Eurodollar deposit of $1,000,000. This is a cash-settled futures contract that does not provide for any delivery of cash financial instrument at the expiration of the contract. Currently, one of the most significant uses of this futures is to arbitrage between cash and futures positions, by creating a synthetic instrument called a "strip". It is known that most traders of Eurodollar futures contracts with multiple immediate delivery quarters are dedicated to implementing this strategy. "Strip" means either a combination of cash deposits and a long position in a futures contract, or a loan and a short position. If Size is the size of the cash deposit, rd is the annual interest rate of the cash deposit, M is the size of the futures contract, T is the time until delivery under the futures contract, Ft is the futures price, then profits/losses from the "strip" are calculated either by the formula

If money is lent, either according to the formula

If money is involved. Such a trade is initiated if it is determined that the trader can expect a higher profit or lower credit charge than would be the case with a trade carried out only in the spot money market. The term "strip" originates from the practice of using two or more consecutive quarterly futures expiries in combination with a dollar cash position. Traders must determine for themselves when the difference between the strip interest rate and the spot rate is sufficient to make the trade worth considering.

In the case of one deposit and one futures contract, the annual interest rate rstrip is determined from the equation

Where rf is the interest rate of the futures contract.

Currency futures contracts can arbitrage against the spot rate and bank deposit rates. The potential profit from this type of arbitrage is relatively immune to movements in interest rates, but is sensitive to small changes in exchange rates.

Arbitrage between short-term interest rate futures and currency futures with the same delivery dates does not require entering the cash market, but it is difficult to select the right number of contracts to obtain full coverage.

More complex intermarket arbitrage transactions simultaneously involve the cash markets for currencies and securities, the interbank market, the forward market, the options market, and the futures contract market.

There are two interest rate arbitrage strategies.

Arbitration during coinciding periods of attracting and placing deposits. This is a risk-free strategy in terms of interest rates, since the rates are already fixed in the transaction.

For example, a bank attracts an interbank deposit of $1,000,000 for a week at 7% and simultaneously places it in another bank for a week at 8%, receiving a net profit of 1% per annum on $1 million.

For the Russian market with an undeveloped information infrastructure, as well as with different needs of banks for funds, the gap in interest rates on attracted and placed deposits can sometimes reach 5%. For example, a large bank, enjoying a good reputation, attracts a monthly dollar deposit from the same large bank at 9%, and places it in a lesser-known bank at 14%, taking on a certain risk in exchange for higher income.

Arbitration for different periods of attracting and placing deposits. This strategy is characterized by the risk of changes in interest rates for the uncovered period - mismatch. Its essence is to use different interest rates for different periods. There are 2 types of such arbitrage.

International deposit dealing with the expectation of changes in the general level of interest rates.

Let us turn again to the Reuters table of world interest rates on dollar deposits.

Interest rates increase with the period of placement or attraction: from 5.78/5.90 for the o/p period to 6.56/6.68 for 12 months. This growth reflects the prevailing expectations in the money markets of an increase in the general level of interest rates on dollar deposits. The current level of interest rates in the country depends, as already mentioned, on the level of the discount rate (or its analogue) of the central bank - the Federal Reserve for the United States. In case of a rate hike, for example by 1%, general level interest rates also increase by 1 percent.

Expectations for an increase in interest rates are based on an analysis of the macroeconomic situation in the country conducted by research institutes, prominent economists, and business leaders. If there is an increasing need to change the level of rates (for example, raising rates to combat inflationary trends or lowering them to stimulate economic growth), this opinion is expressed more and more often from the pages of economic publications, in interviews with economists, in the councils of analytical departments of the central bank and turns into such thus, in anticipation of the market.

In the United States, decisions to change the discount rate are made at meetings of the Federal Open Market Committee (FOMC), which meets on Tuesdays once a month. In Germany, such a decision is made at Bundesbank meetings held on Thursdays every two weeks. The schedule of meetings is known, and the market predicts, with varying degrees of probability, possible decisions to change or maintain the level of interest rates. Moreover, the closer the expected decision, the more significantly market rates react to it for long periods (more than a month). This is explained by the fact that when waiting for an increase in the discount rate, no one wants to place cheap funds for long periods, since soon it will be possible to place funds at a higher price, and the rates will rise. Expecting a reduction in the discount rate, on the contrary, no one wants to attract funds for a long time at an expensive rate, and their level falls. This market expectation is clearly reflected in the table of rates by period: a sharp increase in the level of rates for the period from 2 to 3 months indicates that the market expects a change in the discount rate in the period between the 2nd and 3rd months from the current date . Dealers engaged in interest rate arbitrage open uncovered deposit positions with a “mismatch”, counting on a favorable change in the level of interest rates in a given currency.

If you expect a quick increase in the level of interest rates, it is necessary to attract funds into deposits for long periods, and place them for short periods (borrow long, give short).

For example, on February 1, a dealer of an American bank expects in 2 months (that is, in early April) an increase in the discount rate on dollars by 1%. He attracts an interbank deposit for 6 months at 6.35%, thereby opening a long position. The dealer first covers it by placing funds for 2 months at 6.00%. During these 2 months, the dealer loses 0.35% per annum on the invested funds, but expects to place them subsequently much higher. If his calculation is justified, and in early April the FOMC raises the discount rate by 1%, then the general level of rates for all periods is automatically raised by 1 percent. The dealer closes the remaining mismatch of the long position by placing funds for the remaining 4 months at 7.16%, making a profit of 0.81% for four months, which covers the negative interest for the first 2 months.

The opposite strategy works in anticipation of an imminent decrease in the discount rate: place funds for long periods, covering them by attracting short money (give long, borrow short).

Deposit dealing with a constant gap in interest rates for different periods. This situation is typical for closed foreign exchange markets, for example Russia, where the gap between interest rates for different periods persists for a long time, as well as for money markets in foreign currency, where no change in the level of rates is expected. Such markets are characterized by higher rates for long periods, which act as a payment to the bank for the risk of placing funds for long periods.

Such dealing is characterized by a strategy of placing funds for long periods and covering the position by attracting deposits for short periods.

For example, a deposit dealer of a Moscow commercial bank places dollars on a three-month deposit in another Russian bank at 17 percent, covering the short position by attracting monthly deposits at 11 percent. Arbitration with different terms for attracting and placing deposits involves many options for using mismatch, depending on the degree of risk the bank is willing to accept. The greatest risk will be opening a deposit position for a long period (for example, 6 months) and covering it with overnight deposits.

In addition to cross-trading major currencies, many are interested in interest rate arbitrage between high- and low-interest rate currencies. Sometimes in foreign exchange market analyses, people draw conclusions from charts of currency combinations that are completely irrelevant because they reflect combinations with little turnover. It is a waste of time to plot a small European currency against any other currency other than the euro, since this combination is dominant. To find out the strength of the dollar relative to another small currency, you should first look at the chart of the small currency and the euro, and only then the chart of the dollar and the euro. It is not entirely correct to study the chart of the dollar and any small currency.

3.4. Currency arbitration: types and techniques of implementation
etc.............

What is interest rate arbitrage?

Interest rates in different countries rarely match in size. Their range in different markets around the world is quite wide. Investors are looking to move funds from a market with a low interest rate to a market with a higher one. To do this, they enter into an interest rate arbitrage transaction. If investors want to preserve capital and make a profit, they will do covered arbitrage. Covered interest arbitrage involves exchanging one currency for another. The borrowing process takes place cash in one country and converting them into the currency of another country in which these funds are given on credit. Collateral means that the risk of being converted back into the currency in which the loan was made to pay the loan when it matures is eliminated by purchasing that currency in the forward market. The simultaneous purchase of a currency on a spot basis and its forward sales, that is, a swap operation, reduces or eliminates operational risk. "Swap" has a price. This price (cost) must be calculated from the difference in interest rates of the currencies with which the arbitrage is carried out in order to obtain a net profit.

Let's consider the procedure for choosing interest rate arbitrage to determine the profitability of one or another option (Table 2.5).

Table 2.5. V

Consider the option of moving funds: from New York to Zurich.

Net profit from arbitrage of funds from New York to Zurich - interest spread (difference in interest rates of currencies with which arbitration is carried out) minus swap price (4.25% - 3.25%) - 0.9% - 0.10%.

So, interest rate arbitrage involves taking out loans in one currency and making loans in another. Risks from changes in exchange rates can be reduced by concluding forward contracts for currency exchange for the duration of the loan or deposit.

How does interest rate arbitrage affect forward and spot exchange rates?

Since the interest rate arbitrage operation is associated with supply and demand for both spot and forward transactions, this operation affects spot and forward exchange rates [When forming the answer, used: 92, p. 84-118].

Interest arbitrage (for example, moving the US dollar to country B) involves three operations:

1) borrowing a dollar and converting it into the currency of country B;

2) providing a loan in country B;

3) conclusion of a forward contract at the end of the loan for the reverse exchange of the country’s currency into dollars.

At the end of the loan (£ +1) - refers to the next year) the arbitrageur will be at fault (in dollars): $(1 + Dv gyu - interest rate in the USA.

Will receive in country B: B(+ g) units of currency B. This currency must be converted at the forward rate ($/£),+, into dollars in quantity. B(u + r,H$/B),

The amount of foreign currency (B) is equal to the amount of dollars borrowed ($) divided by the spot rate: ($/

so, the amount of money earned is equal to: ($/($/5), (1 + m) ($/£),♦,.

The arbitrage profit is equal to the number of dollars earned minus the number of dollars the arbitrageur owes to his lender:

The exchange of one currency for another affects supply and demand in the spot and forward markets. By exchanging dollars for currency B, additional demand is created in the spot market for the currency, which causes the value of that currency in dollars ($/#) to increase. On the forward market

Currency B is exchanged for the dollar, which leads to an additional supply of currency and a decrease in its value in foreign exchange terms($/#),♦,. An increase in the spot exchange rate ($/£), and a decrease in the forward rate ($/£), leads to a decrease in the profits of arbitrageurs to the point where the potential profit becomes zero.

Equation (2) describes the equilibrium that is caused by arbitrage actions. If we divide both sides of equation (2) by $(1+r), we find that the ratio of the forward rate to the spot rate is equal to the ratio of the yield in the United States to the yield in the country:

This equation shows that the ratio of the forward rate to the spot rate of currency B is equal to the ratio of the US yield to the yield in country B.

The relationship between spot rates, forward rates and interest rates, expressed by equality (3), is called interest rate parity.

In general, this relationship is written as follows:

where () is the designation of the expected value of the variable taken in brackets; A and B are two currencies; gy and?/, are the interest rates of currencies A and B. Relation (4) is called the international Fisher effect. Since the ratio of the expected future spot exchange rate to the current spot exchange rate can be expressed as one plus the expected percentage change in the spot rate ( (e)), then equation (4) can be written as follows:

Interest rate parity is also expressed by the following formula:

where /" is a forward premium to the currency of country B or a discount from it.

For example, if the US interest rate is 8% and the German euro interest rate is 6%, then interest rate parity results in the euro forward rate being at a 1.89 percent premium, i.e.

The ratio of the forward rate to the spot rate for the euro will be 1.0189.

When setting forward rates for their clients, banks rely on interest rate parity. Deviations from interest rate parity may be caused by barriers to arbitrage.