When you borrow or lend, you normally do so in dollar terms. If you take out a loan, the loan is denominated in dollars, and your promised payments are denominated in dollars. These dollar flows must be corrected for inflation to calculate the repayment in real terms. A similar point holds if you are a lender: you need to calculate the interest you earn on saving by correcting for inflation. The Fisher equation provides the link between nominal and real interest rates. To convert from nominal interest rates to real interest rates, we use the following formula: \[real\ interest\ rate ≈ nominal\ interest\ rate − inflation\ rate.\] To find the real interest rate, we take the nominal interest rate and subtract the inflation rate. For example, if a loan has a 12 percent interest rate and the inflation rate is 8 percent, then the real return on that loan is 4 percent. In calculating the real interest rate, we used the actual inflation rate. This is appropriate when you wish to understand the real interest rate actually paid under a loan contract. But at the time a loan agreement is made, the inflation rate that will occur in the future is not known with certainty. Instead, the borrower and lender use their expectations of future inflation to determine the interest rate on a loan. From that perspective, we use the following formula: \[contracted\ nominal\ interest\ rate ≈ real\ interest\ rate + expected\ inflation\ rate.\] We use the term contracted nominal interest rate to make clear that this is the rate set at the time of a loan agreement, not the realized real interest rate. Imagine two individuals write a loan contract to borrow P dollars at a nominal interest rate of i. This means that next year the amount to be repaid will be \(P \times (1 + i)\). This is a standard loan contract with a nominal interest rate of i. Now imagine that the individuals decided to write a loan contract to guarantee a constant real return (in terms of goods not dollars) denoted r. So the contract provides P this year in return for being repaid (enough dollars to buy) (1 + r) units of real gross domestic product (real GDP) next year. To repay this loan, the borrower gives the lender enough money to buy (1 + r) units of real GDP for each unit of real GDP that is lent. So if the inflation rate is π, then the price level has risen to \(P \times (1 + π)\), so the repayment in dollars for a loan of P dollars would be \(P(1 + r) \times (1 + π)\). Here (1 + π) is one plus the inflation rate. The inflation rate πt+1 is defined—as usual—as the percentage change in the price level from period t to period t + 1. \[\Pi_{t+1}=\left(P_{t+1}-P_{t}\right) / P_{t}\]. If a period is one year, then the price level next year is equal to the price this year multiplied by (1 + π): \[P_{t+1}=(1+\Pi_{t}) \times P_{t}\].Key Insight
The Fisher equation says that these two contracts should be equivalent:
\[(1 + i) = (1 + r) \times (1 + π).\]
As an approximation, this equation implies
\[i ≈ r + π.\]
To see this, multiply out the right-hand side and subtract 1 from each side to obtain
\[i = r + π + r\Pi.\]
If r and π are small numbers, then r\Pi is a very small number and can safely be ignored. For example, if r = 0.02 and \Pi = 0.03, then r\Pi = 0.0006, and our approximation is about 99 percent accurate.
The Main Uses of This Tool
The Fisher effect, also known as the Fisher Hypothesis, is an economic theory which was proposed by an economist named Irving Fisher. The theory states that the real interest rate is independent of monetary measures, specifically the nominal interest rate and the expected inflation rate. It describes the underlying relationship between inflation and both real and nominal interest rates. The theory proposes that the difference between the nominal interest rate and the expected inflation rate is equal to the real interest rate. Consequently, a rise in inflation leads to a fall in real interest rates, unless the same rate of increment occurs in nominal rates as with inflation. Mathematically, Real Interest Rate = Nominal Interest Rate - Inflation Rate.
- The Fisher Effect is an economic theory that was created by Irving Fisher between 1867-1947.
- The theory states that the real interest rate is independent of monetary measures, specifically the nominal interest rate and the expected inflation rate.
- It also states that the real interest rate equals the subtraction of the nominal interest rate from the expected inflation rate.
- In the Fisher Effect equation, all rates provided are seen as a composite.
- The Fisher Effect has been extended to the analysis of the money supply and the trading of international currencies.
- The Fisher Effect claims that all changes in inflation must be mirrored in the nominal interest rate if the real interest rate isn't affected.
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The Fisher Effect Equation
In the Fisher Effect equation, all rates provided are seen as a composite, i.e., they are seen as a whole and not as individual elements. The equation shows how to get the real interest rate by the subtraction of the expected inflation rate from the nominal interest rate. It also assumes that the real rate is constant making the nominal rate change point-for-point when there is a rise or fall in the inflation rate. The implication of the assumed constant real rate is that monetary events such as monetary policy actions will have no effect on the real economy.
Example of the Fisher Effect Theory
A real-world example of this theory can be seen in the banking industry. The nominal interest rate an investor has on a savings account is actually his nominal interest rate. If for instance, the nominal interest rate of an investor's savings account is 5% and its expected inflation rate is 4%, then the money in his account is actually growing at 1%. This implies that the rate of growth of his savings deposits depends on the real interest rate when observed from the perspective of his purchasing power. The lower the real interest rate, the longer it will take for his deposits to grow and vice versa.
Nominal Interest Rates and Real Interest Rates
Nominal interest rates state the monetary return that an investor's deposit will earn in a bank. An example, is a 6% increase in his deposit the next year if the nominal interest rate of the deposit is 6% per year assuming he made no withdrawals the previous year. Real interest rates on the other hand, considers his purchasing power. Using the example above, by the following year, the money in the bank will be able to buy 6% more commodities than if it was withdrawn and spent the previous year. The only connection between the real and nominal interest rates is the inflation rate which changes the quantity of commodity that can be bought by a given amount of money.
Importance in Money Supply
The Fisher Effect appears to be more than just an equation. The tandem effect of the money supply on the interest rate and inflation rate is shown by the Fisher Effect. For instance, if there is a push in a country's inflation rate by a 10% rise, caused by a change in its central bank's monetary policy, there will also be a 10% increase in the nominal interest rate of its economy. In this view, there is an assumption that the real interest rate will not be affected by a change in money supply. Nevertheless, the changes in the nominal interest rate will be directly shown.
The International Fisher Effect (IFE)
The international Fisher effect, which is also referred to as "Fisher's open hypothesis" is a hypothesis in international finance that suggests differences in nominal interest rates showing expected changes in the spot exchange rate between countries. It is specifically stated by the hypothesis that a spot exchange rate is expected to change equally in the opposite direction of the interest rate differential. Hence, the currency of the country which posses the higher nominal interest rate is expected to depreciate against the currency of the country that possesses the lower nominal interest rate. This is because higher nominal interest rates show an expectation of inflation.
Related Topics
The nominal interest rate is equal to the sum of the real interest rate and inflation
The Fisher equation is a concept in economics that describes the relationship between nominal and real interest rates under the effect of inflation. The equation states that the nominal interest rate is equal to the sum of the real interest rate plus inflation.
The Fisher equation is often used in situations where investors or lenders ask for an additional reward to compensate for losses in purchasing power due to high inflation.
The concept is widely used in the fields of finance and economics. It is frequently used in calculating returns on investments or in predicting the behavior of nominal and real interest rates. One example is when an investor wants to determine the actual (real) interest rate earned on an investment after accounting for the effect of inflation.
One interesting finding of the Fisher equation is related to monetary policy. The equation reveals that monetary policy moves inflation and the nominal interest rate together in the same direction. Whereas, monetary policy generally does not affect the real interest rate.
American economist Irving Fisher proposed the equation.
Fisher Equation Formula
The Fisher equation is expressed through the following formula:
Where:
- i – the nominal interest rate
- r – the real interest rate
- π – the inflation rate
However, one can also use the approximate version of the previous formula:
i ≈ r + πFisher Equation Example
Suppose Sam owns an investment portfolio. Last year, the portfolio earned a return of 3.25%. However, last year’s inflation rate was around 2%. Sam wants to determine the real return he earned from his portfolio. In order to find the real rate of return, we use the Fisher equation. The equation states that:
(1 + i) = (1 + r) (1 + π)We can rearrange the equation to find real interest rate:
Therefore, the real interest rate, or actual return on investment, of the portfolio equals:
The real interest that Sam’s investment portfolio earned last year, after accounting for inflation, is 1.26%.
Related Readings
Thank you for reading CFI’s guide to Fisher Equation. To keep learning and advancing your career, the following CFI resources will be helpful: