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, which states that the real interest rate is approximately the
nominal interest rate minus the inflation rate. 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, they 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 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, or not
having the use of that money while it is lent. In addition, they will want to be
compensated for the risks of having less purchasing power 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 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 taxation 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, or GDP deflator. = Fisher equation =
The relation between real and nominal interest rates and the expected
inflation rate is given by the Fisher equation
where i = nominal interest rate;
r = real interest rate; = expected inflation rate.
For example, if somebody lends $1000 for a year at 10%, and receives $1100 back
at the end of the year, this represents a 10% increase in her purchasing power
if prices for the average goods and services that she 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 she wishes to purchase have
increased 25% over this period, she has in fact suffered a real loss of about
15% in her purchasing power. = Variations in inflation =
The inflation rate 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 ratethat 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
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 principal value and coupon rises each year with the rate of
inflation, with the result that the interest rate on the bond approximates a
real interest rate. In the US, Treasury Inflation Protected Securities are
issued by the US Treasury. 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
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,
business cycle and economic bubbles. 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 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 is
If there is a negative real interest rate, it means that the inflation rate
is greater than the nominal interest rate. If the Federal funds rate is 2%
and the inflation rate is 10%, then the borrower would gain 7.27% of every
dollar borrowed per year. Negative real interest rates are an
important factor in government fiscal policy. Since 2010, the U.S. Treasury
has been obtaining negative real interest rates on government debt,
meaning the inflation rate is greater than the interest rate paid on the debt.
Such low rates, outpaced by the inflation rate, occur when the market
believes that there are no alternatives with sufficiently low risk, or when
popular institutional investments such as insurance companies, pensions, or
bond, money market, and balanced mutual funds are required or choose to invest
sufficiently large sums in Treasury securities to hedge against risk.
Lawrence Summers stated that at such low rates, government debt borrowing saves
taxpayer money, and improves creditworthiness. In the late 1940s
through the early 1970s, the US and UK both reduced their debt burden by about
30% to 40% of GDP per decade by taking advantage of negative real interest
rates, but there is no guarantee that government debt rates will continue to
stay so low. Between 1946 and 1974, the US debt-to-GDP ratio fell from 121% to
32% even though there were surpluses in only eight of those years which were
much smaller than the deficits. 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.
Where: r = Real Interest Rate
i = Nominal Interest Rate effect on initial investment
π = 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 i is simply £200,000 ×
1.02 = £204,000. The inflationary effect on the initial
value or π is calculated as £200,000 × 1.1 = £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: i − π = £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, she would gain £16,000 in latest money terms. If this income
grew at 2%, she would find her 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: r = − £16,000/£220,000 × 100 = − 0.07272
× 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
7.27% 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 and business cycles, as the borrower can profit from
a negative real interest rate. See also
Real versus nominal value Inflation
Deflation IS-LM model
Macroeconomics Financial repression
External links "Equilibrium Real Interest Rate," by
Roger Ferguson, 2004. On the distinction between real return
and nominal bonds, by Peter Spiro, 2004. Real interest rates by country via
Quandl References
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^ Grishchenko, Olesya V.; Jing-zhi Huang. "Inflation Risk Premium: Evidence
from the TIPS Market". Finance and Economics Discussion Series. Divisions
of Research & Statistics and Monetary Affairs Federal Reserve Board,
Washington, D.C. Retrieved 26 May 2013. ^ Saint Louis Federal Reserve "5-Year
Treasury Inflation-Indexed Security, Constant Maturity" FRED Economic Data
chart from government debt auctions ^ a b Carmen M. Reinhart and M. Belen
Sbrancia "The Liquidation of Government Debt" National Bureau of Economic
Research working paper No. 16893 ^ David Wessel "When Interest Rates Turn
Upside Down" Wall Street Journal ^ Lawrence Summers "Breaking the
negative feedback loop" Reuters ^ Matthew Yglesias "Why Are We
Collecting Taxes?" Slate ^ William H. Gross "The Caine Mutiny"
PIMCO Investment Outlook ^ "Why the U.S. Government Never, Ever
Has to Pay Back All Its Debt" The Atlantic, February 1, 2013