financial mathematics Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...

and

economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics anal ...

, the Fisher equation expresses the relationship between nominal

interest rate An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, t ...

s and

real interest rate The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approxi ...

s under

inflation In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduct ...

. Named after

Irving Fisher Irving Fisher (February 27, 1867 – April 29, 1947) was an American economist, statistician, inventor, eugenicist and progressive social campaigner. He was one of the earliest American neoclassical economists, though his later work on debt de ...

, an American economist, it can be expressed as real interest rate ≈ nominal interest rate − inflation rate. In more formal terms, where

r

equals the real interest rate,

i

equals the nominal interest rate, and

\pi

equals the inflation rate, the Fisher equation is

r = i - \pi

. It can also be expressed as

i = r + \pi

(1 + i) = (1 + r) (1 + \pi)

Applications

Borrowing, lending and the time value of money

When loans are made, the amount borrowed and the repayments due to the lender are normally stated in nominal terms, before inflation. However, when inflation occurs, a dollar repaid in the future is worth less than a dollar borrowed today. To calculate the true economics of the loan, it is necessary to adjust the nominal cash flows to account for future inflation.

Inflation-indexed bonds

The Fisher equation can be used in the analysis of bonds. The real return on a bond is roughly equivalent to the nominal interest rate minus the expected inflation rate. But if actual inflation exceeds expected inflation during the life of the bond, the bondholder's real return will suffer. This risk is one of the reasons inflation-indexed bonds such as U.S.

Treasury Inflation-Protected Securities United States Treasury securities, also called Treasuries or Treasurys, are government debt instruments issued by the United States Department of the Treasury to finance government spending as an alternative to taxation. Since 2012, U.S. go ...

were created to eliminate inflation uncertainty. Holders of indexed bonds are assured that the real cash flow of the bond (principal plus interest) will not be affected by inflation.

Cost–benefit analysis

As detailed by Steve Hanke, Philip Carver, and Paul Bugg (1975),

cost benefit analysis In production, research, retail, and accounting, a cost is the value of money that has been used up to produce something or deliver a service, and hence is not available for use anymore. In business, the cost may be one of acquisition, in which ...

can be greatly distorted if the exact Fisher equation is not applied. Prices and interest rates must both be projected in either real or nominal terms.

Monetary policy

The Fisher equation plays a key role in the

Fisher hypothesis In economics, the Fisher effect is the tendency for nominal interest rates to change to follow the inflation rate. It is named after the economist Irving Fisher, who first observed and explained this relationship. Fisher proposed that the real i ...

, which asserts that the real interest rate is unaffected by monetary policy and hence unaffected by the expected inflation rate. With a fixed real interest rate, a given percent change in the expected inflation rate will, according to the equation, necessarily be met with an equal percent change in the nominal interest rate in the same direction.

Applications

Borrowing, lending and the time value of money

Inflation-indexed bonds

Cost–benefit analysis

Monetary policy

See also

References

Further reading