# Fisher's International Relations - International Economics

## International Fisher's relationship

■ Nominal rates are the interest rates used in calculations for everyday financial transactions.

They reflect in their essence the exchange rate between current and future money. For example, the interest rates used in the example with interest rate parity indicated that 1 CHF invested in the bank today, in a year will cost 1.08 CHF, and 1 USD - 1.12 USD.

However, nominal rates do not determine how much more goods and services can be purchased at 1.08 CHF or 1.12 USD, as the purchasing power (value) of money for this period may change.

The purchasing power of money changes, as is known, when prices for goods and services change. In particular, a decline in prices means an increase in the purchasing power of money, and a rise means a loss of value for money. The investor is not interested in the amount of American dollars, British pounds or Swiss francs that he owns, but the quantity of goods and services that he can buy with this money.

Therefore, the investor is not interested in the nominal but the real interest rate at which current goods and services are transformed into future goods and services.

All the above-mentioned financial variables, in particular the nominal interest rate r , the real interest rate p, as well as the inflation level i, should obviously be logically interconnected, which makes it widely used in financial management Fisher's formula:

The essence of this equation is quite obvious. If the investor wishes to receive a net income for one invested ruble (1 + ρ), including the return of the invested ruble, then this income should be indexed for the expected inflation rate (i.e., multiplied by (1 + i) i ) ), which will determine, as a result, the amount of the nominal income (1 + r ), and consequently, the nominal interest rate g.

From this relationship, the nominal rate is calculated using the formula

where .

As follows from Fisher's formula, the so-called inflation premium ( r + ρi), on which the real interest rate p increases, exceeds the rate of inflation by the value of ρi, thus illustrating the Fisher effect.

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In conditions of low inflation, in practice, the value ρ i is sometimes neglected, using a simplified form of calculating the nominal interest rate:

However, in the case of high inflation, the Fisher effect becomes very tangible.

Generalize the ratio of Fisher in the case of several currencies, for example, for the United States ruble and the US dollar:

This expression, called Fisher's international attitude , gives the ratio of the values ​​(purchasing power) of nominal deposits in different currencies, expressed through relative real interest rates and expected inflation rates in various countries.

If the expected real return to the same capital will be higher in the first country, then arbitrage is possible, which will cause the flow of capital from the second country to the first.

In conditions of perfect financial markets, this arbitration will continue until real capital prices are equal. In this case, the international attitude of I. Fisher will have the form

The right-hand side of this expression corresponds to the formulation of purchasing power parity, so you can write

Such a representation of Fisher's international attitude testifies that the expected exchange rate in the future can be determined through the ratio of nominal interest rates.

Another common view of Fisher's international relationship is derived by subtracting a unit from both parts of the expression for the Fisherian relationship:

It shows that the expected percentage change in the exchange rate can be calculated as the relative difference in nominal interest rates.

For small values ​​of rUSD

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