Real interest rate

# Real interest rate

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Encyclopedia
The "real interest rate" is the rate of interest an investor expects to receive after allowing for inflation. It can be described more formally by the Fisher equation
Fisher equation
The Fisher equation in financial mathematics and economics estimates the relationship between nominal and real interest rates under inflation....

, which states that the real interest rate is approximately the nominal interest rate
Nominal interest rate
In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation ; or, for interest rates "as stated" without adjustment for the full effect of compounding...

minus the inflation rate
Inflation rate
In economics, the inflation rate is a measure of inflation, the rate of increase of a price index . It is the percentage rate of change in price level over time. The rate of decrease in the purchasing power of money is approximately equal.The inflation rate is used to calculate the real interest...

. If, for example, an investor were able to lock in a 5% interest rate for the coming year and anticipated a 2% rise in prices, he would expect to earn a real interest rate of 3%. This is not a single number, as different investors have different expectations of future inflation. Since the inflation rate over the course of a loan is not known initially, volatility
Volatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...

in inflation represents a risk to both the lender and the borrower.

### Risks

In economics and finance, an individual who lends money for repayment at a later point in time expects to be compensated for the time value of money
Time value of money
The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time. The time value of money is the central concept in finance theory....

, or not having the use of that money while it is lent. In addition, they will want to be compensated for the risk
Risk
Risk is the potential that a chosen action or activity will lead to a loss . The notion implies that a choice having an influence on the outcome exists . Potential losses themselves may also be called "risks"...

s of having less purchasing power
Purchasing power is the number of goods/services that can be purchased with a unit of currency. For example, if you had taken one dollar to a store in the 1950s, you would have been able to buy a greater number of items than you would today, indicating that you would have had a greater purchasing...

when the loan is repaid. These risks are systematic risks, regulatory risks and inflation risks. The first includes the possibility that the borrower will default
Default (finance)
In finance, default occurs when a debtor has not met his or her legal obligations according to the debt contract, e.g. has not made a scheduled payment, or has violated a loan covenant of the debt contract. A default is the failure to pay back a loan. Default may occur if the debtor is either...

or be unable to pay on the originally agreed upon terms, or that collateral backing the loan will prove to be less valuable than estimated. The second includes tax
Tax
To tax is to impose a financial charge or other levy upon a taxpayer by a state or the functional equivalent of a state such that failure to pay is punishable by law. Taxes are also imposed by many subnational entities...

ation and changes in the law which would prevent the lender from collecting on a loan or having to pay more in taxes on the amount repaid than originally estimated. The third takes into account that the money repaid may not have as much buying power from the perspective of the lender as the money originally lent, that is inflation, and may include fluctuations in the value of the currencies involved.
Nominal interest rates include all three risk factors, plus the time value of the money itself.
Real interest rates include only the systematic and regulatory risks and are meant to measure the time value of money.
Real rates = Nominal rates minus Inflation and Currency adjustment. The "real interest rate" in an economy is often the rate of return on a risk free investment, such as US Treasury notes, minus an index of inflation, such as the CPI
CPI
A consumer price index is a measure of the average price of consumer goods and services purchased by householdsCPI may also stand for:*Central Port Injection, see fuel injection...

, or GDP deflator
GDP deflator
In economics, the GDP deflator is a measure of the level of prices of all new, domestically produced, final goods and services in an economy...

.

See Fisher equation
Fisher equation
The Fisher equation in financial mathematics and economics estimates the relationship between nominal and real interest rates under inflation....

where
= nominal interest rate;
= real interest rate;
= expected inflation rate.

For example, if somebody lends \$1000 for a year at 10 percent, and receives \$1100 back at the end of the year, this represents a 10 percent increase in his purchasing power if prices for the average goods and services that he buys are unchanged from what they were at the beginning of the year. However, if the prices of the food, clothing, housing, and other things that he wishes to purchase have increased 20 percent over this period, he has in fact suffered a real loss of about 10 percent in his purchasing power.

The inflation rate
Inflation rate
In economics, the inflation rate is a measure of inflation, the rate of increase of a price index . It is the percentage rate of change in price level over time. The rate of decrease in the purchasing power of money is approximately equal.The inflation rate is used to calculate the real interest...

will not be known in advance. People often base their expectation of future inflation on an average of inflation rates in the past, but this gives rise to errors. The real interest rate ex post may turn out to be quite different from the real interest rate that was expected in advance. Borrowers hope to repay in cheaper money in the future, while lenders hope to collect on more expensive money. When inflation and currency risks are underestimated by lenders, then they will suffer a net reduction in buying power.

The complexity increases for bonds
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...

issued for a long term, where the average inflation rate over the term of the loan may be subject to a great deal of uncertainty. In response to this, many governments have issued real return bonds, also known as inflation-indexed bonds, in which the principle value and coupon
Coupon (bond)
A coupon payment on a bond is a periodic interest payment that the bondholder receives during the time between when the bond is issued and when it matures. Coupons are normally described in terms of the coupon rate, which is calculated by adding the total amount of coupons paid per year and...

rises each year with the rate of inflation, with the result that the interest rate on the bond is a real interest rate. In the US, Treasury Inflation Protected Securities (TIPS) are issued by the US Treasury
United States Department of the Treasury
The Department of the Treasury is an executive department and the treasury of the United States federal government. It was established by an Act of Congress in 1789 to manage government revenue...

.

The expected real interest rate can vary considerably from year to year. The real interest rate on short term loans is strongly influenced by the monetary policy of central banks. The real interest rate on longer term bonds tends to be more market driven, and in recent decades, with globalized financial markets, the real interest rates in the industrialized countries have become increasingly correlated. Real interest rates have been low by historical standards since 2000, due to a combination of factors, including relatively weak demand for loans by corporations, plus strong savings in newly industrializing countries in Asia. The latter has offset the large borrowing demands by the US Federal Government, which might otherwise have put more upward pressure on real interest rates.

Related is the concept of "risk return", which is the rate of return minus the risks as measured against the safest (least-risky) investment available. Thus if a loan is made at 15% with an inflation rate of 5% and 10% in risks associated with default or problems repaying, then the "risk adjusted" rate of return on the investment is 0%.

### Importance in economic theory

Economics relies on measurable variables, chiefly price and objectively measurable production. Since production is "real", while prices are relative to the general price level, in order to compare an economy at two points in time, nominal price variables must be converted into "real" variables. For example, the number of people on payrolls represents a "real" variable, as does the number of hours worked. But in order to measure productivity, the nominal prices of the goods and services that labor produces must be converted to the "real" purchasing power. To do this requires adjusting prices for inflation.

The same is true of investment. Investment produces real gains in efficiency, and purchases productive capacity - factories, machines and so on - which is also real. To find the return on this capital, it is necessary to subtract the increases in its nominal value that are the result of increases in the general level of prices. To do this means subtracting the inflation rate from the nominal rate of return. For example, a portfolio of stocks that returns 10%, when inflation is running at 4% has a 6% real rate of return.

The real interest rate is used in various economic theories to explain such phenomena as the capital flight
Capital flight
Capital flight, in economics, occurs when assets and/or money rapidly flow out of a country, due to an economic event and that disturbs investors and causes them to lower their valuation of the assets in that country, or otherwise to lose confidence in its economic...

The term business cycle refers to economy-wide fluctuations in production or economic activity over several months or years...

and economic bubble
Economic bubble
An economic bubble is "trade in high volumes at prices that are considerably at variance with intrinsic values"...

s. When the real rate of interest is high, that is, demand for credit is high, then money will, all other things being equal, move from consumption to savings. Conversely, when the real rate of interest is low, demand will move from savings to investment and consumption. Different economic theories, beginning with the work of Knut Wicksell
Knut Wicksell
Johan Gustaf Knut Wicksell was a leading Swedish economist of the Stockholm school. His economic contributions would influence both the Keynesian and Austrian schools of economic thought....

have had different explanations of the effect of rising and falling real interest rates. Thus, international capital moves to markets that offer higher real rates of interest from markets that offer low or negative real rates of interest triggering speculation in equities, estates and exchange rates. Related to this concept is the idea of a "natural rate of interest", that is, the expected return on savings and capital invested.

### Negative real interest rates

The real interest rate solved from the Fisher equation
Fisher equation
The Fisher equation in financial mathematics and economics estimates the relationship between nominal and real interest rates under inflation....

is

If there is a negative real interest rate, it means that the inflation rate is greater than the interest rate. If the Federal funds rate
Federal funds rate
In the United States, the federal funds rate is the interest rate at which depository institutions actively trade balances held at the Federal Reserve, called federal funds, with each other, usually overnight, on an uncollateralized basis. Institutions with surplus balances in their accounts lend...

is 2% and the inflation rate is 10%, then the borrower would gain 7.27% of every dollar borrowed per year.

## Calculating Real Interest Rates using Change In Value

Bearing in mind that a real interest rate is simply the proportion of return or proportion of loss of a changed revenue stream after inflation has been factored in, we could use a simple change formula to calculate the real rate of change in income based on the new living costs.

Using the example above, for negative real rates of interest, where the standard bank loan rate is at 2% and the rate of inflation is 10%, we can use the following formula.

RIR =

Where:
RIR= Real Interest Rate
NIR= Nominal Interest Rate effect on initial investment
I= Inflationary effect on initial investment

So let’s assume a consumer borrows £200,000 from this bank.

Calculating the nominal change on initial value or "NIR" is simply £200,000 + 2% = £204,000

The inflationary effect on the initial value or "I" is calculated as £200,000 + 10%= £220,000. We calculate this value because we want to find the amount of money which is required to buy the same volume of goods and services in the following time period as £200,000 did in the preceding period.

So NIR - I = £204,000 - £220,000 = - £16,000.

This difference is the top line of the equation and shows that the ‘real’ debt is negative since the price of the debt rose at a lower rate than the money supply rate. So in effect, the creditor is losing £16,000 at prices in the latest time period. This is because the £204,000 return doesn’t reflect the same purchasing power in the current time period as £200,000 did in the preceding one. Assuming the borrowers annual income is £200,000, if this rose in line with inflation, he/she would gain £16,000 in latest money terms. If this income grew at 2%, he would find his loan no less easy or harder to pay but would find other items which grew at a higher rate of inflation more expensive.

This change represents the inflationary adjusted change in value and so by dividing it by this by the inflationary effect on the initial value and then multiplying by 100, we can get the percentage change on value based on the inflated value.

Therefore: RIR = (-£16,000/£220,000) X 100 = -0.07272 X 100 = -7.27%

This means that assuming a person’s valued income or wealth rose by the same level of inflation, the loan is around 7.3% lower in real value and would therefore represent a transfer of wealth from the bank to the repaying individual. Obviously, this would lead to commodity speculation
Speculation
In finance, speculation is a financial action that does not promise safety of the initial investment along with the return on the principal sum...

The term business cycle refers to economy-wide fluctuations in production or economic activity over several months or years...

s, as the borrower can profit from a negative real interest rate.

• Real versus nominal value (economics)
• Inflation
Inflation
In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...

• Deflation
• IS-LM model
• Macroeconomics
Macroeconomics
Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of the whole economy. This includes a national, regional, or global economy...

• Time value of money
Time value of money
The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time. The time value of money is the central concept in finance theory....