Yields on inflation-indexed government bonds of selected countries and maturities.

Negative real interest rates are a positive occurrence for non-yielding assets. You can see how gold clearly responds directly when real yields fall. With real returns going fully negative, we could really see precious metals go on a tear here if history repeats, or at least rhymes.

A negative real interest rate means that inflation is higher than interest rates. Therefore, savers will see a fall in the real value of their savings. For example in 2011, CPI inflation was 5%. Bank of England Base interest rates are 0.5%. In theory, this means that if you are saving money at the Bank of England base rate, your money is devaluing.
Today, short-term money market rates in Denmark, Germany (and much of the euro area), Japan, Sweden, and Switzerland all remain below zero (see chart). Nominal three-month interbank rates, 2007-October 2019. Recently, attention has focused on the large volume of long-term bonds with negative nominal yields (see chart).

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 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%.^[1] The expected real interest rate 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.

In the case of contracts stated in terms of the nominal interest rate, the real interest rate is known only at the end of the period of the loan, based on the realized inflation rate; this is called the ex-post real interest rate. Since the introduction of inflation-indexed bonds, ex-ante real interest rates have become observable.^[2]

Compensation for lending[edit]

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 expected value of the loss of purchasing power when the loan is repaid. These expected losses include 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 possibility of changes in taxation and regulatory changes which would prevent the lender from collecting on a loan or having to pay more in taxes on the amount repaid than originally estimated; and the loss of buying power compared to the money originally lent, due to inflation.

Nominal interest rates measure the sum of the compensations for all three sources of loss, plus the time value of the money itself.

Real interest rates measure the compensation for expected losses due to default and regulatory changes as well as measuring the time value of money; they differ from nominal rates of interest by excluding the inflation compensation component.

On an economy-wide basis, the 'real interest rate' in an economy is often considered to be the rate of return on a risk-free investment, such as US Treasury notes, minus an index of inflation, such as the rate of change of the CPI or GDP deflator.

Fisher equation[edit]

The relation between real and nominal interest rates and the expected inflation rate is given by the Fisher equation

{displaystyle 1+i=(1+r)(1+pi _{e})}

where

i = nominal interest rate;

r = real interest rate;

{displaystyle pi _{e}}

= 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. (Notice that the approximation here is a bit rough; since 1.1/1.25 = 0.88 = 1 - 0.88 = .12, the actual loss of purchasing power is exactly 12%.)

If the inflation rate and the nominal interest are relatively low, the Fisher equation can be approximated by

{displaystyle r=i-pi _{e}.}

After-tax real interest rate[edit]

The real return actually gained by a lender is lower if there is a non-zero tax rate imposed on interest earnings. Generally taxes are imposed on nominal interest earnings, not adjusted for inflation. If the tax rate is denoted as t, the before-tax nominal earning rate is i, the amount of taxes paid (per dollar or other unit invested) is i × t, and so the after-tax nominal earning is i × (1–t ). Hence the expected after-tax real return to the investor, using the simplified approximate Fisher equation above, is given by

Expected real after-tax return =

{displaystyle i(1-t)-pi _{e}.}

Variations in inflation[edit]

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 rate (ex-ante 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 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. (E.g., the three-month indexation lag of TIPS can result in a divergence of as much as 0.042% from the real interest rate, according to research by Grishchenko and Huang.^[3]) In the US, Treasury Inflation Protected Securities (TIPS) 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

Negative Real Money Yields