NOTE: this is not Fisher's equation in differential equations NOTE: this is not the Fisher equation in financial mathematics. ... An illustration of a differential equation. ...

The Fisher equation in financial mathematics and economics estimates the relationship between nominal and real interest rates under inflation. In finance, this equation is primarily used in YTM calculations of bonds or IRR calculations of investments. In economics, this equation is used to predict nominal and real interest rate behavior. Mathematical finance is the branch of applied mathematics concerned with the financial markets. ... Face-to-face trading interactions among on the New York Stock Exchange trading floor Economics, as a social science, studies the production, distribution, and consumption of commodities. ... An interest rate is the price a borrower pays for the use of money he does not own, and the return a lender receives for deferring his consumption, by lending to the borrower. ... Finance studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. ... Yield to maturity (YTM) is the internal rate of return on cash flow of a fixed income security, often bond, if the security were to be held until maturity. ... In finance, a bond is a debt security, in which the issuer owes the holders a debt and is obliged to repay the principal and interest (the coupon) at a later date, termed maturity. ... The internal rate of return (IRR) is defined as the discount rate that gives a net present value (NPV) of zero. ... Invest redirects here. ...

Let r_r denote the real interest rate, r_n denote the nominal interest rate, and let π denote the inflation rate. The real interest rate is the interest rate charged to a risk free borrower, minus the inflation rate. ... A nominal interest rate is a rate as stated. ... In economics, the inflation rate is the rate of increase of the average price level (a measure of inflation). ...

The Fisher equation is the following:

r_n = r_r + π

The equation can be used in either ex-ante (before) or ex-post (after) analysis. Ex ante is a Latin term meaning beforehand. Ex ante evaluations deal with forecasting and forecasted returns on invested money. ... Ex ante is a Latin term meaning beforehand. Ex ante evaluations deal with forecasting and forecasted returns on invested money. ...

This equation is named after Irving Fisher who was famous for his works on the theory of interest. This equation existed before Fisher, but Fisher proposed a better approximation which is given below. The estimated equation can be derived from the proposed equation Irving Fisher, born (February 27, 1867 Saugerties, New York — April 29, 1947, New York) was an American economist, health campaigner, and eugenicist. ... In finance, interest has three general definitions. ...

1 + r_n = (1 + r_r)(1 + π).

Derivation

From

1 + r_n = (1 + r_r)(1 + π)

follows

1 + r_n = 1 + r_r + π + r_rπ

and hence

r_n = r_r + π + r_rπ

Drop r_rπ because r_r + π is much larger than r_rπ:

r_n = r_r + π

is the result.

Example

The market rate of return on the 4.25% UK government bond maturing on 7 March 2036 is currently 3.81% per annum. Let's assume that this can be broken down into a real rate of exactly 2% and an inflation premium of 1.775% (no premium for risk, as government bond is considered to be risk-free): A government bond is a bond issued by a national government denominated in the countrys own currency. ...

1.02 x 1.01775 = 1.0381

This article implies that you can ignore the third term (0.02 x 0.01775 = 0.00035 or 0.035%) and just call the nominal rate of return 3.775%, on the grounds that that is almost the same as 3.81%.

At a nominal rate of return of 3.81% pa, the value of the bond is £107.84 per £100 nominal. At a rate of return of 3.775% pa, the value is £108.50 per £100 nominal, or 66p more.

The average size of actual transactions in this bond in the market in the final quarter of 2005 was £10 million. So a difference in price of 66p per £100 translates into a difference of £66,000 per deal.

See also

• yield
• interest rate, inflation
• Term Structure of Interest Rates
• Fisher hypothesis