Nominal and real interest. Real and nominal interest rates

a) an interest rate established without taking into account changes in the purchasing value of money due to inflation (or a general interest rate in which its inflationary component is not eliminated);

B) the interest rate on a fixed income security that refers to the par value rather than the market price of the security.

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The term "interest rate" is one of the most commonly used phrases in the consumer finance and fixed income investing industry. Of course, there are several types of interest rates: real, nominal, effective, annual, etc.

The differences between different types of rates, such as nominal and real, are based on several key economic factors. But while these technical variables may seem trivial, lending institutions and retailers have taken advantage of the public's general ignorance of these differences to rake in hundreds of billions of dollars over the years. Thus, those who understand the difference between nominal and real interest rates have taken an important step toward becoming smarter consumers and investors.

Nominal interest rate

The nominal interest rate is conceptually the simplest type of interest rate. It is simply the stated interest rate on a given bond or loan. This type of interest rate is called a fixed income investment coupon rate because it is the issuer-guaranteed interest rate that was traditionally printed on the coupons that were redeemed by bondholders.

The nominal interest rate is essentially the actual money price that borrowers pay lenders for using their money. If the nominal loan rate is 5%, then borrowers can expect to pay $5 for every $100 they lend.

Real interest rate

The real interest rate is a little more complicated than the nominal rate, but is still fairly simple. The nominal interest rate does not tell the whole story because inflation reduces the purchasing power of the lender or investor so that they cannot buy the same amount of goods or services at payment or maturity with a certain amount of money as they can now.

The real interest rate is so named because it states the “real” rate that a lender or investor receives after inflation; that is, an interest rate that exceeds the rate of inflation. If a compounding bond has a nominal yield of 6% and the inflation rate is 4%, the real interest rate is only 2%.

The real interest rate can be considered the actual mathematical rate at which investors and lenders increase their purchasing power through their bonds and loans. It is possible that real interest rates will be negative if the inflation rate exceeds the nominal investment rate. For example, a bond with a nominal rate of 3% will have a real interest rate of -1% if the inflation rate is 4%. So the comparison between real and nominal interest rates can be summarized in this equation:

Nominal Interest Rate - Inflation = Real Interest Rate

From this formula several economic terms can be derived that lenders, borrowers and investors can use to make more informed financial decisions.

• Real interest rates can not only be positive or negative, but can also be higher or lower than nominal rates. Nominal interest rates will exceed real rates when the inflation rate is a positive number (as it usually is). But real rates can also exceed nominal rates during periods of deflation.

• The hypothesis states that the inflation rate moves in tandem with nominal interest rates over time, meaning that real interest rates become stable over longer periods of time. Thus, investors with longer time horizons can more accurately estimate their investment returns on an inflation-adjusted basis.

Effective interest rate

Another type of interest rate that investors and borrowers should be aware of is called the effective rate, which takes into account compliance.

For example, if a bond pays 6% interest and is compounded biannually, then an investor who invests $1,000 in that bond will receive $30 after the first 6 months ($1,000,000) and $30. 90 percent after the next 6 months (1,030 x 03). The investor received a total of $60. 90 for the year, which means that while the nominal rate was 6%, the effective rate was 6.09%.

From a mathematical perspective, the difference between the nominal and effective rates increases with the number of compounding periods within a given period. Please note that the rules regarding how the AER on a financial product is calculated and advertised are less strict than for the annual percentage rate (APR).

Applications

The main benefit of knowing the difference between nominal, real and effective rates is that it allows consumers to make better decisions about their loans and investments.

For example, a loan with frequent prescriptions will be more expensive than one that is collected annually. Keep these differences in mind when shopping for a mortgage.

Understanding interest rates also applies to investing. A bond that pays only 1% in real interest may not be worth investors' time if they are looking to increase their holdings over time. These rates effectively reveal the true return that will be posted on a fixed income investment and the true cost of borrowing for an individual or business.

Investors looking for inflation protection in a fixed-income rental can turn to instruments such as Treasury Inflation-Protected Securities (TIPS), which pay an interest rate indexed to inflation. In addition, mutual funds invest in bonds, mortgages and senior secured loans that pay variable interest rates that are adjusted periodically to current rates.

Bottom line

Interest rates can be broken down into several subcategories that include various factors such as inflation. Smart investors know that they can look beyond the par or coupon rate of a bond or loan to make sure it meets their investment goals. Contact your financial advisor if you need professional advice on interest rates and investments that keep up with inflation.

The interest rate is the relative amount of interest payments on loan capital over a certain period of time (usually a year). It is calculated as the ratio of the absolute amount of interest payments for the year to the amount of loan capital.

There are nominal and real interest rates. When people talk about interest rates, they mean real interest rates. However, actual rates cannot be directly observed. By concluding a loan agreement, we receive information about nominal interest rates.

The nominal interest rate is interest in monetary terms. The real interest rate is the increase in real wealth, expressed as an increase in the purchasing power of the investor or lender, or the exchange rate at which today's goods and services, real goods, are exchanged for future goods and services.

The relationship between the rates can be represented by the following expression:

where i is the nominal, or market, interest rate;

r - real interest rate;

r - inflation rate.

Only in special cases, when there is no price increase in the money market (p = 0), do real and nominal interest rates coincide. Equation (2) shows that the nominal interest rate can change due to changes in the real interest rate or due to changes in inflation. Since the borrower and lender do not know what rate inflation will take, they proceed from the expected rate of inflation. The equation becomes:

where r e is the expected inflation rate.

Equation (3) is known as the Fisher effect. Its essence is that the nominal interest rate is determined not by the actual rate of inflation, since it is unknown, but by the expected rate of inflation. The dynamics of the nominal interest rate repeats the movement of the expected inflation rate. It must be emphasized that when forming a market interest rate, it is the expected rate of inflation in the future, taking into account the maturity of the debt obligation, that matters, and not the actual inflation rate in the past.

If unexpected inflation occurs, then borrowers benefit at the expense of lenders, since they repay the loan with depreciated money. In the event of deflation, the lender will benefit at the expense of the borrower. If we compare the actual inflation index with the dynamics of the average rate on short-term loans, we can confirm the existence of a relationship between the nominal interest rate and the level of inflationary depreciation of money. Sometimes a situation may arise where real interest rates on loans are negative. This can happen if the inflation rate exceeds the growth rate of the nominal rate. Negative interest rates can be established during periods of runaway inflation or hyperinflation, as well as during an economic downturn, when demand for credit falls and nominal interest rates fall. Positive real interest rates mean higher income for lenders. This occurs if inflation reduces the real cost of borrowing (credit received).

Interest rates can be fixed or floating. A fixed interest rate is established for the entire period of use of borrowed funds without the unilateral right to revise it. A floating interest rate is a rate on medium- and long-term loans, which consists of two parts: a moving basis, which changes in accordance with market conditions and a fixed value, usually unchanged throughout the entire period of lending or circulation of debt securities. The interest rate system includes rates of the monetary and stock markets: rates on bank loans and deposits, treasury, bank and corporate bonds, interbank market interest rates and many others. Their classification is determined by a number of criteria, including: forms of credit, types of credit institutions, types of investments involving credit, loan terms, types of operations of a credit institution. bank loan interest rate

The main types of interest rates that both lenders and borrowers rely on include: the base bank rate, the money market interest rate, the interest rate on interbank loans; interest rate on Treasury bills.

Let's look at some types of nominal interest rates.

The base bank rate is the minimum rate set by each bank for loans provided. Banks provide loans by adding a certain margin, i.e. a premium to the base rate on most retail loans. The base rate includes the bank's operating and administrative expenses and profit. The rate is set independently by each bank. An increase or decrease in the rate of one bank will cause similar changes in other banks.

Interest rates for commercial, consumer and mortgage loans. This type of rate is well known both to entrepreneurs who take out loans from banks to develop their business, and to individuals. The actual loan rate will be determined as the sum of the base rate and the premium. The premium represents a premium for the risk of default by the borrower, as well as a premium for the risk associated with the maturity of the loan. However, if in commercial lending the interest rate is known to the borrower in advance, then in consumer loans the real effective rate is veiled by various marketing ploys and burdened with additional deductions: for example, with an announced rate of 20% per annum, the real payment turns out to be much higher, sometimes reaching 80-100% per annum .

Rates on time deposits (deposits) of individuals and companies in commercial banks. The overwhelming majority of enterprises, as well as an increasing number of individuals, have accounts in commercial banks, place ruble funds in time deposits (i.e. deposits), receiving interest for this, expressed when concluding a deposit agreement in the form of an interest rate. Deposit rates on passive operations of banks are influenced by the same market processes as rates on active operations. Deposit rates are closely related to other rates in the monetary and stock markets. A legal entity that wants to deposit a certain amount of money can buy bonds on the organized market or promissory notes on the unorganized market. A deposit with a bank is more convenient in terms of registration, but the availability of alternative options for placing funds means that banks cannot lower interest rates on deposits too much.

Rates on debt securities (bonds, certificates of deposit, bills, commercial paper, notes, etc.) refer to capital market interest rates. In debt securities there is an interest rate at which the borrower - the issuer of the security - borrows money. These rates are also very diverse: coupon on multi-year bonds, interest rate on bills and certificates of deposit, yield to maturity. Coupon rates indicate the interest income on the face value of the bonds. Yield to maturity shows interest income taking into account the market value of bonds and reinvestment of the resulting coupon income.

The Treasury bill interest rate is the rate at which Western central banks sell Treasury bills on the open market. Treasury bills are discounted securities, i.e. they are sold below par, so the rate is considered a discount yield.

The interest rate on interbank loans refers to money market interest rates. Many media outlets publish lending rates on the interbank market, when one commercial bank lends to another for a certain period in the form of transactions. These interbank lending rates (IBC) are less known to the general public in contrast to bank rates on private deposits. Such rates are the most flexible and more focused on market conditions.

The reference rate is a necessary infrastructure element of any loan market for transactions with interest-bearing instruments. When making a decision to issue or receive a loan, to invest or save funds, any economic individual (both banks and enterprises and individuals) needs a basic indicator - a generally accepted indicator of the interest rate, which would serve as a guideline for the general level of interest rate in a given currency, with which it would be possible to compare all kinds of rates on various financial instruments and deposit and credit products in the money market. In international practice, the role of a universal guiding light among numerous rates is played by interest rate indices, also called reference rates. For longer periods of lending money (and this is the capital market), the role of a general reference point is played by the rate of return on long-term government bonds.

It is customary to evaluate the interest rate in two projections: nominal and real values.

The essence of the nominal rate

Based on the definition of this concept, it is clear that the nominal interest rate does not take into account changes in price growth and other financial risks. The nominal rate can be taken into account by market participants only as an indicative value.

Mathematical effect of the nominal rate

Real rate + Expected inflation rate = Nominal rate

What matters when setting a market rate is the future rate of inflation, taking into account the maturity of the debt claim, and not the actual rate that was in the past.

Equality between the nominal and real rates is possible only in the complete absence of deflation or inflation. This state of affairs is practically unrealistic and is considered in science only in the form of ideal conditions for the functioning of the capital market.

Nominal compound interest rate

In order to correctly assess the expected income from the use of financial resources over a long period of time, economists advise taking into account the compound interest scheme. When calculating profit using the compound interest method, at the beginning of each new standard period, profit is calculated on the amount received based on the results of the previous period.

Any market mechanism in a changing environment, especially such as the domestic economy, is always associated with high risks. Be it a loan agreement or investing in securities, opening a new business or depository cooperation with a bank. When always assessing potential profit, you need to pay attention to external factors and the real state of the market. Based only on nominal profitability, you can make an incorrect, obviously unprofitable, or even potentially disastrous financial decision.

When people talk about interest rates, they usually mean real interest rates as opposed to nominal interest rates. However, actual rates cannot be directly observed. When concluding a loan agreement or viewing financial bulletins, we receive information primarily about nominal interest rates.

The nominal interest rate is interest in monetary terms.

For example, if a $1,000 annual loan pays $120 in interest, the nominal interest rate would be 12% per annum.

Having received an income of $120 on a loan, will the lender become richer? It depends on how prices have changed during the year. If prices rose by 8%, then the lender's real income increased by only 4% (12%-8%=4%).

The real interest rate is the increase in real wealth, expressed as an increase in the purchasing power of the investor or lender, or the exchange rate at which today's goods and services, real goods, are exchanged for future goods and services. Essentially, the real interest rate is the nominal rate adjusted for price changes.

The above definitions enable us to consider the relationship between nominal and real interest rates and inflation.

It can be expressed by the formula

i = r + r,(1.1)

Where i- nominal interest rate;

r- real interest rate;

R- inflation rate.

This equation shows that the nominal interest rate can change for two reasons: due to changes in the real interest rate and (or) due to changes in the inflation rate.

Real interest rates change very slowly over time because changes in nominal interest rates are caused by changes in the inflation rate.

A 1% increase in the inflation rate causes a 1% increase in the nominal rate.

When the borrower and lender agree on a nominal rate, they do not know what rate inflation will take at the end of the contract. They are based on expected inflation rates. The equation becomes:

i = r + r e . (1.2)

This equation is known as the Fisher equation, or the Fisher effect. Its essence is that the nominal interest rate is determined not by the actual inflation rate, since it is not yet known, but by the expected inflation rate ( R e).

The dynamics of the nominal interest rate follows the movement of the expected inflation rate.

Since it is impossible to accurately determine the future rate of inflation, rates are adjusted according to the actual level of inflation. Expectations match current experience.

If the inflation rate changes in the future, there will be deviations in the actual rate from the expected rate.

These are called the inflation surprise rate and can be expressed as the difference between the future actual rate and the expected inflation rate ( r - r e).

If the unexpected inflation rate is zero ( p = p"), then neither the lender nor the borrower loses or gains anything from inflation.

If unexpected inflation occurs ( r - r" > 0 ), then borrowers benefit at the expense of lenders, since they repay the loan with depreciated money.

In case of unexpected deflation, the situation will be reversed: the lender will benefit at the expense of the borrower.

From the above, three important points can be highlighted: 1) nominal interest rates include a markup or premium on expected inflation; 2) due to unforeseen inflation, this premium may turn out to be insufficient; 3) as a result, there will be an effect of redistribution of income between lenders and borrowers.

This problem can be looked at from the other side - from the point of view of real interest rates. In this regard, two new concepts arise:

• - expected real interest rate - the real interest rate that the borrower and lender expect when granting a loan. It is determined by the expected inflation rate ( r = i - r e);
• - actual real interest rate. It is determined by the actual inflation rate ( r = i - r).

Since the lender expects to earn income, the nominal interest rate on new borrowings must be at a level that will provide good prospects for real income consistent with current estimates of future inflation.

Deviations of the actual real rate from the expected one will depend on the accuracy of the forecast of future inflation rates.

At the same time, along with the accuracy of forecasts, there is difficulty in measuring the real rate. It consists of measuring inflation and choosing a price index. In this matter, one must proceed from how the funds received will ultimately be used. If loan proceeds are intended to finance future consumption, then the appropriate measure of income is the consumer price index. If a company needs to estimate the real cost of borrowed funds to finance working capital, then the wholesale price index will be adequate.

When the rate of inflation exceeds the rate of increase in the nominal rate, the real interest rate will be negative (less than zero). Although nominal rates typically rise when inflation rises, real interest rates have been known to fall below zero.

Negative real rates are holding back lending. At the same time, they encourage borrowing because the borrower gains what the lender loses.

Under what conditions and why does a negative real rate exist in financial markets? Negative real rates may be established for some time:

• - during periods of runaway inflation or hyperinflation, lenders provide loans even if real rates are negative, since receiving some nominal income is better than holding cash;
• - during an economic downturn, when demand for loans falls and nominal interest rates decrease;
• - at high inflation, to provide income to creditors. Borrowers won't be able to borrow at such high rates, especially if they expect inflation to slow soon. At the same time, rates on long-term loans may be lower than the inflation rate, since financial markets will expect a fall in short-term rates;
• - if inflation is not sustainable. Under the gold standard, the actual rate of inflation may be higher than expected, and nominal interest rates will not be high enough: “inflation takes merchants by surprise.”

Positive real interest rates mean higher income for lenders. However, if interest rates rise or fall in line with inflation, then the lender suffers a potential capital gain loss. This happens in the following cases:

• 1) inflation reduces the real cost of a loan (loan received). A homeowner who takes out a mortgage loan will find that the amount of debt they owe decreases in real terms. If the market value of his home rises but the face value of his mortgage remains the same, the homeowner benefits from the decreasing real real value of his debt. The lender will suffer a capital loss;
• 2) the market value of securities, such as government bonds, falls if the market nominal interest rate rises, and, conversely, rises if the interest rate falls.