Real interest rate

Last updated June 01, 2023

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

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

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

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

where

i

= nominal interest rate;

r

= real interest rate;

\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 - 1 = 0.88 - 1 = -.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

r=i-\pi _{e}.

After-tax real interest rate

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 =

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

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 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 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

The amount of physical investment—in particular the purchasing of new machines and other productive capacity—that firms engage in partially depends on the level of real interest rates because such purchases typically must be financed by issuing new bonds. If real interest rates are high, the cost of borrowing may exceed the real physical return of some potentially purchased machines (in the form of output produced); in that case those machines will not be purchased. Lower real interest rates would make it profitable to borrow to finance the purchasing of a greater number of machines.

The real interest rate is used in various economic theories to explain such phenomena as capital flight, business cycles and economic bubbles. When the real rate of interest is high, because demand for credit is high, then the usage of income will, all other things being equal, move from consumption to saving, and physical investment will fall. Conversely, when the real rate of interest is low, income usage will move from saving to consumption, and physical investment will rise. 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 -- assuming risks are constant -- international capital moves to markets that offer higher real rates of interest from markets that offer low or negative real rates of interest. Capital flows of this kind often reflect speculation in financial and foreign exchange rate markets.

Real federal funds rate

In setting monetary policy, the U.S. Federal Reserve (and other central banks) uses open market operations, affecting the amounts of very short-term funds (federal funds) supplied and demanded and thus affecting the federal funds rate. By targeting this at a low rate, they can encourage borrowing and thus economic activity; or the reverse by raising the rate. Like any interest rate, there are a nominal and a real value defined as described above. Further, there is a concept called the "equilibrium real federal funds rate" (r*, or "r-star"), alternatively called the "natural rate of interest" or the "neutral real rate", which is the "level of the real federal funds rate, if allowed to prevail for several years, [that] would place economic activity at its potential and keep inflation low and stable." There are various methods used to estimate this amount, using tools such as the Taylor Rule. It is possible for this rate to be negative.^[4]

Negative real interest rates

The real interest rate solved from the Fisher equation is

{\frac {1+i}{1+\pi }}-1=r

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.

{\frac {1+0.02}{1+0.1}}-1=-0.0727

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.^[5] 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.^[6]^[7] Lawrence Summers stated that at such low rates, government debt borrowing saves taxpayer money, and improves creditworthiness.^[8]^[9] 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.^[6]^[10] 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.^[11]

Related Research Articles

In economics and finance, arbitrage is the practice of taking advantage of a difference in prices in two or more markets; striking a combination of matching deals to capitalise on the difference, the profit being the difference between the market prices at which the unit is traded. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage opportunity is present when there is the possibility to instantaneously buy something for a low price and sell it for a higher price.

In finance, a bond is a type of security under which the issuer (debtor) owes the holder (creditor) a debt, and is obliged – depending on the terms – to provide cash flow to the creditor. The timing and the amount of cash flow provided varies, depending on the economic value that is emphasized upon, thus giving rise to different types of bonds. The interest is usually payable at fixed intervals: semiannual, annual, and less often at other periods. Thus, a bond is a form of loan or IOU. Bonds provide the borrower with external funds to finance long-term investments or, in the case of government bonds, to finance current expenditure.

In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of zero- or negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of borrowed funds is less than the total amount of money paid to the lender.

A government bond or sovereign bond is a form of bond issued by a government to support public spending. It generally includes a commitment to pay periodic interest, called coupon payments, and to repay the face value on the maturity date.

In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate. It is distinct from a fee which the borrower may pay the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.

<span class="mw-page-title-main">Interest rate</span> Percentage of a sum of money charged for its use

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed.

In finance, a loan is the transfer of money by one party to another with an agreement to pay it back. The recipient, or borrower, incurs a debt and is usually required to pay interest for the use of the money.

<span class="mw-page-title-main">Money market</span> Type of financial market providing short-term funds

The money market is a component of the economy that provides short-term funds. The money market deals in short-term loans, generally for a period of a year or less.

<span class="mw-page-title-main">Monetary policy</span> Policy of interest rates or money supply

Monetary policy is the policy adopted by the monetary authority of a nation to control either the interest rate payable for very short-term borrowing or the money supply, often as an attempt to reduce inflation or the interest rate, to ensure price stability and general trust of the value and stability of the nation's currency.

<span class="mw-page-title-main">Government budget balance</span> Difference between revenues and spending

The government budget balance, also referred to as the general government balance, public budget balance, or public fiscal balance, is the difference between government revenues and spending. For a government that uses accrual accounting the budget balance is calculated using only spending on current operations, with expenditure on new capital assets excluded. A positive balance is called a government budget surplus, and a negative balance is a government budget deficit. A government budget presents the government's proposed revenues and spending for a financial year.

In financial mathematics and economics, the Fisher equation expresses the relationship between nominal interest rates and real interest rates under inflation. Named after Irving Fisher, an American economist, it can be expressed as real interest rate ≈ nominal interest rate − inflation rate. In more formal terms, where $equals the real interest rate, equals the nominal interest rate, and equals the inflation rate, the Fisher equation is . It can also be expressed as or .$

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. government debt has been managed by the Bureau of the Fiscal Service, succeeding the Bureau of the Public Debt.

<span class="mw-page-title-main">Repurchase agreement</span> Form of short-term borrowing

A repurchase agreement, also known as a repo, RP, or sale and repurchase agreement, is a form of short-term borrowing, mainly in government securities. The dealer sells the underlying security to investors and, by agreement between the two parties, buys them back shortly afterwards, usually the following day, at a slightly higher price.

In finance, the yield curve is a graph which depicts how the yields on debt instruments - such as bonds - vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or years remaining to maturity, with the shortest maturity on the left and progressively longer time periods on the right. The vertical or y-axis depicts the annualized yield to maturity.

<span class="mw-page-title-main">Fixed income</span> Type of investment

Fixed income refers to any type of investment under which the borrower or issuer is obliged to make payments of a fixed amount on a fixed schedule. For example, the borrower may have to pay interest at a fixed rate once a year and repay the principal amount on maturity. Fixed-income securities — more commonly known as bonds — can be contrasted with equity securities – often referred to as stocks and shares – that create no obligation to pay dividends or any other form of income. Bonds carry a level of legal protections for investors that equity securities do not — in the event of a bankruptcy, bond holders would be repaid after liquidation of assets, whereas shareholders with stock often receive nothing.

A mortgage-backed security (MBS) is a type of asset-backed security which is secured by a mortgage or collection of mortgages. The mortgages are aggregated and sold to a group of individuals that securitizes, or packages, the loans together into a security that investors can buy. Bonds securitizing mortgages are usually treated as a separate class, termed residential; another class is commercial, depending on whether the underlying asset is mortgages owned by borrowers or assets for commercial purposes ranging from office space to multi-dwelling buildings.

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 interest rate is independent of monetary measures, therefore, the nominal interest rate will adjust to accommodate any changes in expected inflation.

Fixed income analysis is the process of determining the value of a debt security based on an assessment of its risk profile, which can include interest rate risk, risk of the issuer failing to repay the debt, market supply and demand for the security, call provisions and macroeconomic considerations affecting its value in the future. It also addresses the likely price behavior in hedging portfolios. Based on such an analysis, a fixed income analyst tries to reach a conclusion as to whether to buy, sell, hold, hedge or avoid the particular security.

<span class="mw-page-title-main">Mortgage loan</span> Loan secured using real estate

A mortgage loan or simply mortgage, in civil law jurisdicions known also as a hypothec loan, is a loan used either by purchasers of real property to raise funds to buy real estate, or by existing property owners to raise funds for any purpose while putting a lien on the property being mortgaged. The loan is "secured" on the borrower's property through a process known as mortgage origination. This means that a legal mechanism is put into place which allows the lender to take possession and sell the secured property to pay off the loan in the event the borrower defaults on the loan or otherwise fails to abide by its terms. The word mortgage is derived from a Law French term used in Britain in the Middle Ages meaning "death pledge" and refers to the pledge ending (dying) when either the obligation is fulfilled or the property is taken through foreclosure. A mortgage can also be described as "a borrower giving consideration in the form of a collateral for a benefit (loan)".

This article provides background information regarding the subprime mortgage crisis. It discusses subprime lending, foreclosures, risk types, and mechanisms through which various entities involved were affected by the crisis.

References

↑ Marc Levinson, 2006, "Guide to Financial Markets", The Economist, page 24
↑ "FRB: Speech with Slideshow--Bernanke, Long-Term Interest Rates--March 1, 2013". www.federalreserve.gov. Retrieved 2017-03-07.
↑ Grishchenko, Olesya V.; Jing-zhi Huang (June 2012). "Inflation Risk Premium: Evidence from the TIPS Market" (PDF). Finance and Economics Discussion Series. Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Retrieved 26 May 2013.
↑ U.S. Federal Reserve-Remarks by Vice Chairman Roger W. Ferguson Jr. October 29, 2004
↑ Saint Louis Federal Reserve (2012) "5-Year Treasury Inflation-Indexed Security, Constant Maturity" FRED Economic Data chart from government debt auctions (the x-axis at y=0 represents the inflation rate over the life of the security)
1 2 Carmen M. Reinhart and M. Belen Sbrancia (March 2011) "The Liquidation of Government Debt" National Bureau of Economic Research working paper No. 16893
↑ David Wessel (August 8, 2012) "When Interest Rates Turn Upside Down" Wall Street Journal (full text Archived 2013-01-20 at the Wayback Machine )
↑ Lawrence Summers (June 3, 2012) "Breaking the negative feedback loop" Reuters
↑ Matthew Yglesias (May 30, 2012) "Why Are We Collecting Taxes?" Slate
↑ William H. Gross (May 2, 2011) "The Caine Mutiny (Part 2)" PIMCO Investment Outlook
↑ "Why the U.S. Government Never, Ever Has to Pay Back All Its Debt" The Atlantic, February 1, 2013

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[1] Marc Levinson, 2006, "Guide to Financial Markets", The Economist, page 24

[2] "FRB: Speech with Slideshow--Bernanke, Long-Term Interest Rates--March 1, 2013". www.federalreserve.gov. Retrieved 2017-03-07.

[3] Grishchenko, Olesya V.; Jing-zhi Huang (June 2012). "Inflation Risk Premium: Evidence from the TIPS Market" (PDF). Finance and Economics Discussion Series. Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Retrieved 26 May 2013.

[4] U.S. Federal Reserve-Remarks by Vice Chairman Roger W. Ferguson Jr. October 29, 2004

[5] Saint Louis Federal Reserve (2012) "5-Year Treasury Inflation-Indexed Security, Constant Maturity" FRED Economic Data chart from government debt auctions (the x-axis at y=0 represents the inflation rate over the life of the security)

[liquidation-6] 1 2 Carmen M. Reinhart and M. Belen Sbrancia (March 2011) "The Liquidation of Government Debt" National Bureau of Economic Research working paper No. 16893

[7] David Wessel (August 8, 2012) "When Interest Rates Turn Upside Down" Wall Street Journal (full text Archived 2013-01-20 at the Wayback Machine )

[8] Lawrence Summers (June 3, 2012) "Breaking the negative feedback loop" Reuters

[9] Matthew Yglesias (May 30, 2012) "Why Are We Collecting Taxes?" Slate

[10] William H. Gross (May 2, 2011) "The Caine Mutiny (Part 2)" PIMCO Investment Outlook

[11] "Why the U.S. Government Never, Ever Has to Pay Back All Its Debt" The Atlantic, February 1, 2013

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