The difference between duration and the nominal period of circulation of a financial instrument. Method of managing interest rate risk using duration. Determination of the duration of short-term financial instruments. The relationship between duration and elasticity of a security.

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Duration Analysis

Weighted average maturity (duration) is a measure of the present value of a financial instrument, which shows the average length of the period during which all income streams for this instrument flow to the investor. duration shows the payback period of a financial instrument, i.e. the time after which the bank will be able to return the funds spent on its purchase.

The duration indicator can characterize any financial instrument: an individual security, a portfolio of securities, a bank loan, or the total dynamic balance of a bank. However, duration is most often used to analyze long-term financial instruments, namely debt securities with long maturities.

The duration of a security is calculated according to the formula of F. Macuoli and is the ratio of the present value of the sum of all expected income streams for a security, weighted by the time of receipt, to its market price: where D is the duration of the security (years, months); Si -- expected flows of interest income in and period; and -- payment periods; n -- total number of periods; d -- discount rate; N -- nominal amount of debt; p -- market price of the security.

When calculating the duration of a security, it is necessary to consistently calculate the cash flow, discount factor, net present value and its weighted value. At the final stage, duration is determined by dividing the weighted present value by the market price of the security. The duration indicator calculated in this way makes it possible to take into account all the main factors that affect the sensitivity of a debt security to changes in market rates, namely: the circulation period, the amount of coupon income, the coupon payment schedule, the current yield of the security, the nominal amount of the debt. So, duration is a relative measure of the sensitivity of a debt instrument to changes in interest rates.

Duration should be distinguished from the nominal maturity of a financial instrument, which shows the length of the period from the occurrence of an obligation to its full repayment. If a security generates cash flow only once when it reaches maturity, then its duration is equal to its period of maturity. For example, a three-year certificate of deposit with a provision for payment of principal and interest after the expiration of the circulation period and sold at par value has a duration of three years. But for all securities for which payments are made several times before reaching maturity, the duration will be less short over the duration of the circulation period. We illustrate the methodology for calculating duration with an example.

Process control methodnt risk using duration

The method of managing interest rate risk using duration is to minimize the reduction in bank income that may arise through changes in interest rates in the market. When this method is applied, a basic ratio is used: the duration of a security or portfolio of securities must be equal to the duration of the bank’s planned storage period for this security or portfolio.

So, when a bank considers it advisable not to take risks and has the goal of minimizing the variability of income through changes in interest rates in the market, then the bank’s planned storage period for a security should be equal to its duration:

D = IGpl, (6.27)

where IGpl is the planned storage period of the security.

The mechanism for minimizing income variability is based on the existence of an inverse relationship between changes in interest rates in the market and the price of a debt security. If interest rates increase after purchasing a security, its market price decreases. But in this case, the bank has the opportunity to reinvest the resulting income stream at the highest market rate. For a decrease in interest rates, the bank is forced to reinvest income at lower interest rates, but an increase in securities prices compensates for losses from reinvestment. Thus, if the duration of securities is equal to the planned period of their storage by the bank, then capital losses on the security are repaid by increasing reinvestment income, and capital gains, on the contrary, will be offset by a decrease in reinvestment rates. Based on this pattern, the bank can fix the overall level of return on the security.

As noted, the duration indicator can be applied to various financial instruments and characterize not only an individual security, but also a portfolio of securities or the totality of assets and liabilities as a whole (balance sheet). So, the techniques just discussed for analyzing price sensitivity and minimizing interest rate risk also apply to bank portfolios or bank balance sheets. Depending on the specifics of the object, the methodology for calculating and analyzing duration is modified.

So, if the bank’s management forms a portfolio of securities, coming out with the ratio (6.27) (in this case, IGpl is the planned investment horizon of the portfolio), then the result will be the immunization (protection) of acquired securities from capital losses, regardless of the dynamics of interest rates in the market. This method allows you to fix the total profitability of the bank's portfolio by mutually repaying two key types of risks - interest and reinvestment.

Using this technique, it is necessary to calculate the duration of the entire portfolio. To do this, calculate the duration of each financial instrument that is included in its composition, and weigh the found indicators by the market price. The sum of all obtained values ​​is the weighted average maturity (duration) of the portfolio as a whole.

The duration of the portfolio is calculated by the formula: where Dp is the duration of the portfolio (year); DFIm -- duration of the m-th financial instrument that is part of the portfolio; FІm -- market price of the m-th financial instrument; M -- the number of financial instruments in the portfolio.

Duration management is one of the methods for reducing interest rate risk, which can be applied not only in relation to the securities portfolio, but also in relation to the total portfolio of assets and liabilities (dynamic balance) of the bank. The content of this approach is discussed in detail in the next section “Managing Bank Assets and Liabilities”.

Determining the duration of short-term financial instruments

Let's consider determining the duration of short-term financial instruments using the example of credit operations. Let us point out that for instruments with a maturity of one year, it is more convenient to measure duration in months.

Example 6.7

Calculate the duration of a loan in the amount of UAH 15,000, which was issued at a fixed interest rate of 24% (per annum) for four months.

During the lending period, the bank receives monthly interest payments in the amount of 300 UAH (0.24 H 15000 H30:360 = 300). The discount rate per month is 2%.

So, the duration of the loan is 3.8 months. The interest rate risk of such a loan will be the same as that of securities with a maturity of 3.8 months. This means that in the process of analyzing interest rate risk, a more accurate measure of sensitivity is the duration, and not the nominal maturity.

Let's assume that the terms of the credit transaction involve repaying the loan in installments: at the end of the first month - 15%, the second - 20%, the third - 25%, and the fourth - 40% (all other conditions remain the same). Then the duration of the loan will be 2.9 months:

0,15 + 0,2 ? 2 + 0,25 ?3 + 0,4 ? 4 = 2,9.

The economic content of duration in this case is that the bank's interest income is the same as if it were received from the initial loan amount during the lending period, which is equal to the duration of the duration. Let's check this statement (we assume that each month has 30 days, and the calculation base is 360 days).

Thus, bank income (UAH):

for the first month - 0.24 · 15000 30: 360 = 300;

for the second month - 0.24 · (15000 - 0.15 · 15000) · 30: ​​360 = 255;

for the third month - 0.24 · (15000 - 0.35 · 15000) · 30: ​​360 = 195;

for the fourth month - 0.24 · (15000 - 0.6 · 15000) · 30: ​​360 = 120.

The total amount of bank income is 870 UAH.

If we calculate the bank’s interest income taking into account the duration of the loan, we will get the same amount:

0.24 · 15000 · 2.9 H 30: 360 = 870 (UAH).

The weighted average maturity (duration) indicator is used in investment management in many techniques and methods: for predictive analysis of changes in the price of a security during the period of its storage; to reduce the bank's interest rate risk by immunizing the balance sheet; to manage the bank's assets and liabilities.

The method of providing for price changes is based on the assumption that there is a linear relationship between changes in market interest rates and the price of securities, expressed as a percentage. To characterize this dependence, the concept of price elasticity of a security is used, which shows the change in its price in percentage terms for changes in market rates by 1% and is calculated using the formula: where e is the elasticity coefficient; Dр -- change in the market price of a security; p -- market price of the security; Dr -- change in interest rate; r -- current interest rate.

duration paper financial instrument

The relationship between duration and elasticity of a security

The relationship between duration and elasticity of a security is expressed by the formula:

Since the left-hand sides in formulas (6.22 and 6.23) are the same, then, by equating the right-hand sides, we obtain an equation from which we find the relationship between changes in the price of a security (Dр) and changes in market rates:

To estimate the change in the price of a security, the duration with a minus sign must be multiplied by its current price and the change in interest rates on the market, taking into account the discount.

The resulting formula indicates the existence of a linear relationship between changes in market interest rates and the price of the security. This makes it possible to analyze the impact of any changes in rates on the price of securities (in monetary terms).

The influence of interest rates on the change in the price of securities, expressed as a percentage, is calculated using the formula: where Dp* is the change in the price of a security in percentage terms.

Example 6.8

Estimate the change in the price of a three-year bond with a par value of 1000 UAH, which is currently sold at a price of 950 UAH, if its duration is 2.68 years, and the forecast indicates an increase in interest rates on the market during the current year from 25 to 32%.

So, an increase in market rates by 7% will lead to a decrease in the price of the bond by 15%, or by 142.57 UAH, and its market price in a year under such conditions will be 807.43 UAH (950 - 142.57 = 807.43 ).

Thus, price sensitivity analysis allows the bank to make informed decisions regarding the acquisition of certain securities and decide whether such price sensitivity is acceptable for it or whether other securities will more accurately meet the bank's investment strategy. During the analysis, it is also necessary to assess the likelihood of significant changes in interest rates in the market during the period of circulation of the security. Application of the considered methodology will help the bank make an informed decision regarding the purchase or sale of securities.

A comparative analysis of the price sensitivity of different financial instruments makes it possible to choose those that best suit the strategy of a particular bank. Thus, securities with a high coupon income have a shorter duration compared to securities that are characterized by a low interest income per coupon and the same level of market return. Therefore, securities with a high coupon yield have a lower level of price risk. Conversely, low-coupon securities can bring high returns to the bank based on changes in market interest rates, but they also carry higher price risk. Considering these patterns, the first type of securities is more suitable for the portfolio of a bank that adheres to a conservative policy of approaches, and the second is for obtaining speculative income.

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The owner of a security receives income from its possession and disposal. Income from the disposal of a security is income from its sale at market value when it exceeds the face value or original value at which it was purchased.

Credit- economic relations between various partners that arise when transferring property or money to another person on the terms of urgency, repayment, payment and security.

To determine the effectiveness of a loan, a distinction is made between the full and average loan terms. Full The term is calculated from the moment the loan begins to be used until its final repayment. It includes:

1) period of use of the provided loan;

2) grace period - deferment of repayment of the used loan;

3) the repayment period when the principal and interest are paid.

Full loan term calculated using the following formula: Sp=Pi+Lp+Pp, where Sp is the full term of the loan; Pi – period of use; Lp – grace period; Pp – repayment period.

Unlike a bank loan, the period for using a company loan essentially coincides with the delivery period of the goods under the contract. In this case, the beginning of the full period is the date of acceptance by the buyer of drafts issued by the exporter after delivery of the last consignment of goods, i.e. after the exporter fulfills contractual obligations. The grace period of the loan is especially important for commercial transactions and the supply of complete equipment, since in this case the start of its repayment is as close as possible to the moment of commissioning of the purchased equipment. This reduces the payback period for the importer’s investment. During this period you will typically be charged a lower interest rate than during the rest of the loan period. Grace periods usually occur:

· in international long-term bank loans guaranteed by the state;

· in consortium eurocredits, with large supplies of machinery and equipment;

· when implementing investment projects abroad.

However, the full term does not show during what period the borrower had the entire loan amount at his disposal. Therefore, to compare the effectiveness of loans with different conditions, the average term is used, which shows the average period for which the entire loan amount falls. Average loan term with equal use and repayment, it is calculated according to the following formula: SSr =1/2Pi +Lp+1/2Pp, where ССр – average loan term.

The average loan term is usually less than the full term. They coincide if the loan is provided immediately in full and is repaid in a lump sum. But if the use or repayment of the loan occurs unevenly, then the average term can be determined using the following formula: ССр=(Н31+Н32+...+H3N)/Lim, where ССр – average loan term; NZ – outstanding debt (as of a certain date); Lim – loan amount (limit).

The most important indicators of credit statistics are: the average loan term, loan turnover, characterized by the number of turnovers per period, the efficiency of average investments, the share of overdue loans, the duration of overdue loans, the average interest rate.

The average size loan(loans) is determined by the weighted arithmetic average formula:

		average loan size;

Average loan term can be calculated using the formulas:

arithmetic average weighted (in this case, the weights are the sizes of loans issued):

;

weighted harmonic mean:

.

Average duration of loan use by industry sector (taking into account loans not repaid to the bank on time) is determined by the formula:

,

		average loan balances;
		credit turnover (amount of repaid loans);
		number of calendar days in the period.

Due to the fact that information about loan balances is usually shown as of the date, the average balance is calculated using the chronological average:

.

Average duration of overdue loans allows you to establish a measure of the stability of the borrower's debt based on the following expression:

,

Average loan turnover determined by dividing the turnover of loans for repayment by their average balance:

.

The economic meaning of this indicator is that it characterizes the number of turnovers made by a short-term loan during the period under study.

Average number of loan turnovers per year will be:

;
,

A fee equal to interest rates is charged for using the loan.

Average annual loan rate (i ):

,

Along with the average values, the share of overdue debt in total debt is revealed - the share of untimely repaid loans.

An idea of ​​the effectiveness of government credit operations is given by the indicator (
) characterizing the percentage of the amount of excess of revenues over expenses under the public credit system:

,

To analyze credit investments and their dynamics, statistical methods such as balance sheet and index are widely used, so it is necessary to understand the methodology for constructing aggregate indices and indices of average quality indicators.

To study the influence of individual factors on changes in the average duration of using a loan, a system of interrelated indices is constructed, consisting of indices of variable composition ( ), permanent staff ( ) and structural changes (
):

.

Let us consider, for example, the index of the average duration of use of a variable loan:

,

Where
- one-day loan repayment turnover equal to
.

If we accept
is an indicator of the structure of one-day turnover for repayment, then the formula of this index will take the form

.

The value of the variable composition index is influenced by two factors: changes in the duration of loan use in industries and structural changes in the daily turnover of loan repayments.

Absolute change in the average duration of loan use due to two factors:

.

The index of the average duration of using a loan of a constant composition is used to determine the influence of only the first factor on the change in the average duration of using a loan:

,
.

The absolute change in the average duration of credit use in industries will be:

The index of structural changes allows us to determine the impact of structural changes in the composition of one-day repayment turnover on changes in the average duration of using a loan:

,
.

The absolute change in the average duration of using a loan due to structural changes in one-day turnover will be:

The absolute change in the average number of loan turnover due to two factors will be:

.

The study of the dynamics of loan turnover by industry can be done using indexes of the average number of loan turnovers.

Index of average number of loan turnovers of variable composition shows relative and absolute changes in the average number of turnovers by industry and structural changes in average loan balances and is determined by the formulas:

;
;.

Index of average number of loan turnovers of a constant composition shows relative and absolute changes in the average number of loan turnover due to one factor - changes in loan turnover in industries and is determined by the formulas

;
;.

Index of structural changes shows relative and absolute changes in average loan turnover due to structural shifts in average loan balances:

;
;.

Opening a loan (line of credit) is an agreement under which the lender undertakes, under certain conditions, to provide the client with a certain amount, which he can use at his own discretion.

The main indicators of credit statistics can be grouped as follows:

indicators related to the conditions and possibilities of issuing a loan;

indicators for calculating interest on loans issued;

indicators related to the analysis of the level of credit risk for the borrower (bank) or the level of creditworthiness of the client.

TO first The group includes the following indicators.

Maximum risk per borrower or group of related borrowers:

,

Where
- the total amount of the bank’s claims to the borrower or a group of related borrowers for loans, discounted bills, deposits in precious metals, other debt obligations, as well as off-balance sheet claims (guarantees, guarantees) of the bank in relation to this borrower, providing for execution in cash. Requirements are included in the calculation based on the degree of risk. This includes the amount of overdue loans, overdue debt, as well as acquired debt obligations of the borrower client;

- bank capital, which includes the authorized capital, additional capital, borrower funds and the amount of retained earnings.

Under interconnected borrowers refers to legal entities and individuals - borrowers related to each other economically or legally (i.e. having common property and (or) mutual guarantees, obligations; there is also the combination of a number of management positions by one individual). In other words, the financial difficulties of one of the borrowers make it likely that the other borrower(s) will have financial difficulties.

When calculating this indicator, all subsidiaries and dependent organizations are included in the group of related borrowers.

In accordance with the regulations of the Central Bank of the Russian Federation, the value of this indicator is set at 25%.

The maximum size of large loans is set as a percentage of the total amount of large loans and the bank’s own funds (capital).

A large loan is understood as the total amount of claims against one borrower (or group of related borrowers) of a bank for loans, taking into account 50% of the amount of off-balance sheet claims - guarantees, guarantees available to the bank in relation to one borrower (or group of related borrowers), exceeding 5% of its own funds (capital) of a banking institution.

The decision to issue large credits (loans) must be made by the board of the bank or its credit committee, taking into account the conclusion of the bank’s credit division.

The Bank of Russia has established that since 1998, the total amount of large loans and borrowings issued by the bank, including related borrowers, taking into account 50% of the requirements for guarantees and guarantees, cannot exceed the size of the bank’s capital by more than 8 times.

The maximum amount of risk per creditor (depositor), which is calculated as a percentage of the amount of deposits, deposits or loans received by the bank, guarantees and sureties, account balances of one or related creditors (depositors) and the bank’s own funds (capital). The maximum allowable value of the indicator is 25%.

The bank's lending ratio to its shareholders (participants) and insiders, which is defined as the ratio of the amount of loans, guarantees and guarantees provided by the bank to its participants to the bank's own funds (capital):

,

Where
- the total amount of the bank’s claims (including off-balance sheet), weighted taking into account the risk, in relation to one shareholder (participant) of the bank, legal entity or individual or a group of related shareholders (participants) of the bank, legal entities or individuals. The total amount of the bank's claims against the bank's shareholders (participants) also includes acquired debt obligations.

Under interrelated shareholders refers to legal entities or individuals related to each other by economic and (or) legal relations (i.e. having common property, guarantees or guarantees, as well as holding management positions). This may lead to the possibility of a domino effect if financial difficulties arise.

Control is understood as direct or indirect (through subsidiaries) ownership of more than 50% of the votes of a party or the ability to influence more than half of the votes by special agreement.

The total value of this standard is set by the Bank of Russia at 20%.

Let's look at the indicators second group.

Depending on the loan agreements, there are different ways of calculating interest on the principal amount of loans. Consequently, there are different types of interest rates for each specific loan or specific period of its repayment.

Depending on whether the interest on the loan changes during the period of its repayment, the following indicators are distinguished.

Simple interest rates:

,

		the amount of interest that the client pays for the entire period of using the loan;
		initial loan amount;
		credit term;
		credit growth rate.

increased loan amount.

The increased loan amount is understood as the entire amount of money that the client must return to the bank - the amount of the original loan plus interest (fee) for using the loan.

As a rule, short-term, small loans are issued at simple interest. In addition, in practice, interest is not added to the amount of the loan (loan, debt), but is paid periodically at a fixed interest rate. Thus, simple interest and fixed rate loans are issued if calculated:

exact (fixed) interest for a specific period (mostly in days);

regular interest with a fixed period (in days);

ordinary interest with an approximately fixed term for the loan.

Simple interest rates with interest accrual in adjacent calendar periods are calculated using the formula

Rollover loans (reinvestment loans):

If the accrual periods and rates do not change, then we have the following formula:

,

Compound interest rates.

In long-term credit transactions, interest is paid, as a rule, not immediately after it is accrued, but is added to the amount of debt, i.e. The compound interest rule applies. The basis for calculating compound interest, unlike simple interest, changes over time.

The absolute amount of accrued interest increases, and the process of accumulating the amount of debt accelerates.

Adding accrued interest to the amount of debt (the basis for their calculation) is called interest capitalization.

The basic formula for calculating compound interest is as follows:

,

Hence, .

Size
called the compound interest multiplier.

It should be noted that with a significant accumulation period, even a small change in the interest rate significantly affects the value of the multiplier.

If there are adjacent calendar periods, we have the following formula:

,

In case of variable rates:

In the case of fractional years, i.e. incomplete years or incomplete periods, the formula for calculating compound interest rates is as follows:

From the point of view of socio-economic statistics, of particular interest is the relationship between the size, the amount of interest when carrying out credit and deposit operations and some conditions that have a positive or negative impact on the size of the margin for banking institutions and profits for individual clients.

In a number of countries, interest received by legal entities and/or individuals is taxed, which reduces the actual accrued amount and negatively affects the popularity of credit and deposit banking services. As a result, part of the money falls out of circulation, which affects the amount of money in circulation, the speed of circulation, and, consequently, the effectiveness of the results of the monetary policy.

If there is a tax on interest accrued and received as a result of a deposit or credit transaction, the formula for the accrued amount is as follows:

to calculate simple interest:

to calculate compound interest:

in the case where tax is charged on the entire amount at once:

if the tax is calculated for each past year (period), then the amount of the accrued amount after payment of the tax will have the form

Where - tax for the period (for a year).

The rate of inflation also actively affects the size of the interest margin received by the bank or client. Inflation affects the amount of money received when calculating the accumulated amount of money.

TO third group These include indicators that analyze the level of creditworthiness, solvency of the client, as well as the level of credit risk for the bank. The Central Bank of the Russian Federation determines only economic standards for credit institutions, which the bank must adhere to in order to maintain its stability. Next, each bank itself determines and develops a methodology for analyzing the level of its credit risk. There are quite a large number of methods for analyzing the creditworthiness of clients, so we will give only some basic (desirable) requirements for them.

The most traditional indicators of statistical analysis of a client’s financial stability include:

the “2K + Z” indicator, which is used to analyze the borrower’s credit rating (K), the amount of his capital (K) and borrowing capacity (Z);

the “2K - Z - D - Zg” indicator, which makes it possible to analyze the credit rating (K), capital (K), borrowing capacity (Z), cash flow (D), collateral (Zg);

system of indicators “Five Pillars of Credit Quality”, with the help of which the general state of the industry (sector), competitiveness, financial management of the borrower, the quality of its marketing activities and the quality of the offered collateral are analyzed;

“6S” indicator system. It includes the following indicators:

C1 - client characteristics, taking into account: the client’s credit history; the experience of other lenders associated with the client; purpose of obtaining a loan; client experience in making realistic forecasts; borrower's credit rating; the presence of collateral or guarantee, analysis of their quality and prospects for maintaining their market value;

C2 - ability (potency) of the client, characterized by the authenticity and legal status of the client and his guarantors; historical status of the borrower;

C3 - the borrower’s funds in statics and dynamics, namely: the amount of profit, the amount of dividends and sales volumes in specific market segments in retrospect; sufficiency of the planned cash flow, i.e. availability of highly liquid assets; availability and quality of sufficiently liquid reserves; comparability of the size and timing of repayment of accounts payable and receivable; speed of circulation of material and financial assets; the borrower's capital structure and leverage level; quality of cost control; coverage ratio; the amount of profit (loss) on the primary and secondary stock markets in statics and dynamics; quality of management and marketing; content of the auditor's report; quality of accounting and statistical reporting;

C4 - security, which analyzes: ownership of assets; asset life; the likelihood of physical and moral wear and tear; residual value of real fixed capital (fixed assets); the degree and structure of specialization of all types of assets and liabilities; quality of insurance and reinsurance of various areas of activity; forecast and degree of financial stability in the future;

C5 - conditions for the client’s activities: his belonging to a certain industry (sector) of the economy; the size and quality of controlled market segments, windows and niches; comparison of the performance of a particular client with similar institutional units; sensitivity of the client, industry (sector) to short-term and long-term changes in the business and technological cycles of the economy; the level of inflation and its impact on the balance sheet and cash flow structure; environmental issues in specific market segments; conditions on the labor market, etc.;

C6 - control over the activities of the borrower.

Let's consider the main coefficients used in the statistical analysis of the creditworthiness of borrowers or the level of credit risk for the bank. In organizational terms, this analysis consists of two stages - express analysis and detailed analysis. Express analysis is performed using a certain set of standard coefficients and indices using various economic and statistical methods. To implement it, it is necessary to analyze the basic relationships, the real value of which is compared with the optimal one. If the actual values ​​are comparable to the optimal ones, then there is no need to conduct further analysis, since the borrower is creditworthy. If some coefficients deviate from the optimal ones, then an in-depth analysis is carried out in order to identify factors that influence the value of a particular coefficient. If the real and optimal values ​​of all coefficients are incommensurable, then proceed to a detailed analysis. It should be noted that a detailed analysis is carried out if a credit institution decides to lend to a new, unfamiliar client, as well as if the client has financial difficulties or insolvency. At the end of the financial year, all clients are subject to a detailed analysis.

Optimal value - 0.5-0.6. This means that the amount of the borrower's own funds should be approximately half of the total funds of the enterprise. The coefficient characterizes the interests of the founders, shareholders and creditors, and reflects the financial structure of funds, which is expressed in a low proportion of borrowed capital and a higher level of funds secured by own funds. This is protection against losses during periods of depression and a guarantee of obtaining loans.

Some situations require structuring the denominator of the coverage ratio, namely the amount of short-term debt. It can be debt of the first (up to 7 days), second (up to 14 days) and third (up to 1 month) degree.

Modification
is liquidity ratio(), which is the ratio of the sum of high and medium liquidity funds to short-term debt.

Approximately
And should be at least 0.5-0.6.

Lack of liquid funds indicates a delay in payments for current transactions and thereby reduces the liquidity of the balance sheet. The reasons for the lack of liquid funds are the following factors:

losses from the current activities of the borrower in an amount exceeding depreciation charges;

extraordinary losses and losses from previous years;

markdown of liquid funds;

the amount of capital investments is higher than the amount accumulated for this purpose;

overinvestment in long-term investments.

Excess liquid funds is also an undesirable phenomenon. If such a situation arises, the following conclusions can be drawn:

current assets are not used effectively;

the amount of accumulated profit is not commensurate with the size of capital investments;

delay in replacement of depreciation objects, etc.

It shows the amount of borrowed funds that the borrower attracted per monetary unit invested in the equity asset. characterizes the client’s dependence on external loans. The higher the value of this indicator, the riskier the current situation and the less likely it is that the borrower will be able to pay off its obligations, the higher the likelihood of a period of financial instability.

For the normal functioning of a company, it always needs sources of financing. In addition to own assets, borrowed funds can also be used, for example, loans from third parties. However, each borrower has the right to set their own interest rates on loans, which complicates the assessment of the cost of the organization’s loans. It is in such cases that an indicator such as the weighted average interest rate on loans is used.

Concept

The concept of a weighted average rate can be interpreted differently, based on the level at which it is applied. For example, if we are talking about a specific financial organization, then the weighted average rate on loans is the average cost of all loans (both issued and received). In other words, the average value of an individual bank's loan portfolio. This indicator is considered within the organization to analyze the effectiveness of its financial activities.

If we consider the weighted average interest rate at the level of the entire banking system, then this term means the cost of loans taken and issued by all banks of the Russian Federation. It is used by the Central Bank to study the efficiency and success of the country's banking system as a whole. In addition, the weighted average interest rate on loans from the Central Bank of the Russian Federation can be used as a criterion for assessing the dynamics of the promotion of the unified credit policy of our state.

Types of loans

The calculation of the average interest rate arose due to the need to conduct a general financial analysis of the organization’s activities. But using the simplest arithmetic) it is impossible to make such calculations, since credit organizations work with different types of loans, which are issued at different interest rates.

Loans are:

• long-term;
• short-term;
• investment;
• negotiable.

Also, the weighted average interest rate can be calculated by the Central Bank separately for individuals and legal entities. These indicators are available for public use. For example, the weighted average interest rate on loans to individuals for a period of over 365 days in December 2016 was 15.48%.

Why calculate the average cost of loans?

For stable operation of banking organizations, they need to control their own liquidity. Liquidity is the real ability of assets to become easily negotiable funds. This means that an asset is considered liquid if it can be sold at a market price in the shortest possible time.

When, when analyzing current activities, a financial organization discovers that it is excessively liquid (has many liquid assets), it needs to issue as many interbank loans as possible. Conversely, when liquidity is low, banks are forced to raise assets externally.

Interest rates on loans for individuals and organizations are directly dependent on the golden rule of “supply and demand”. Therefore, the Central Bank of the Russian Federation constantly monitors the volume of lending operations by calculating the weighted average interest rate on loans. This makes it possible to quickly respond to changes in the financial market and, if necessary, reduce or increase the level of interest rates on interbank credit transactions.

What is included in bank assets?

To assess a bank's liquidity, you need to know what is included in its assets. Bank assets are the organization's resources that it owns. Moreover, she has the right to dispose of them at her own discretion. Bank assets include:

• equity;
• balances on current accounts of individuals and legal entities;
• funds in deposit accounts of organizations;
• bank deposits of individuals;
• interbank and other loans.

When a bank falls out of balance and becomes overly liquid, it simply loses its profits. Because free funds can be invested and receive a certain percentage of profit from them. However, during the time when the money was simply lying in the accounts, it did not work, but lay there as a useless burden.

Formula for calculating the weighted average interest rate on a loan

To correctly calculate the average value of a loan portfolio, organizations use a special formula that differs significantly from the simple arithmetic average. Because the cost of a loan depends not only on its interest rate, but also on its amount.

This formula looks like this:

SPS=∑(K*P)/∑K, where:

• SPS - weighted average interest rate;
• K - loan balance;
• P - interest rate.

Calculation example

To understand how to use this formula, you need to apply it in practice. Let's assume that an organization has three loans:

• in the amount of 15 million rubles at 10% per annum;
• in the amount of 10 million rubles at 8% per annum, while the organization has already paid 8 million rubles to the creditor;
• in the amount of 2 million rubles at 15% per annum, with the remaining loan amount being 1.5 million rubles.

Knowing the formula, you can find out that the weighted average interest rate on loans provided to the company is equal to:

ATP=(15*0.1+8*0.08+1.5*0.15)/(15+8+1.5)*100% =0.097*100%=9.7%

In this case, the weighted average rate may change if:

• the company will receive another loan;
• the interest rate on any of the current loans will change;
• the company will make full or partial repayment of loan obligations.

The weighted average interest rates on loans in rubles are similar to those on foreign currency loans. But since the analysis of financial activity is carried out only in national currency, it is necessary to take into account the exchange rate of the Central Bank at the time of assessing the loan portfolio.

How to reduce the average interest rate on loans?

To make the most efficient use of borrowed funds, it is necessary to keep the weighted average interest rate at the lowest possible level. To do this you need to follow some rules:

1. Take out loans only at the lowest interest rates.
2. Pay back loans with the highest interest rates first.
3. If the interest rate has increased during the loan period, you need to restructure or refinance the loan.
4. Draw up a debt repayment schedule taking into account that at the end of the term only low-interest loans should remain open.

Weighted average interest rates on loans provided by credit institutions within one enterprise must be kept under constant control. This will allow you to manage the company's resources wisely and maintain maximum efficiency of its work.

The same rule applies to the cost of all credit resources in the country. After all, the efficiency of the entire financial system of the state depends on the weighted average interest rate. However, we will leave this responsibility to the Central Bank, which copes with it very well.

A term most often applied to mortgage-backed securities. The weighted average shows how much time remains until the mortgages that make up the underlying pool are fully repaid. The weighting coefficients are the balances of each of the mortgages as of the issue date. The higher the weighted average repayment period, the longer the time until the mortgages securing the securities are fully repaid.

How to calculate the weighted average repayment period?

The calculation of the weighted average maturity period begins with determining the total value of all assets that back the securities. The value of each asset is divided by the total value. The result of the division is multiplied by the number of years remaining until the mortgage is fully repaid. This step is repeated for each and every asset included in the portfolio. The results of the multiplication are summed up - the result is weighted average repayment period package of securities.

In mathematical calculations, the term "weight" describes the relative importance of one value compared to others. Dividing the value of one asset by the total value everyone assets and gives weight relative to the overall portfolio.

Why is a weighted average repayment period needed?

For those valuing a stock or bond, the weighted average maturity period provides no information about either the quality of the specific mortgages that back the security or the overall quality of the assets. The value of the weighted average repayment period tells you how long the assets will continue to generate income, provided that the underlying mortgages turn out to be “healthy” (that is, they are repaid by borrowers on time). Analyzing the weighted average maturity period over time can give the investor a clear idea of ​​how long to invest money.

Duration and bonds

The term “weighted average maturity period” is also found in bond valuations, often replaced by a simpler synonym - duration. The American economist F. Macauley first mentioned duration in the 50s of the last century. Macauley argued that the profitability of investments in bonds should be assessed not by the date of full repayment, but by the date of receipt of coupon payments. For example, if a zero-coupon bond was purchased, then the duration period will be equal to the maturity date, if a simple bond, the duration period will come earlier. Duration Macauley named the average volume of all payments on the security from the current day until its full repayment. A high duration value can cause instability in bond prices, but only with small fluctuations in profit.