Fisher Equation
It gives us the relationship between the nominal interest rate, real interest rate, and inflation.
What is the Fisher Equation?
The Fisher equation shows the relationship between nominal interest rate, real interest rate, and inflation. It was named after Irving Fisher, an American economist famous for his contributions to the quantity theory of money.
In economics, according to the equation, the nominal interest rate is equal to the real interest rate plus inflation. Thereby stating that as inflation increases, real interest falls as long as nominal interest rates increase at a lower rate than inflation.
The real interest rate is the most important for investment and saving decisions, as it represents the true cost of borrowing and the actual return on saving.
When the central bank sets the nominal interest rate, it intends to achieve a particular real interest rate since it aims to affect interest-sensitive spending.
A fascinating result of the Fisher equation has to do with monetary policy. The equation shows that the direction of monetary policy is the same for both inflation and the nominal interest rate. The real interest rate, however, is typically unaffected by monetary policy.
Bond analysis can be done using the Fisher equation. The nominal interest rate, less the anticipated inflation rate, essentially represents the real yield on a bond.
The bondholder's real return will be negatively impacted if actual inflation during the bond's life exceeds expected inflation. Therefore, inflation-indexed bonds like U.S. Treasury Inflation-Protected Securities were developed to reduce this risk and inflation uncertainty.
The real cash flow of an indexed bond will not be impacted by inflation, assuring bondholders.
Suppose bonds have been used in the economy to protect against inflation because the inflation rate indexes the face value. In that case, the yield on such a bond is a real interest rate and can provide a third measure.
There are only a few countries that have issued index-linked or inflation-proof bonds (the UK in 1981, the USA in 1997, and France in 1998).
The amount borrowed and the payback obligations to the lender are typically stated in nominal terms or terms before inflation when loans are made.
However, a dollar borrowed now is worth less than a dollar repaid in the future when inflation occurs. It is required to adjust the nominal cash flows to account for future inflation to determine the loan's actual economics.
Key Takeaways
- The Fisher equation gives the relationship between nominal interest rate, real interest rate, and inflation.
- The nominal interest rate equals the real interest rate plus inflation.
- i ≈ r + π
- In a hypothetical situation, if the inflation is zero, the real interest rate equals the nominal interest rate.
- The Fisher equation helps investors calculate the real rate of return on their investments.
- According to the International Fisher Effect (IFE), there is a direct correlation between changes in the nominal interest rates of two countries' currencies at any given moment.
Fisher Equation formula
Fisher argued that the real interest rate is a better indicator of a country’s economic state as it is adjusted for inflation.
The formula for the equation is as follows:
(1 + i) = (1 + r) (1 + π)
Where
- i = nominal interest rate
- r = real interest rate
- π = inflation
Using linear approximation in the above equation, we can get a simplified version of the fisher equation as
i ≈ r + π
Fisher Equation Example
Suppose in a year, you are getting a return of 4.75% on your investment portfolio. The inflation rate for that year was 2%; now, you want to know the real return you earned from the portfolio.
r = 1- π
r = 4.75 - 2
r = 2.75%
The real return adjusted for inflation you earned through your portfolio is 2.75%.
In a hypothetical situation, if the inflation is zero, then the real interest rate equals the nominal interest rate.
r ≈ i - π
Since inflation is seen as a risk by most countries, it is always in positive terms; therefore, in most cases, the real interest rate is always lower than the nominal interest rate.
For example, you go to the bank, and your savings account's interest rate is 3%. This is your nominal interest rate.
Suppose the inflation rate (in expected terms) is 2%, so your real interest rate equals 1%. Therefore, your savings accounts are growing at just 1%.
The equation is important because it helps investors calculate the real rate of return on their investments.
International fisher effect
According to the International Fisher Effect (IFE), there is a direct correlation between changes in the nominal interest rates of two countries' currencies at any given moment.
It is used to forecast and comprehend current and upcoming spot currency price fluctuations because it is based on past, present, and future risk-free nominal interest rates rather than pure inflation.
According to a hypothesis, a country experiences lower levels of inflation when it has lower interest rates; this might result in an increase in the real worth of the country’s currency compared to the currencies of other countries.
When a country’s interest rates are high, there will be more inflation, resulting in the country’s currency being depreciated.
To monitor that the expected appreciation or the expected depreciation of the country’s currencies remains proportional to the difference in their nominal interest rates, the International Fisher Effect builds upon the Fisher Effect idea.
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