Real interest rate as a measure of investment success

Irving Fisher is an American economist, a representative of the neoclassical movement in economics. Born February 27, 1867 in Saugerties, Co. NY. He made a great contribution to the creation of the theory of money, and also derived the “Fisher equation” and the “equation of exchange”.

His works were taken as the basis for modern methods for calculating inflation rates. In addition, they greatly helped to understand the patterns of inflation and pricing.

Types of interest rates

There are several types of interest rates.

Fixed and floating rates

See also: Swaption

Depending on whether the rate changes over time, fixed and floating interest rates are distinguished:

• A fixed interest rate
  is constant, set for a certain period and does not depend on any circumstances.
• The floating interest rate
  is subject to periodic review. The rate is changed based on fluctuations in certain indicators. A classic example of such indicators is the London Interbank Offered Rate (LIBOR, the weighted average rate on the London interbank lending market). Accordingly, a floating rate of LIBOR+5% will mean that the nominal interest rate is 5% higher than the LIBOR rate.

Decursive and anticipatory bets

Depending on the timing of interest payments, there are two types of interest rates:

• decursive rate
  - interest is paid at the end along with the principal amount of the loan
• anticipatory rate
  - interest is paid at the time the loan is granted (in advance) and is determined based on the final amount of the debt.

An anticipatory rate is more profitable for the lender, and a decursive rate is more profitable for the borrower. So, if the interest rate is 10%, then with a decursive rate for a loan of 1000 rubles. the creditor will receive 1100 rubles. at the end of the term. At an anticipatory rate, he will give the borrower 900 rubles. and at the end of the term will receive 1000 rubles.

Real and nominal rates

There is a distinction between nominal and real interest rates.

Nominal interest rate

is the market interest rate without taking into account inflation, reflecting the current valuation of monetary assets.

Real interest rate

is the interest rate taking into account inflation.

The relationship between real,
nominal
rates and
inflation
is generally described by the following (approximate) formula:
ir=in−π{\displaystyle i_{r}=i_{n}-\pi },
where

• in{\displaystyle i_{n}} — nominal interest rate,
• ir{\displaystyle i_{r}} — real interest rate,
• π{\displaystyle \pi } is the expected or planned inflation rate.

Irving Fisher proposed a more precise formula for the relationship between real, nominal rates and inflation, expressed by the Fisher formula named after him:

ir=1+in1+π−1=in−π1+π{\displaystyle i_{r}={\frac {1+i_{n}}{1+\pi }}-1={\frac {i_{ n}-\pi }{1+\pi }}}

For π={\displaystyle \pi =0} and π=in{\displaystyle \pi =i_{n}} both formulas give the same value. It is easy to see that for small values ​​of the inflation rate π{\displaystyle \pi } the results differ little, but if inflation is high, then the Fisher formula should be applied.

According to Fisher, the real interest rate must be numerically equal to the marginal productivity of capital.

Inflation forecasting

The phenomenon of inflation is an excessive amount of money circulating in a country, which leads to its depreciation.

Inflation is classified according to the following criteria:

Uniformity - dependence of the inflation rate on time.

Homogeneity - distribution of influence across all goods and resources.

Inflation forecasting is calculated using the inflation index and hidden inflation.

The main factors when forecasting inflation are:

• changes in exchange rates;
• increase in the amount of money;
• changes in interest rates;

Another common method is to calculate the inflation rate based on the GDP deflator. For forecasting, this methodology records the following changes in the economy:

• change in profit;
• changes in payments to consumers;
• changes in import and export prices;
• change in rates.

Calculation of investment returns taking into account inflation and without it

The return on investment is considered to be the percentage of the profit received to the amount of the initial contribution.

The return formula without taking into account inflation will look like this:

X = ((Pn - P) / P )*100%

Where:

• X - profitability;
• Pn—total amount;
• P - initial payment;

In this form, the final profitability is calculated without taking into account the time spent.

In order to calculate the yield as a percentage per annum, you must use the following formula:

Xt = ((Pn - P) / P ) * (365 / T) * 100%

Where T is the number of days of holding the asset.

Interesting: Liquidity: what is it in simple words

Both methods do not take into account the impact of inflation on profitability.

Inflation-adjusted return (real return) should be calculated using the formula:

R = (1 + X) / (1 + i) - 1

• R - real profitability;
• X is the nominal rate of return;
• i — inflation.

Based on Fisher's model, one main conclusion can be drawn: inflation does not bring income.

The increase in the nominal rate due to inflation will never be greater than the amount of money invested that has depreciated. In addition, a high rate of inflation growth implies significant risks for banks, and compensation for these risks falls on the shoulders of depositors.

Fisher equation

Fisher equation

Regulating the amount of money in circulation and the price level is one of the main methods of influencing a market-type economy.

The connection between the quantity of money and the price level was formulated by representatives of the quantity theory of money.

In a free market (market economy), it is necessary to regulate economic processes to a certain extent (Keynesian model). Regulation of economic processes is carried out, as a rule, either by the state or by specialized bodies. As the practice of the 20th century has shown, many other important economic parameters, primarily the level of prices and interest rates (credit prices), depend on the amount of money used in the economy. The relationship between the price level and the amount of money in circulation was clearly formulated within the framework of the quantity theory of money.

Fisher equation

Prices and the amount of money are directly related.

Depending on various conditions, prices may change due to changes in the money supply, but the money supply can also change depending on changes in prices.

The exchange equation looks like this:

Fischer formula

There is no doubt that this formula is purely theoretical and unsuitable for practical calculations. The Fisher equation does not contain any single solution; Within this model, multivariance is possible. At the same time, with certain tolerances, one thing is certain: the price level depends on the amount of money in circulation. Usually two assumptions are made:

• the speed of money turnover is a constant value;
• All production capacities on the farm are fully utilized.

The point of these assumptions is to eliminate the influence of these quantities on the equality of the right and left sides of the Fisher equation. But even if these two assumptions are met, it cannot be unconditionally stated that the growth of the money supply is primary, and the rise in prices is secondary. The dependence here is mutual.

In conditions of stable economic development, the money supply acts as a regulator of the price level. But with structural imbalances in the economy, a primary change in prices is possible, and only then a change in the money supply (Fig. 17).

Normal economic development:

Disproportion of economic development:

Rice. 17. Dependence of prices on the money supply in conditions of stability or economic growth

Fisher's formula (equation of exchange) determines the amount of money used only as a medium of exchange, and since money also performs other functions, determining the total need for money involves a significant improvement in the original equation.

Amount of money in circulation

The amount of money in circulation and the total amount of commodity prices are related as follows:

Where:

The above formula was proposed by representatives of the quantity theory of money. The main conclusion of this theory is that each country or group of countries (Europe, for example) should have a certain amount of money corresponding to the volume of its production, trade and income. Only in this case will price stability be ensured. In case of inequality in the quantity of money and the volume of prices, changes in the price level occur:

• — prices are stable;
• - prices are falling;
• — prices are rising (inflationary situation).

Thus, price stability is the main condition for determining the optimal amount of money in circulation.

Sergey Yakovenko

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Fisher's formula applied to monopoly and competitive pricing

A pure monopoly primarily presupposes that one producer has complete control of the market and perfect awareness of its state. The main goal of a monopoly is to maximize profits with minimal costs. A monopoly always sets its price above marginal cost and output below that of perfect competition.

The presence of a monopolist manufacturer in the market usually has serious economic consequences: the consumer spends more money than in conditions of fierce competition, while prices rise along with the inflation index.

If the change in these parameters is taken into account in the Fisher formula, then we get an increase in the money supply and a constant decrease in the number of goods in circulation. This situation leads the economy to a vicious cycle in which an increase in the inflation rate only leads to an increase in prices, which ultimately further stimulates the rate of inflation.

A competitive market, in turn, reacts to an increase in the inflation index in a completely different way. Market arbitrage brings prices into line with market conditions. Thus, competition prevents an excessive increase in the money supply in circulation.

Face value of money

The essence of inflation is well understood in classical examples borrowed from the depths of economic theory.

First, let's illustrate what the nominal value of money is and what the nominal interest rate is.

Imagine yourself as an investor who placed $650 in a bank deposit or purchased a savings certificate for the same amount.

Let's assume the annual interest rate on the deposit (certificate) is 8%.

Accordingly, your reasonable expectations regarding capital increase are easy to calculate: $650 * 1.08 = $702 (+$52).

The bank, of course, will fulfill its obligations and benefit you with the promised amounts.

But what the bank definitely cannot do is guarantee that you will maintain the price level that was in effect at the time of opening the deposit (purchasing the certificate) until it is closed (redemption of the certificate).

In other words, the bank will not be able to promise you that at the end of the investment year you will become RICHER

.

This is because the bank is well aware of the insatiable appetite of mother inflation, which does not spare either depositors, bankers, the poor (which is understandable), or, less obviously, the rich.

It may happen that inflation rises above 8%, and then, despite the nominal capital gain, you will end up poorer...

The $702 we discussed above is a NOMINAL

the value of your savings. Accordingly, 8% is the nominal interest rate.

To get to real interest rates, we will have to resort to some simple calculations presented below.

International Fisher effect

The International Fisher Effect is an exchange rate theory put forward by Irving Fisher. The essence of this model is to calculate present and future nominal interest rates in order to determine the dynamics of changes in currency exchange rates. This theory works in its pure form if capital moves freely between states whose currencies can be correlated with each other in value.

Analyzing the precedents of rising inflation in different countries, Fisher noticed a pattern that real interest rates, despite the growth in the quantity of money, do not increase. This phenomenon is explained by the fact that both parameters are balanced over time through market arbitrage. This balance is maintained because the interest rate is set taking into account the risk of inflation and market forecasts for the currency pair. This phenomenon is called the Fisher effect .

Extrapolating this theory to international economic relations, Irving Fisher concluded that changes in nominal interest rates have a direct impact on the rise or fall in price of a currency.

This model has never been tested in real conditions. Its main disadvantage is considered to be the need to implement purchasing power parity (the same cost of similar goods in different countries) for accurate forecasting. And, besides, it is not known whether the international Fisher effect can be used in modern conditions, taking into account fluctuating exchange rates.

Estimation of the relationship between profit and costs using the FISHER function

Example 1. Using data on the activity of commercial organizations, it is required to make an assessment of the relationship between profit Y (million rubles) and costs X (million rubles) used for product development (shown in Table 1).

Table 1 – Initial data:

The scheme for solving such problems is as follows:

1. The linear correlation coefficient r xy is calculated;
2. The significance of the linear correlation coefficient is checked based on Student's t-test. In this case, a hypothesis is put forward and tested that the correlation coefficient is equal to zero. The t-statistic is used to test this hypothesis. If the hypothesis is confirmed, the t-statistic has a Student distribution. If the calculated value t p > t cr, then the hypothesis is rejected, which indicates the significance of the linear correlation coefficient, and therefore the statistical significance of the relationship between X and Y;
3. An interval estimate is determined for a statistically significant linear correlation coefficient.
4. An interval estimate for the linear correlation coefficient is determined based on the inverse Fisher z-transform;
5. The standard error of the linear correlation coefficient is calculated.

The results of solving this problem with the functions used in Excel are shown in Figure 1.

Figure 1 – Example of calculations.

Thus, with a probability of 0.95, the linear correlation coefficient lies in the range from (–0.386) to (–0.990) with a standard error of 0.205.

S.n.d.
- one of the main concepts of monetarism. M. Friedman even wrote “The quantity theory of money, in a first approximation, is the theory of the demand for money”77. Formulating the function S.n.d. on a larger number of factors than Keynesians (for example, including the rate of interest on bonds, the market rate of return on stocks, the rate of change in prices of durable goods in percentage, etc.), monetarists base conclusions and recommendations on the monetary policy of states as an instrument on their model regulation of social production. See Fisher effect. [p.340] Fiscal policy 37, 342, 376 Fisher’s “ideal index” 124 Fisher’s index 376 Fisher’s equation 376 Fisher’s effect 377 Fund of accumulation 83, 377 Fund of accumulation in national income [p.494]

We discussed the Fisher effect in Section 23-1. [p.955]

A systematic study of the fundamentals of investment behavior of an enterprise (firm) and its modeling is usually associated with the neoclassical direction, in particular with the American economist I. Fisher. The conclusion of this study was that each economic entity in its investment behavior is guided by subjective motives focused on maximizing future income (income effect), but the criteria for such a choice are objective. I. Fischer was the first to set out a system of such economic criteria. [p.32]

A significant contribution to the analysis of consumer preferences was made by F. Edgeworth, I. Fisher, J. Johnston, who paid special attention to the fact that when considering the individual utilities of goods and consumer effects in the process of consuming a product, it is extremely important to take into account their interconnectedness and the characteristics of their relationships. [p.56]

The effect of inflation on interest rates is described by the Fisher effect, known in macroeconomics, the meaning of which we will explain here with simple calculations. Suppose the change in prices over the observed period was AP, that is, the price of a certain set of goods and services from P became P + AP. Let us call the inflation coefficient the magnitude of the relative change P = AP/P. Then the price change can be represented as [p.47]

19th century economists believed that pleasure could be measured. There are two known approaches. Thus, W. Jevons, K. Menger, L. Walras proposed a quantitative (cardinalist) theory of utility, which was based on the hypothesis of the commensurability of the utility of various goods. A. Marshall also shared it. But V. Pareto, I. Fisher, and subsequently J. Hicks proposed an alternative option - the ordinal (ordinal) theory of utility, the essence of which is the consumer’s ability (skills) to compare possible sets of goods and services according to their preference. Here the concept utility means order of preference. The goal of both approaches is to figure out how to measure, compare, contrast the utility of various goods and services in order to maximize the expected consumer effect. [p.56]

The Fisher Effect is a theory by Irving Fisher, an early 20th century economist who argued that national interest rates reflect expected levels of inflation. -This economist is also given credit for his theory, which relates expected changes in exchange rates to differences in interest rates in the countries being exchanged. This theory is now known as the international Fisher effect. [p.213]

The Fisher effect is a concept that expresses the accounting for the effect of inflation on the interest rate on a loan or bond. Named after the outstanding American economist. [p.438]

This identity is known as the Fisher equation. It assumes, essentially, that changes in short-term rates can be inferred from changes in either expected inflation or expected yields. A more accurate version of the Fisher equation takes into account the compounding effect [p.1189]

Supporters of monetarism continued to view the interest rate in line with the traditions of the classical economic school. One of the developers of the new classical macroeconomic theory, Robert Lucas notes that there are two central consequences from the quantity theory of money: a change in the growth rate of the quantity of money leads to 1) an equal change in inflation and 2) an equal change in the nominal interest rate. The second consequence of the quantity theory of money is mixed. Economic theory suggests that there are two relationships between the money supply and interest rates. One hypothesis, which can be referred to as the liquidity effect, states that there is a negative relationship between money and rates. An increase in money supply is accompanied by an expansion of liquidity in the financial sector and, as a consequence, leads to a decrease in nominal rates. The opposite view stems from the Fisher equation, [p.343]

Thus, from the perspective of the Fisher equation, there should be a positive relationship between the supply of money and interest rates. A compromise between opposing approaches can be found by dividing the time horizon of analysis into short- and long-term. In the short term the relationship should be negative, and in the long term it should be positive. Modern econometric estimates suggest that nominal rates rise by 50–70 basis points for every 1% increase in money supply. Thus, empirical analysis refutes the liquidity effect hypothesis - at any period of time, an increase in the quantity of money inevitably leads to a positive change in the nominal rate. [p.344]

The distinction between nominal and real interest rates only makes sense under conditions of inflation (an increase in the general price level) or deflation (a decrease in the general price level). American economist Irving Fisher put forward a hypothesis regarding the relationship between nominal and real rates. It is called the Fisher effect, which means that when the nominal interest rate changes, the real interest rate remains unchanged. In mathematical form, the Fisher effect takes the form of the formula [p.285]

Inflation expectations. Fisher effect [p.556]

This familiar Fisher equation was briefly analyzed in Chap. 12. It shows that the nominal interest rate is affected by changes in the real interest rate and the inflation rate. It follows from this that the Fisher effect means that the nominal rate changes in conditions of inflation so that the real interest rate remains unchanged, i.e., by the same percentage that l increases, u increases by the same percentage. Such a relationship between the nominal interest rate and inflation rates was indeed observed in countries with developed market economies. For example, in the United States over the past forty years, this dependence has been observed during periods of relatively low (up to 15% per year) inflation rates. [p.557]

It is important to note that the Fisher effect manifests itself only in conditions of predicted (expected) inflation with stable inflation expectations of economic agents. However, there is also the concept of unpredictable (unexpected) inflation. For example, during the era of the gold standard, inflation was not sustainable. There was the same possibility of both increasing and decreasing its rates in the future, and therefore the hypothetical possibility of the market’s automatic exit from deflation, described by neoclassics. What is its mechanism? Economic agents, when the general price level decreases, begin to feel actually richer (wealth effect) and, not expecting a further decline in prices, will strive to maintain the volume of real money reserves (M/P) that has increased in relation to the fallen prices at the same level. Therefore, buyers will increase their purchases on the goods market. Growing consumer demand will begin to push prices up, and the downward trend in the price level will stop. Thus, in the absence of price expectations, the effect of real money reserves is triggered, which in economic literature is called [p.558]

Demand inflation Cost inflation Fisher effect Inflation expectations Stagflation Seigniorage [p.583]

The existence of this kind of effects has long been no secret for specialists working with real data. So, I. Fischer at the beginning of the 20th century. [p.60]

Changes over time in the proportions between prices and/or production volumes of various goods and services are usually called structural shifts. Thus, the discussed element of the specificity of the Russian transition economy is that the transition period is accompanied by a sharp intensification of structural changes. The existence of this kind of effects has long been no secret for specialists working with real data. Thus, I. Fisher wrote at the beginning of the 20th century that during periods of wars, crises or any other factors that disturb the national economy, the dispersion of prices is usually very [p.172]

These examples show how unexpected price hikes can change the financial situation of the borrower and lender. As a result of hyperinflation, Sam will become richer at the bank's expense because he will pay back the loan in dollars, the value of which has become many times less. Deflation will allow the bank to enrich itself at Sam's expense, since it will be forced to repay the debt in monetary units of increased value. When inflation is predictable, both the bank and Sam have the opportunity to take its magnitude into account when setting the nominal interest rate on the loan (remember the Fisher effect). If price behavior cannot be predicted, both parties take risks. [p.623]

One of the manifestations of the principle of neutrality of money is described by the Fisher effect, according to which, when the inflation rate increases by a certain amount, the nominal interest rate increases by the same amount, with [p.627]

Real values ​​Velocity of circulation of money Fisher effect [p.628]

How, according to the Fisher effect, an increase in inflation rates affects nominal and real interest rates [p.628]

The second of these prerequisites is the rate of interest. Each enterprise, knowing the current interest rate, optimizes the distribution of its income over time, accordingly consuming or saving it as an investment resource (since the transformation of today's income into future income is carried out only through investment). At the same time, the interest rate forms two different mechanisms for motivating the accumulation of one’s own investment resources, formulated by I. Fischer: 1) a decrease in the interest rate in the financial market stimulates the immediate consumption of income, and its increase stimulates an increase in savings (in I. Fischer’s terminology, the substitution effect) 2) an increase in the interest rate, and, accordingly, future income, narrows the base of current savings, due to the fact that a smaller amount of savings used in the investment process can bring a business entity greater future income, and therefore, it can increase current consumption, ensuring an unchanged future income (in the terminology of I. Fisher - the income effect"). The level of accumulation of equity capital as an investment resource depends on which motivation mechanism will be more effective for the enterprise. [p.36]

FISCHER EFFECT - a fundamental difference discovered by I. Fisher in the behavior of the money market in the short and long term; in the latter case, the dependence of the demand for money on the interest rate, characteristic of the first, is lost. [p.377]

Fisher effect Pigou effect [p.51]

As already discussed, in the long run, relative inflation rates have a significant impact on exchange rates. If purchasing power parity were maintained, then the change in the exchange rate over a certain period would depend on the relative changes in prices over the same period. From Ch. 3, where inflation and interest rates were discussed, we know that inflation also affects the nominal interest rate. According to the Fisher effect, the nominal interest rate is

It is a mistake to assume that the rate of interest, and not the marginal efficiency of the available fund of capital, is precisely the factor to which future changes in the value of money directly respond. The prices of existing assets always automatically adjust to changes in expectations about the future value of money. The significance of such changes in expectations is that they affect (through the marginal efficiency of capital) the willingness to produce new assets. The stimulating effect of the expected rise in prices is not due to the increase in the interest rate in connection with this (it would be strange to stimulate output in this way - after all, if the interest rate increases, the stimulating effect is weakened to the same extent), but due to the increase in the marginal efficiency of a given capital fund. If the rate of interest were to rise pari passu with the marginal efficiency of capital, the expectation of rising prices would have no stimulating effect. After all, the incentive to expand output is determined by how much the marginal efficiency of capital increases relative to the rate of interest. Undoubtedly, the theory of Prof. Fisher would be much better stated using the concept of the “real rate of interest”, considering it to be that rate of interest which, if established in response to changes in expectations regarding the future value of money, would eliminate the influence of these changes on current output (72) [p.62 ]

II borrowers), and in conditions of deflation - more. It is clear from this that unlike Pigou, in whom the fall in prices through the effect of real cash balances had a stabilizing effect on omics, Fischer rather saw it as a factor destabilizing omics due to the connection between the real interest rate and price dynamics. [p.287]

Let's assume that the Central Bank decided to pursue a policy of stimulating economic growth and increased the money supply in order to lower interest rates. However, a consequence of the increase in money supply was an increase in the rate of inflation in the country. Rising prices forced banks to raise the level of nominal interest rates (in order, according to the Fisher effect, to keep the real interest rate unchanged - see Chapter 12). An increase in nominal interest rates has a disincentive effect on investors; investment growth does not occur. Consequently, the policy of the Central Bank did not lead to the set goal - GDP growth. [p.462]

The Fisher test value calculated using formula (10.10) is compared with the table value for the selected significance level. If the calculated value does not exceed the tabulated value, then the adequacy hypothesis is accepted. To find the tabular value of the criterion, you also need to know the number of degrees of freedom associated with the numerator and denominator of expression (10.10). They represent the denominators of the formulas used to calculate the corresponding variances. Along with the direct assessment of adequacy, which is described above, there are a number of indirect signs by which one can judge the degree of adequacy of the model. Parallel experiments at the zero point are often used to estimate the variance of experience. The difference between the average value from these experiments and the free term of the linear equation characterizes the total contribution of quadratic effects. If this difference is insignificant, for example, according to Student’s test, then we can assume that the model is adequate. Such a check is not absolute, since it is possible that the sum of the positive coefficients of the squares is close to the sum of the negative ones. [p.231]

This property does not hold true for all index formulas. Thus, the product of price and quantity indices calculated using the Las Peires formula is, in general, not equal to the value index. In accordance with the Gerschenkron effect, this product will most likely be higher than the value index. Similarly, the product of price and quantity indices calculated using Paasche’s formula is, in the general case, also not equal to the cost index. Most likely, it will be lower than the cost index. Of the indices discussed above, only the Fisher index (6.6) has this property, and therefore it is the one that is preferable in this sense. [p.123]

The magnitude of the bias caused by the use of outdated weights in index formulas can be assessed by comparison with a specially constructed index in which this effect is smaller in order of magnitude. As such an index, as discussed in Section 2, one can use a chained index with a small time step, at each step of which the Fisher, Tornquist or some other index formula is used, which provides significantly higher accuracy compared to the Laspeyres or Paasche formulas . In our case, we could use, for example, the linked Fisher index with a step of one year. However, as already noted, reliable data to obtain a system of weights for the first years of reforms are not available, so such indices cannot be constructed correctly. Only annual information is available on the sectoral value structure of industrial production, so it seems possible to estimate only the shift due to inter-industry structural changes, without taking into account intra-industry shifts. To do this, we will use the direct sectoral indices of industrial production discussed above [p.142]

The Fisher effect provides the key to understanding changes over time in the nominal interest rate. In Fig. Figure 28.5 shows changes in the nominal pro-tent rate and the rate of inflation in the US economy since 1950. The graph gives a clear picture of [p.617]

The figure shows changes in the nominal interest rate, calculated from the yield on three-month Treasury bills, and the inflation rate, measured based on changes in the CPI. The close relationship between changes in both variables confirms the Fisher effect: as inflation rates increase, the value of the nominal interest rate also increases. Source USDdepartment of Treasury, [p.617]

In Economy 2, the real interest rate is also 4%, but the inflation rate is 8%. According to the Fisher effect, the nominal interest rate will reach 12%. Since the income tax law considers this 12% as income, the government takes 25% of it for its benefit. As a result, after tax, the nominal interest rate will drop to 9% and the real interest rate to 1%. Thus, with a 25% income tax, real interest income in Economy 1 is 4%, but in Economy 2 it is only 1%. Since the value of real interest income after tax serves as the main incentive for directing funds to savings, the attractiveness of savings in non-inflationary Economy 2 is higher than in inflationary Economy 1. [p.622]

Interest rates and inflation

The most important characteristic of a market economy is the presence of inflation, which determines the classification of interest rates (and, naturally, the rate of return) into nominal and real. This allows you to fully assess the effectiveness of financial transactions. If the inflation rate exceeds the interest rate received by the investor on investments, the result of the corresponding operation will be negative. Of course, in terms of absolute value, his funds will increase significantly, that is, for example, he will have more money in rubles, but the purchasing power that is characteristic of them will drop significantly. This will lead to the opportunity to buy only a certain amount of goods (services) with the new amount, less than would have been possible before the start of this operation.

Quantity theory of money

The quantity theory of money is an economic theory that studies the effects of money on the economic system.

In accordance with the model put forward by Irving Fisher, the state must regulate the volume of money supply in the economy in order to avoid its shortage or excessive quantity.

According to this theory, the phenomenon of inflation occurs due to non-compliance with these principles.

An insufficient or excessive amount of money supply in circulation entails an increase in the rate of inflation.

In turn, an increase in inflation implies an increase in the nominal interest rate.

• The nominal interest rate reflects only the current income from deposits without taking into account inflation.
• The real interest rate is the nominal interest rate minus the expected inflation rate.

The Fisher equation describes the relationship that arises between these two indicators and the inflation rate.

Video

We recommend watching this video to better understand the theory:

How inflation affects bank deposits (using an example)

Deposit rates are almost always lower than real price increases. This means that by opening a deposit with a bank, you can protect your funds from depreciation as much as possible, but you will not earn anything. Banks formulate their proposals based on the Central Bank refinancing rate and the projected inflation rate.

It is important for an investor to understand that there are two types of deposit rates:

• Nominal, which is indicated in the bank’s advertising brochure and serves to attract depositors, for example, 12% per annum.
• Real, the size of which is affected by the increase in consumer prices during the period of validity of the deposit agreement with the bank. If they rose by 4%, the investor added not 12, but 8% to the invested amount.

Let's look at an example.

The Federal State Statistics Service (Rosstat) regularly calculates the consumer price index and posts this data on its website. The Central Bank sets the key rate, that is, the percentage for using money for commercial banks. One of them, Home Credit and Finance Bank, accepts deposits from citizens on favorable terms.

As you can see, in 2011 and 2012, consumer prices grew moderately, and the deposit rate remained at the same level, twice the inflation rate. In 2013, the Central Bank introduced a key rate of 5.5%, but Home Credit Bank began offering clients only 9%, while their real income on deposits decreased, and the share of inflation in the rate increased from 55 to 72%. In the crisis year of 2014, all indicators jumped up, but with a nominal increase in the rate to 19%, depositors earned almost the same amount as during the years of strong economic growth.

The bank chosen as an example is indicative of its desire for high returns on deposits. Most Russian financial institutions included in the top 10 do not indulge their clients with such high interest rates on deposits. Thus, in April 2015, when inflation reached 16.4%, the average profitability indicators of Sberbank, VTB-24, Gazprombank and other financial market leaders were 10–12%.

Let's see how inflation affects bank deposits using a specific example. In 2014, prices increased by 11.4%. Let's say you deposited 100 thousand rubles. in Home Loan at 9% for a year with monthly capitalization. A loan calculator, which is available on many online services, will help you calculate that after 12 months you would receive a profit of RUB 9,353.88.

It seems to be good, but inflation of 11.4% led to the fact that real losses for the year amounted to 11,400 rubles. from the deposit amount. This means that in fact, not only did you not earn anything on your deposit, but you also ended up in the red:

9353.88 – 11400 = -2046.12 rubles

A deposit rate of 11% would help protect savings from depreciation, but not a single financial institution has made such generous offers. See for yourself: by placing money in a bank under these conditions, you could keep up with inflation and even earn a little money. Nominal income would be 11,538.32 rubles, and real:

11538.32 – 11400 = 138.32 rubles

Application of the Fisher formula in international investment

As you can see, in the above formulas and examples, a high level of inflation always reduces the return on investment, given a constant nominal rate.

Thus, the main criterion for the reliability of an investment is not the volume of payments in percentage terms, but the target inflation rate .

This is confirmed by the ranking of countries that receive the most investments. The first places in it are occupied by China and the USA. Inflation growth in these countries over the past 5 years has not exceeded 3%.

Description of the Russian investment market using the Fisher formula

The above model can be clearly seen in the example of the investment market of the Russian Federation.

The fall in inflation in 2011-2013 from 8.78% to 6.5% led to an increase in foreign investment: in 2008-2009 they did not exceed 43 billion. dollars per year, and by 2013 reached 70 billion. dollars.

The sharp increase in inflation in 2014-2015 led to a decrease in foreign investment to a historical low. Over these two years, the amount of investments in the Russian economy amounted to only 29 billion. dollars.

At the moment, inflation in Russia has fallen to 2.09%, which has already led to an influx of new investments from investors.

In this example, it can be noted that in matters of international investment, the main parameter is the real interest rate, which is calculated using the Fisher formula.

How is the goods and services inflation index calculated?

The inflation index or consumer price index is an indicator that reflects changes in the prices of goods and services purchased by the population.

Numerically, the inflation index is the ratio of prices for goods in the reporting period to prices for similar goods in the base period.

ip = p1/p

Where:

• ip — inflation index;
• p1 - ​​prices for goods during the reporting period;
• p2 - prices for goods in the base period.

Simply put, the inflation index indicates how many times prices have changed over a certain period of time.

Knowing the inflation index, we can draw a conclusion about the dynamics of inflation. If the inflation index takes values ​​greater than one, then prices rise, which means inflation also rises. The inflation index is less than one - inflation takes negative values.

To predict changes in the inflation index, the following methods are used:

Laspeyres formula:

IL = (∑p1 * q) / (∑p0 * q0)

• IL—Laspeyres index;
• Numerator - the total cost of goods sold in the previous period at prices of the reporting period;
• The denominator is the real cost of goods in the previous period.

Inflation, when prices rise, is given a high estimate, and when they fall, it is underestimated.

Paasche index:

Ip = (∑p1 * q) / (∑p0 * q1)

Numerator - actual cost of production of the reporting period;

The denominator is the actual cost of production of the reporting period.

Interesting: CAPEX and - OPEX what is it?

Fisher's ideal price index:

Ip = √ (∑p1 * q) / (∑p0 * q1) * (∑p1 * q) / (∑p0 * q0)

Notes

If any of the arguments are not a number, FRATE returns the #VALUE! error value.

If "probability" is 1, FRIST returns the #NUM! error value.

If the value of degrees_freedom1 or degrees_freedom2 is not an integer, it is truncated.

If "degrees_freedom1"

If "degrees_of_freedom2"

The FDIST function can be used to determine the critical values ​​of the F distribution. For example, ANOVA results typically include data for the F statistic, F probability, and the critical value of the F distribution at a significance level of 0.05. To determine the critical value of F, you need to use the significance level as the “probability” argument of the FDIST function.

Given a probability value, the FDIST function searches for a value of x for which FDIST(x,degrees_of_freedom1,degrees_of_freedom2) = probability. Thus, the accuracy of the FDIST function depends on the accuracy of FDIST. To search, the FRIST function uses an iteration method. If the search does not end after 100 iterations, the #N/A error value is returned.

How is inflation calculated?

Rosstat monthly calculates inflation based on the cost of the consumer basket. This includes about 500 goods and services - almost everything that an ordinary household might need.

The set of these goods and services is determined by Rosstat. Every year, he evaluates the total expenses of residents of the entire country and individual regions and looks at what types of goods and services turned out to be the most in demand. These are the ones he includes in the basket. For example, the most popular cereals turned out to be buckwheat, rice and semolina - they were included in the basket, but spelled and quinoa were not.

This basket includes not only food, clothing, transport tickets and housing and communal services. It also contains furniture, appliances, building materials, toys and even pet food.

When new goods and services appear on the market and this leads to a change in consumer preferences of households, the composition of the consumer basket also changes slightly. For example, it now includes a smartphone, an energy-saving light bulb, an electronic blood pressure monitor and the installation of plastic windows. Previously, their prices were not taken into account when calculating inflation.

The cost of the consumer basket is different every month. This change is considered official inflation.

Read more about inflation in the article Inflation: why prices are rising and who can contain them.”

Real inflation - how to calculate and calculate real inflation

Today, a rather interesting topic is real inflation. Do you know what she really is? Or how to calculate it?

How not to calculate inflation

I think almost everyone knows about inflation, and every time it is mentioned in a conversation, it causes a storm of negative emotions among citizens of Russia and beyond. Statements that everyone is being deceived, that she is several times taller can be heard on “every corner.” Plus, all sorts of resources telling about 50% in a year add fuel to the fire! And all because people do not know the real meaning of the word .

On the Internet you can find comparisons of prices for the year of certain niche foreign goods, where prices differ by tens of percent. And they present this % as the average (or real) inflation in the country! So, one more time.

They simply took a few goods and, based only on their prices, said: look, this is real inflation! To put it mildly, this is not a correct calculation, since it is not a representative sample. Of course, if we take foreign goods before 2014 and two years later, then a 100% increase in price was easy to find. For example, smartphones have risen in price very much during this time.

But things need to be called by their proper names. This is not inflation, but a devaluation of the ruble against the dollar (due to the floating ruble policy). After all, now Russian companies need to exchange more rubles. Because the same iPhones are sold for dollars.

Official inflation is not for us

Great! Now it’s clear what you shouldn’t “fall for” and how to incorrectly . But Rosstat also presents only generalized figures. They do not reflect reality. Moreover, even these official figures may not be correct. I think good financiers can find evidence that the consumer basket has risen in price more than Rosstat tells us.

Previously, I did not understand that my inflation was not equal to the official one. And looking at these numbers on TV I thought: “Well, that’s probably true.” Therefore, now for me this indicator is simply statistical, practically unrelated to my life.

For example, my purchases, oligarchs and pensioners in the store will be clearly different. Starting from the variety of goods to the number of zeros in the receipt. A person with money, I think, will not buy the cheapest buckwheat, bread and spend half of his income on housing and communal services. At the same time, the average pensioner will not eat king prawns, lobsters, truffles and drive a brand new Bently, Mercedes Benz, etc.

Real inflation - how to calculate

From the paragraph above, it is clear that the official percentage cannot correspond to any of the residents of the country (an exception is if you live on the food basket according to Rosstat, and buy absolutely everything from it), since everyone has their own. You can calculate real inflation only for yourself personally . And this is provided that your needs remain the same from year to year.

“But this is impossible,” you say, and you will most likely be right. Show me a person who will buy strictly the same thing for many years! Some kind of crazy guy! But there is still a calculation option and, I think, it is more accurate than official statistics. To do this, you do not need to count the quantities/prices of each item purchased. Just start counting your expenses.

For example, consider all expenses in grocery stores separately (I do this in Excel). And if your needs remain the same from year to year (for example, you ate without denying yourself anything, and you don’t limit yourself now), you can compare the numbers for different years. With this calculation, you understand how much more you start spending on food.

Of course, this option is far from the exact figures of real inflation; nevertheless, a person can gradually, without even realizing it, buy more often and more (or vice versa, less). But I think that with the right approach it will be clearly more accurate than the official one .

Conclusion

If you want to find out real inflation, try the method described above. If your numbers are lower than those in the country, then you are spending better and, most likely, living better than most.

Start tracking your expenses and income. This will help save money from unnecessary expenses. And instead of personal inflation, you get deflation . In this case, costs will decrease, but quality of life will not. Because you manage your budget correctly. But of course we don’t forget about investments , money should bring more money. Good luck!

Source: https://CashKopilka.ru/poleznaya-informaciya/pro-dengi/realnaya-inflyaciya-poschitat/

Interest rate concept

The interest rate should be understood as the most important economic category that reflects the profitability of any asset in real terms.

It is important to note that it is the interest rate that plays a decisive role in the process of making management decisions, because any economic entity is very interested in obtaining the maximum level of revenue at minimum costs in the course of its activities. In addition, each entrepreneur, as a rule, reacts to the dynamics of the interest rate in an individual way, because in this case the determining factor is the type of activity and the industry in which, for example, the production of a particular company is concentrated

Thus, owners of capital assets often agree to work only if the interest rate is extremely high, and borrowers are likely to acquire capital only if the interest rate is low. The examples discussed are clear evidence that today it is very difficult to find equilibrium in the capital market.

Problems to solve independently

Problem 7.3.5.

Determine the class of financial stability of the FM enterprise using the methods of Dontsova and Nikiforova.

Guidelines

:
1) the initial data are presented in table. 7.3.1 and 7.3.2; 2) use the table. 7.3.2 content.

Problem 7.3.6.

Determine the probability of bankruptcy of the FM enterprise using the Altman model.

Guidelines

:
1) the initial data are presented in table. 7.3.1 and 7.3.2; 2) use formula 7.3.8.

Problem 7.3.7.

Determine the Z-score according to the Fox model of the FM enterprise.

Guidelines

:
1) the initial data are presented in table. 7.3.1 and 7.3.2; 2) use formula 7.3.9.

Problem 7.3.8.

Determine the probability of delayed payments for the FM enterprise using the Connan and Golder model.

Guidelines

:
1) the initial data are presented in table. 7.3.1 and 7.3.2; 2) use formula 7.3.11.

Hamburger index

An interesting technique that cannot be ignored. The name "hamburger" has a direct meaning

After all, in fact, this popular fast food is sold in every country, so it immediately attracted attention. Thanks to it, you can determine the index for assessing the cost of identical products in different countries

According to numerous calculations, it turned out that in the previous year Switzerland took first place in the sale of expensive hamburgers costing $6.80, and the cheapest was found in Venezuela, for only 0.67 cents.

Such a simple and unique method was able to show the discrepancy between currencies in countries where the income level is almost the same.

Inflation is always bad for the average person.

We calculate the return on investment according to Fisher: why does an investor need macroeconomics?

Irving Fisher is an American economist, a representative of the neoclassical movement in economics. Born February 27, 1867 in Saugerties, Co. NY. He made a great contribution to the creation of the theory of money, and also derived the “Fisher equation” and the “equation of exchange”.

His works were taken as the basis for modern methods for calculating inflation rates. In addition, they greatly helped to understand the patterns of inflation and pricing.

How to take into account the real rate

The main difficulty in calculating the real rate is that the inflation rate is a forecast indicator. It is impossible to know this figure in advance. Therefore, when building a strategy, you have to use an expert analysis of the situation. The easiest way is to refer to the Central Bank data.

In this case, you will have to take into account two facts:

• price increases may differ from those predicted;
• What is important for each person is not the average indicator fixed by the regulator, but his personal level of real inflation.

Most services that allow you to take into account the real interest rate are intended for banking products. However, with their help, you can also calculate how the capital invested in bonds will change. An example of such a resource is planetcalc.ru/26/ As initial parameters you need to set:

• amount of capital;
• nominal yield;
• inflation rate;
• investment period.

As a result, you will be offered two values:

• the amount that will be in your account after the agreed time;
• its value, discounted to today's prices (the inflation rate you specify is used as the discount rate).

The disadvantage of such calculators is that they make calculations taking into account the capitalization (reinvestment) of income. Therefore, it is not suitable for analyzing assets that generate profit not through regular payments, but due to an increase in their value.

Using such calculations, you can determine what is more profitable: saving or using a loan. If your real rate is negative, you will be further away from your goal every year. Such an analysis is also required when choosing instruments for forming a pension portfolio. In this case, your task is to create a source of livelihood that can replace your salary and allow you to maintain your usual standard of living. When determining the amount of passive income it should generate, you need to consider inflation-adjusted prices.

Why is it important to calculate your personal inflation?

Recently, you can often hear in the news that official inflation in Russia is at a record low level in the entire history of observing this indicator in our country and amounts to just over 2%, although three years ago this figure was much more impressive and amounted to more than 16%.

I remember how in 2014-2015, in order to “save” money, people bought TVs and washing machines, and then sold them on Avito for 30-50% of the cost. A stunning example of financial illiteracy multiplied by emotions. Personally, I am convinced that buying shares in high-quality and profitable companies is the best protection against any inflation and devaluation. Therefore, around the same time, I was actively buying shares of Russian companies, especially those whose business was export-oriented.

And I am still very pleased that I chose to buy securities over unnecessary household appliances, because this decision helped me subsequently receive a return much higher than not only official, but also personal inflation. I would like to dwell on the latter in more detail.

There is amazingly little information about personal inflation, and most people in our country don't even know what it is. Although for me, control and assessment of this particular parameter are key when taking into account the financial situation of my family.

The personal inflation rate allows you to track the increase in the cost over time of a specific family's consumer basket in specific circumstances. This is the most important difference from official inflation, which in a certain sense is a spherical horse in a vacuum, since it shows an increase in prices for a certain average consumer basket, which in reality, most likely, is not consumed by any family.

Why do we need to know the average temperature in the hospital? After all, it can be very cold in the morgue, and very hot in the physiotherapy room. What benefit do I have from the information that official inflation in the country is 16-20% if, on the contrary, deflation was observed in our family at that time?

Deflation is the reverse process when the cost of the food basket becomes cheaper. And should I be happy when the Central Bank reports that inflation has been brought down to 2.2%, while my personal inflation has risen to 10% since last year?

Assessing personal inflation is not difficult for us, since we keep fairly detailed records of our family’s income and expenses (and we advise everyone to do so). In general, I try to avoid fanaticism in this matter, and calculating personal inflation is only a rough guideline for understanding the financial situation of our family. Accuracy down to the ruble or a fraction of a percent, in my opinion, is not required at all.

Nevertheless, when calculating, I adhere to some rules:

• We use the matching principle to estimate our inflation rate. This means that we compare the cost of our consumer basket for the period (month/season) of this year with the same period last year. Comparing June with January or winter with summer is largely a pointless task, since the composition of goods and services is too different.
• The composition of our basket is not static and changes from year to year depending on how our consumer preferences change. If some product that we regularly used last year leaves our current shopping list, then it no longer participates in the assessment of inflation - no matter how much it has become more expensive/decreased in price over the year.
• We exclude one-time expenses that occur less frequently than a certain period (2-3 years). The main emphasis when assessing personal inflation is on regular expenses - food, household goods, transport and utility bills, clothing, recreation, entertainment, etc.

The approximate calculation is as follows: The cost of the basket of the current period / the cost of the basket of the previous period is 1 * 100%. For example, a food basket this year cost the family 300,000 rubles, and last year - 270,000 rubles, then: 300,000/270,000 − 1 * 100% = 11.11% - there will be the family’s personal annual inflation.

This simple technique allows us to form a fairly objective picture of what is happening with the cost of our consumer basket, and evaluate our own data instead of relying on official data, which, even if true, still have almost no relation to the situation in our family. Therefore, I recommend that everyone consider their personal inflation and generally try to focus on their own figures in assessing their financial situation, and not on someone else’s, averaged, calculated by no one knows who, how or why.

For a private investor, the personal inflation parameter is especially important, since this is what one should focus on when assessing the required return. Obviously, the return on capital must be higher than personal inflation in order not to lose its purchasing power.

A return on capital of 7% with personal inflation of 2% is, in my opinion, better than a return of 15% with inflation of 20%. Therefore, you should not consider profitability and inflation in isolation from each other, otherwise you can be greatly deceived in assessing the results of your investment activities.

Source: https://journal.open-broker.ru/investments/pochemu-vazhno-schitat-svoyu-lichnuyu-inflyaciyu-i-chem-ona-otlichaetsya-ot-oficialnoj/

Real yield

Real yield is the yield that takes into account inflation.

It is necessary to take into account the final increase in the investor's portfolio and divide it by inflation.

Formula and example of real profitability

Why do you need real profitability?

Real yield shows how much richer a person has actually become, taking into account rising prices.

For example, at the end of 2013, a standard grocery set cost 1,000 rubles. Inflation for 2014 was 11.36%.

Let the investor have 100,000 rubles. At the end of 2013, he could have bought 100 sets. (100,000/1000).

Over the course of the year, the price of the food package rose to 1,113.6 rubles.

Let's consider 3 cases of using money

Case 1: we keep money at home. We still have 100,000 rubles left. Now we can buy:

Case 1: keeping money at home

The “investor” became 10.2% poorer.

Case 2: we invest money in a bank. The bank promised us 10% per year, capitalization once at the end of the term. As a result, we will be able to buy the following number of food sets:

Case 2: investing in a bank

In reality, the investor became poorer by 1.22%. Inflation “ate up some of the money.” The bank was unable to increase the money. This is fine.

Case 3: we invest money on the stock exchange. Let’s assume that the client’s account ended up with 115,780 rubles.

Case 3: investing on the stock exchange

The “investor” became richer by 3.97%. Let’s make sure using the formula for calculating real profitability:

Check using the formula