The modern banking system is the most important area national economy any developed country and the state.

Commercial banks, acting in accordance with the country's monetary policy, regulate the flow of Money, influencing the speed of their circulation, total mass, issue, including the amount of cash in circulation.

The current difficult economic situation in Russia due to the sanctions imposed against enterprises and organizations shows a number of negative factors that, among other things, affect the profit and profitability of banks.

The main goal of a commercial bank is to maximize profits, subject to its long-term functioning and a stable position in the market.

The amount of profit or loss received by the bank, being the final financial result, reflects the results of all types of its activities, active and passive operations.

The profit of a commercial bank is the main financial result of its activities, defined as the difference between the income received and the expenses. In turn, the bank's profitability is an indicator of the efficiency of its use of monetary or other resources.

Revenues, expenses and profits are a reflection of a set of objective and subjective factors affecting the bank's activities: customer base, location, availability of sufficient premises to serve customers, level of competition, etc.

Incomes are cash receipts from his production and non-production activities. A commercial bank can receive income from both main and secondary activities, as well as have incidental income classified as other. It follows from this that the source of the bank's income is its main and secondary activities. Part of the income received by a commercial bank is used to create reserves to cover potential risks. The aggregate of all the income of a commercial bank is called gross income.

PJSC Sberbank of Russia is the largest universal bank Russia, which provides banking services to legal entities and individuals. License number 1481 dated August 11, 2015. The bank is a member of the deposit insurance system. The authorized capital is 67.7 billion rubles. Is public joint stock company, 52.3% of shares are owned by the Central Bank of the Russian Federation, the remaining 47.6% of shares are in public circulation, the owners of which have not been established (including those owned by minority shareholders).

Let's analyze the main financial results activities of PJSC "Sberbank of Russia" for 2010-2016. according to the profit and loss statement of a commercial bank for seven reporting periods (table 1).

Table 1.

Main financial results of the activities of Sberbank of Russia PJSC for 2010-2016.(billion rubles)

Indicators
Indicators
Net interest income
Net fee and commission income
Operating income before provisions
Operating income
Allowance for loan impairment
Operating expenses
Profit before tax
Net profit

More clearly the indicators of table 1 are presented in figure 1.

Figure 1. Dynamics of the main financial results of the activities of Sberbank of Russia for 2010-2016.

The data in Table 1 and Figure 1 show a positive upward trend in profit indicators. It can be seen that over 7 years the bank's operating income increased by 1,047.7 billion rubles. or by 161.2%. Profit before tax from 2010 to 2016 also increased by 447.4 billion rubles. or almost three times. The net profit of Sberbank of Russia increased by 360.3 billion rubles. or almost three times.

Figure 2 shows the dynamics of the bank's net profit. In 2014-2015, the bank's net profit tended to decline due to the current economic crisis in the country. The bank's net profit from 362 billion rubles. in 2013 decreased to 290.3 billion rubles. in 2014 and further up to 222.9 billion rubles. in 2015. For two years, the bank has lost 139.1 billion rubles. However, in 2016 compared to 2015, the net profit of Sberbank of Russia increased by RUB 319 billion. or almost 2.5 times.

Next, we will conduct a trend analysis. Trends can be represented by various equations - logarithmic, linear, power, etc. A trend is the main tendency for a certain series (indicator) to change.

Based on the data of the graph for 2010-2016, in Figure 2, a polynomial trend line is built, which well approximates the empirical share.

Figure 2. Dynamics of the net profit of Sberbank of Russia for 2010-2016

Thus, in Figure 2, there is a clear upward trend in 2010-2016. If there are no major changes in politics and economics, and Sberbank of Russia continues to operate without slowing down, then we can expect that profit in the next year, 2017, will also grow.

Bibliography:

Bukato, V.I. Banks and banking operations in Russia / V.I. Bukato, Yu.I. Lviv. - M .: Finance and statistics, 2012 .-- 498 p.
Bondar A.P., Kondrasikhin I.A. The main ways to increase the profit and profitability of regional banks on the example of JSC "Sevastopol Sea Bank" [Electronic resource]. Access mode: http://elibrary.ru/query_results.asp (date of access 25.04.2017)
Zhukov E.F. Money. Credit. Banks. Securities: textbook. allowance. - M .: New knowledge, 2011 .-- 735 p.
Zagidullina A.M., Araslanbaev I.V. Profit formation in commercial bank[Electronic resource]. Access mode: http://elibrary.ru/query_results.asp (date of access 25.04.2017)
Official site of PJSC "Sberbank of Russia" [Electronic resource]. Access mode: http://www.sberbank.com (date of access 24.04.2017)

Theoretical foundations of banking statistics. Analysis of the structure of the loan portfolio. Determination of the concentration index of financial flows. Calculation of dynamics indicators and trend detection. Study of the dependence of bank assets on the amount of deposits of individuals.

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MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

Bryansk State Technical University

Department of "Economics, organization of production, management"

Course work

in the discipline "Statistics"

Statistical analysis of the bank's activities (on the example of Sberbank of Russia PJSC)

Completed by: Student Damansky D.A.

Checked by: Ph.D., Assoc. A.V. Novikova

Bryansk 2016

Introduction

Chapter 1. Theoretical basis banking statistics

1.1 Socio-economic essence banking system and banking statistics

1.2 Key performance indicators of the bank

1.3 Overview banking services for 2010-2015

1.4 Forecast of the banking system development

Chapter 2. Calculation and analysis of performance indicators of PJSC "Sberbank of Russia"

2.1 Calculation of the number of groups and interval values

2.2 Calculation of relative values

2.3 Averages and indices of variation

2.4 Application of the sampling method

2.5 Calculation of dynamics indicators and trend detection

2.6 Correlation-regression analysis

Conclusion

Bibliography

Application

Introduction

Development of banks' activities - necessary condition real creation market mechanism... The emergence of new structures (in the area of individual banking operations) increases the likelihood of unpredictable changes and forces banks to develop flexible policies to manage their activities. Therefore, it is important to study the financial performance of banks. After all, they reflect the main aspects of the bank's activities. Of particular relevance is knowledge of the nature and strength of the relationships between these indicators, which makes it possible to manage socio-economic processes and predict their development.

Statistical analysis of the bank's activities is one of the main conditions for ensuring the quality and efficiency of management decisions. Reliable work the bank depends on its ability at any time and in full to fulfill the requirements for its obligations, i.e. the bank must at any time quickly make payments to customer orders and be responsible for its obligations in case of crisis situation in a bank or in the financial market. The course work focuses on the statistical study of the performance indicators of Sberbank of Russia.

The object of the research is Sberbank of Russia PJSC.

The subject of the research is banking statistics.

Target term paper consists in the study of statistical indicators of the activities of PJSC "Sberbank" of Russia.

Work tasks:

Outline the theoretical foundations of banking statistics;

Calculate the statistical indicators characterizing the bank's activities.

Chapter1. Theoretical foundations of banking statistics

Banking system - an integral part of economy of any state. Modern banking systems different countries have a multilevel structure. The main link in any banking system is the Central (national) bank. It belongs to the organs government controlled(monetary authorities) and performs the functions of monetary regulation:

Issue of national currency;

Management of the country's international reserves;

Acceptance of obligations in the form of deposits from other banks;

The role of the lender of last resort;

The role of the central government's fiscal agent.

The banking system includes operating banks, credit institutions and organizations that perform some banking operations, support the activities of banks and credit institutions (settlement and cash centers, bank audit firms, etc.). The banking system is basic part of credit system which is included in economic system countries. Thus, the banking system actively interacts with other links of the social and economic mechanism.

Distinguish between one-tier and two-tier banking system. One - tier banking system is talked about in the case when the state does not have a central bank or all banks function as central ones. This type of banking system is not typical for market economy... A developed economy is characterized by a two-tier banking system, the first tier of which is the central bank, the second - commercial banks and credit institutions. Such a banking system takes into account the freedom of entrepreneurship, on the one hand, and allows controlling the activities of commercial banks, on the other hand.

There is a two-tier banking system in Russia, which includes the Central Bank of the Russian Federation (Bank of Russia) and credit institutions, as well as their branches and offices, representative offices of foreign banks.

The main areas of socio-economic statistical analysis are:

Developing a strategy and tactics for monetary credit policy monetary authorities of the country;

Determination of the size of the official refinancing rate depending on the state and prospects of economic development;

Development of strategy and tactics of payment policy;

Monitoring the performance of individual credit institutions and the banking system as a whole;

Control over foreign exchange policy;

Compilation of the balance of payments of the Russian Federation.

1.1 Socio-economic essence of the banking system and banking statistics

Let's consider some basic concepts of the subject of study.

A bank is a credit institution that has the exclusive right to carry out, in aggregate, the following banking operations: attraction of funds from individuals and legal entities to deposits; placing funds on its own behalf and at its own expense on terms of repayment, payment, urgency; discovery and maintenance bank accounts individuals and legal entities.

A credit institution is a legal entity that, in order to generate profit, as the main purpose of its activities, on the basis of a special permit (license) The Central Bank The Russian Federation has the right to carry out banking operations provided for by the Federal Law "On Banks and banking". A credit institution is prohibited from engaging in production, trade and insurance activities.

A non-bank credit institution has the right to carry out certain banking operations provided for by federal law. Non-bank credit institutions include: insurance, leasing, financial companies; pension, investment, charitable funds; pawnshops; credit unions, societies and partnerships, etc.

A commercial bank is a multifunctional institution performing operations in all sectors of the capital market. In other words, banks provide loans, settlements and financing of individual enterprises, groups of enterprises, industries, trade, other legal and individuals at the expense of attracted funds (deposits). All these operations are carried out on a paid basis.

Banking statistics is a branch of financial statistics, the tasks of which are to obtain information to characterize the functions performed by the banking system, to develop analytical materials for the needs of managing the country's monetary system, primarily credit and cash planning and control over the use of plans.

The following objects are distinguished in banking statistics:

Bank resources and their use;

Short-term loan;

Cashless payments;

Cash circulation;

Savings business;

Financing and lending of capital investments;

Cash execution of the state budget.

An example of the result of banking statistics is Table 1.

Table 1 - Number and structure of credit institutions

Definition
The number of credit institutions registered in the Russian Federation
including those entitled to carry out banking operations (existing)
The number of credit institutions with foreign participation in the authorized capital, entitled to carry out banking operations
including:
with 100% foreign participation
with foreign participation from 50 to 100%
The number of branches of operating credit institutions in the Russian Federation

Sberbank of Russia
banks with 100% foreign participation in the authorized capital
The number of branches of operating credit institutions abroad
Registered authorized capital operating credit institutions, billion rubles
The number of credit institutions that have licenses (permits) granting the right:
to attract deposits from the population
to carry out operations in foreign currency
for general licenses
to carry out operations with precious metals

Thus, the subjects of statistical analysis are both banks themselves and other credit institutions, real and potential customers, and correspondents, individuals and legal entities.

1.2 Key performance indicators of the bank

The main statistical indicators used by the Central Bank of the Russian Federation are grouped into 6 blocks:

Structures banking sector;

Adequacy of capital and liquidity;

Loan portfolio structures;

The size and structure of gold and foreign exchange reserves;

The main factors that determine the official exchange rate;

Indicators that determine official interest rates.

Of these, the first 3 blocks are directly related to banking statistics. Let's consider in more detail exactly their indicators.

The structure of the banking sector includes the following indicators:

The number of registered and the number of operating banks in Russia and their distribution in the regional context;

The number of branches of credit institutions and their distribution by region.

Index of the number of banking institutions in the region. It is calculated as the ratio of the number of banking institutions in the region to the same average Russian indicator, expressed as a percentage. It is used to calculate the concentration index of financial flows.

Average number of branches established by one bank. It is calculated by dividing the number of branches of banks registered in a given region, regardless of the location of these branches, by the number of banks registered in the territory.

Grouping of credit institutions according to the amount of total or paid-in capital.

Grouping of credit institutions in accordance with the type of licenses issued by the Central Bank of the Russian Federation.

Capital adequacy is an indicator of a bank's performance, expressed as a ratio own funds the bank to the total volume of risk-weighted assets.

Capital adequacy and liquidity implies the study of the following indicators:

Growth rate of aggregate equity capital banks;

Banking sector capital, including as a percentage of GDP; to the value of assets of the banking sector;

The ratio of banks' capital to the value of risk-weighted assets;

The ratio of fixed capital to risk-weighted assets;

Attitude highly liquid assets to the value of the total assets of the banking sector;

The ratio of liquid assets to total assets;

The ratio of highly liquid assets to demand liabilities;

The ratio of customer funds to total loans.

Indicators of the structure of the loan portfolio of the banking system:

Attitude total amount attracted bank deposits(with and without taking into account the received interbank deposits) in domestic and foreign currency to GDP;

The ratio of the total amount of loans issued by banks (including and excluding provided interbank loans) in domestic and foreign currency to GDP;

The ratio of the total amount of interbank loans (deposits) in domestic and foreign currency to GDP;

Growth rates of banks' aggregate credit investments (with and without interbank loans);

Growth rates of short-term credit investments of banks (with and without taking into account the corresponding interbank loans);

Growth rates of total (short- and long-term) deposits banking clients(including and excluding interbank deposits);

The specificity of banks as intermediaries is that most of their income depends on interest rates Moreover, if the level of both real and nominal interest rates is important for bank customers, then for banks the most important parameter is the difference between interest rates.

Assets financial institution usually reflected in balance sheet of a particular institution. Assets are defined as the resources at the disposal of the organization.

The return on bank assets is a single indicator for assessing the effectiveness of a bank, characterizing in relative units the use of all resources received by the bank at its disposal. The return on bank assets is the ratio of profit to average total assets.

The return on assets ratio (Kda) is defined as the ratio of total income to the value of the bank's assets:

Kd.a = D / A (1),

A - the value of the bank's assets.

2) The rate of return on income-generating assets (KD APD) is defined as the ratio of total income to the value of income-generating assets:

K D APD = D / APD (2),

where D is the total income of the bank;

Coefficient interest rate generating income (K PD APD) is defined as the ratio of interest income to the value of working assets:

K PD ADF = DP / ADF (3),

where Дп - interest income of the bank;

APD - income-generating assets (working).

The non-interest rate of return on income-generating assets (KND APD) is defined as the ratio of non-interest income to the value of income-generating assets:

K NDAAP = Dn / ADF (4),

where Дн - non-interest income of the bank.

The return on assets ratio shows the amount of income per 1 ruble. bank assets.

The profitability of a bank is an indicator of a bank's performance, characterizing:

For shareholders - return on invested capital;

For depositors - a guarantee of the reliability and efficiency of the bank;

For the bank - the main source of equity capital

The main criteria for profitability are the return on assets and net income. The main and most stable component of a commercial bank's net profit is the net interest margin, which makes it possible to determine the efficiency of using paid resources in the assets placed at interest.

The interest margin can be determined as follows:

PMCh = (DP - Rp) / APD * 100% = PP / APD * 100% (5),

where Дп - interest income of the bank; Рп - interest expenses of the bank;

APD - income-generating assets (working);

PP - interest income.

If in formula (5) instead of income-generating assets, total assets (averaged) are used, then this indicator is called the total interest margin (PM O):

PMO = PP / A * 100% (6),

where A is the value of the bank's assets.

Let us compile a table of ranking by experts of bank performance indicators according to their importance for the concept of bank reliability (tab. 2).

Table 2 - Ranking by experts of bank performance indicators according to their importance for the concept of bank reliability

Indicator	% of experts who indicated this indicator as one of the most important
Share of overdue debt in loans
Current liquidity
Adequacy of equity capital
Equity
Share of long-term liabilities in the balance sheet
Share of non-performing assets in balance sheet

Return on equity
Instant liquidity
The share of long-term loans in the balance sheet

The table shows that experts consider the share of overdue debts in issued loans to be the most important characteristic of the bank's activities. The group of the most influencing on reliability also includes indicators of asset liquidity, capital adequacy, profitability and equity capital. The share of long-term loans in the economy did not make it into the top five; nevertheless, 20% of experts consider this indicator important.

1.3 Overview of banking services 2010-2015

According to the Bank of Russia, according to the results of the first seven months of 2015, banks received a total profit (before taxes) in the amount of 34 billion rubles, which turned out to be 15 times less than in 2014.

Considering that in the first half of 2015 the sector's profit amounted to 51.5 billion rubles, banks completed July 2015 with losses of 17.5 billion rubles. It should be noted that the depth of the recession in the banking system is smoothed out by a significant positive contribution from Sberbank of Russia, which continued to increase its profit, having received 32.8 billion rubles in July. profit (before taxes), and according to the results of seven months - 127.8 billion rubles. Excluding Sberbank of Russia, losses in the banking sector in January-July amounted to 93.8 billion rubles, and in July - 50.3 billion rubles. The cause of the colossal losses of the majority banking organizations in Russia there is a continuing rapid decline in asset quality, which leads to an increase in arrears. In particular, in July, the growth in the total share of overdue debt accelerated, increasing by 0.2 percentage points. and reaching 6.5% by August 1, 2015, which is only 0.2 percentage points. below the peak value reached in May 2010.

One of the reasons for the continued high growth rates of overdue debt is the difficult financial position of most corporate borrowers, largely due to the continuing contraction in consumer and investment demand - retail turnover in July fell by 9.2% yoy.

Under these conditions, banks are forced to adhere to a more conservative credit policy, which also leads to the fact that interest rates on short-term loans required for replenishment working capital, which are extremely important for the life of companies, have become prohibitively high for many borrowers. In particular, in June 2015, the weighted average rate on corporate loans up to 1 year (excluding Sberbank) amounted to 15.62%, which is only 1.11 percentage points. below the level of December 2014.

A similar situation has developed with regard to interest rates on loans to small and medium-sized enterprises. After a sharp increase at the end of last year and the beginning of this year (from 16.3% in December 2014 to 18.9% in January 2015), the level of interest rates for small and medium-sized businesses practically did not decrease, remaining critically high, which signals the preservation of increased lending risks in this segment compared to the corporate sector as a whole.

In retail lending, the overall situation looks even more unfavorable. Interest rates on loans to individuals (up to 1 year, in rubles, excluding Sberbank of Russia) decreased by 2.16 percentage points in June. to 27%, however, they could not level the May jump by 2.73 p.p. at once. The reason for the continued high level of interest rates, despite the decrease in the cost of funding from the Bank of Russia, is also the growing costs of creating reserves associated with the outstripping growth of bad debts. In addition, the continued decline in real disposable income and salaries population does not allow banks to increase lending, as a result of which the retail loan portfolio steadily decreased in the first six months of 2015, having lost 5.3% of its volume during this time. The accumulated problems in the banking system eventually led to an acceleration in the growth of total losses of unprofitable banks in July to 337.2 billion rubles. (+ 31.5% to June 2015) and an increase in the number of unprofitable credit institutions to 234. At the same time, a significant part of losses falls on retail banks: in the first half of the year, 6 out of 10 largest retail banks accounted for 74% of all losses among unprofitable retail banks according to RAS. In addition, the net loss of Russian Standard Bank under IFRS for the first half of 2015 reached a record 22 billion rubles, against a loss of 4.7 billion rubles. for the same period last year. The loss turned out to be higher than the expectations of analysts at Standard & Poor's and UBS, who had previously predicted it at the level of 15-16 billion rubles.

1.4 Forecast of the banking system development

The growth of the banking sector in April-May 2015 slowed sharply. This is largely due to the currency revaluation associated with the strengthening of the ruble in this period (as well as the large-scale increase in bank balances at the end of 2014 was caused by a sharp weakening Russian currency). At the same time, there is reason to believe that the current decline in growth rates is structural in nature and is associated with two important factors:

The effect associated with the closure of external financial markets due to sanctions (which de facto affected almost all large Russian borrowers) and the urgent need to receive funding from Russian banks, it is fading away;

Investments Russian companies production capacity has been decreasing since the beginning of 2014 - enterprises simply do not need loans for development.

Thus, in the near future, the current trend towards a slowdown in the growth of the banking system will continue. Moreover, most likely, anemic growth is expected for Russian banks in the medium term.

Preconditions for a strategic forecast

The baseline scenario for the development of the banking sector in 2015-19 based on the following assumptions regarding key factors:

The dynamics of the main macro variables corresponds to the baseline scenario of our macro forecast;

The revocation of licenses from Russian banks continues at the current pace during 2015-16, and has been gradually slowing down since 2017;

The gradual lifting of EU and US financial sanctions against Russian banks and enterprises does not begin until 2017.

Assets: The growth rate of banks' assets will decline sharply until the end of 2015. After reaching a minimum of about + 6%, growth will recover in early 2016, but it will remain at a low level until the end of 2019. The penetration of banking services to GDP on the planning horizon will increase up to 120%.

Capital: It is assumed that in 2015-19. Russian banks will manage to maintain the level of capital adequacy at 12%. In addition, as the situation in the economy stabilizes, banks' appetite for risk will gradually begin to grow, and by the beginning of 2017, the ratio of risk-weighted assets (RWA) to total assets will return to pre-crisis values.

An unexpected peak in the capital growth of the banking system at the end of 2015 and the beginning of 2016 due to the effect of the low base in terms of RWA.

Banking services for companies: Corporate lending, including the small and medium-sized business (SME) segment, will continue to slow down compared to the 2014 record.In early 2016, a decline in growth rates is expected due to the high base of early 2015. Subsequently, the loan portfolio growth will return to its average long-term level of 12-13%.

The growth of funds raised from corporate clients will also slow down. However, the collapse in early 2016 will most likely be avoided due to the excess liquidity accumulated by companies in bank accounts (Figure 1).

Figure 1 - Accounts and deposits

Retail banking: The retail loan portfolio will begin to decline in the second half of 2015 and is unlikely to reach positive growth rates before Q2. 2016 Trends in retail lending in the medium term:

The greatest growth potential remains with secured loans - mortgages and car loans (saturation in both market segments is low, consumers will continue to show demand for real estate and cars);

In the segment of unsecured consumer lending, market oversaturation is already noticeable; in the future, this segment is unlikely to be able to grow rapidly;

The Bank of Russia's attitude to unsecured consumer lending is negative, so we can expect further "tightening the screws" in regulating this type of loans in favor of credit cards, which are a more civilized type of retail loans.

After a slight slowdown in 2015, the dynamics of household deposits will return to average long-term growth rates of about 14-15% (Figure 2).

Figure 2 - Retail loans

In general, the growth of the banking system in the medium term can be divided into two stages:

The period of stagnation or decline in 2015-16;

Growth resumed in 2017-19

Chapter2. Calculation and analysis of performance indicators of PJSC "Sberbank of Russia"

2.1 Calculation of the number of groups and interval values

Let's analyze the 30 most reliable small and medium-sized banks in the Russian Federation using the grouping method according to the following data from Appendix A.

Let us take the authorized capital as a grouping criterion. Let's form four groups of banks at equal intervals. The interval values are determined by the formula:

Let's mark the boundaries of the groups:

2100-7350 - 1st group

7350-12600 - 2nd group

12600-17850 - 3rd group

17850-23100 - 4th group.

After the grouping attribute is determined - the authorized capital, the number of groups is set - 4 and the groups themselves are formed, it is necessary to select indicators that characterize the groups and determine their values for each group.

The indicators characterizing the banks are divided into the four indicated groups and the group totals are calculated. The grouping results are entered into a table and the overall totals are determined for the totality of observation units for each indicator (table 3).

Table 3 - Grouping of commercial banks by the size of the authorized capital

Number of banks	Authorized fund, million rubles	Working assets, million rubles	Capital, million rubles

The structural grouping of commercial banks based on the data in Table 4 will be as follows (Table 4):

Table 4 - Grouping of commercial banks by the size of the authorized capital (in %% to the total)

Bank groups by size of authorized capital, mln rubles	Number of banks	Statutory fund	Working assets

Table 4 shows that mainly small banks dominate 60%, which account for 42.5% of total capital. A more specific analysis of the relationship between indicators can be done on the basis of the analytical grouping (table 5).

Table 5 - Grouping of commercial banks by the size of the authorized capital

Bank groups by fund size, RUB mln statutory	Number of banks	Capital. million rubles Total	Working assets, million rubles On average for one bank	On average for one bank

The amount of capital and working assets are directly dependent on each other, and what larger bank, the more efficient is the management of operating assets.

2.2 Calculation of relative values

Using relative benchmarks, compare the net profit volumes in the largest Russian banks for 2015 (table 6):

Table 6 - Volumes of net profit in the largest Russian banks for 2015

The relative indicator of comparison is the ratio of the same absolute indicator (in our case, the volume of net profit), which characterizes different objects (banks):

To determine the relative value of the comparison, let us compare the initial data on the volume of net profit:

The volume of net profit of Sberbank of Russia in April 2015 exceeded the same indicator of Alfa-Bank by more than 9 times.

Sberbank's net profit is 14.6 times higher than Raiffeisenbank's net profit; VTB - 17.4 times; UniCredit Bank - 18.4 times.

2.3 Averages and indices of variation

To construct a statistical series of distribution, we determine the size of the interval by the formula:

where n is the number of groups

million rubles - interval size

Let's compile a table of the distribution of banks by the volume of loans issued by commercial banks (table 7).

Table 7 - Calculation of average values

Initial data	Calculated values
Bank groups by the volume of loans issued commer. banks, million rubles	Number of banks in group f	Midpoint of the interval, x	Accumulated frequencies

Find the arithmetic mean.

For the calculation, we take the midpoints of these intervals (x) as the values of the attributes in the groups, since the values of the averaged attribute are given in the form of intervals. Let's calculate and substitute the obtained values into the table.

So, the average volume of loans issued by commercial banks is 59,450 million rubles.

Let's find the standard deviation by the formula:

To do this, we will make intermediate calculations and substitute them into the table.

Let's find the coefficient of variation:

Let's find the fashion by the formula:

where is the lower limit of the modal interval;

Modal interval;

Frequencies in modal, previous and following modal intervals (respectively).

The modal series is determined by the highest frequency. The table shows that this interval is (34250 - 59450 million rubles).

Let's find the median by the formula:

where is the lower border of the median interval;

Median interval;

Half of the total number of observations;

The sum of observations accumulated before the beginning of the median interval; - the number of observations in the median interval.

First of all, let's find the median interval. This interval will be (34250 - 59450 million rubles).

Conclusions: Since V> 33%, this indicates a significant variability of the trait, about non-typicality average size, about the heterogeneity of the population.

Since> 0, i.e. (59450 - 44330)> 0, then right-sided asymmetry is observed.

2.4 Application of the sampling method

Sample observation is a non-continuous observation in which the selection of the units to be surveyed is carried out in a random order, the selected part is studied, and the results are extended to the entire original population.

The population from which the selection is made is called the general population (N). The set of selected units is a sample set (n).

Let's make an additional table "Calculation of indicators of sample observation" (table 8).

Table 8 - Calculation of indicators of sample observation

The average value of a feature in the sample is found by the formula (11)

The sampling error must be found by non-repetitive sampling according to the formula (12)

where, is the variance in the general population (found by formula 13)

n is the number of units in the sample

N is the number of units in the general population.

The condition says that the sample is 3%, mechanical.

Therefore, n = 37 is 3% and N = x is 100%.

Let's find x according to the rule of proportion (formula 14)

Using formula 22, we find the sampling error for non-repetitive sampling

The boundaries in which the average profit in the general population will be located are found by the formula (15)

t - The coefficient of confidence, which depends on the probability (table 9).

Table 9 - Dependence of the confidence coefficient on the probability

Probability

By condition, probability = 0.683. Therefore, t = 1

Let's find the boundaries in which the average profit in the general population will be, according to the formula 15

Conclusion: in 683 cases out of 1000, the average profit in the general population will range from 169.58 million rubles. up to 192.04 million rubles.

In the remaining 317 cases out of 1000, it will go beyond these boundaries.

The sampling error of the share of banks with a profit of 153 million rubles. and more we find by the formula (16)

To find the value of u (share in the sample), it is necessary to find out which number of banks will have a profit of 153 million rubles. and more. According to table 1.3, the number of such banks = 24 (N).

Let us find the share in the sample population by the formula (17)

Let us find the sampling error for the share of banks with a profit of 153 million rubles. and more according to formula (16), using the value N = 1233.34 already found in paragraph 1

Let us find the boundaries in which the general share will be located, according to the formula (18)

57,16 < p < 72,56

Conclusion: in 683 cases out of 1000 the share of banks with a profit of 153 million rubles. and more in the general population will lie within the range from 57.16% to 72.56%.

In the remaining 317 cases, the share of such banks will go beyond these boundaries.

2.5 Calculation of dynamics indicators and trend detection

To calculate the absolute and relative indicators of dynamics, we will use the formulas from Table 10.

Table 10 - Formulas for absolute and relative indicators of dynamics

Indicator		Basic
Absolute gain
Growth rate
Growth rate
Rate of increase
Absolute value of 1% gain

Legend:

U1,2,3… n - all levels of consecutive periods;

n is the number of levels in the row.

Let's calculate the absolute and relative indicators using data from Appendix B for 2003-2015.

The results are presented in Table 11.

Table 11 - Calculation of indicators of dynamics

Accounts payable, billion rubles

Indicators

Absolute growth, billion rubles

Growth rate

Growth rate, %

Growth rate,%

Absolute value of 1% growth, billion rubles

Average dynamics for the analyzed period:

The average level of the interval of a series of dynamics:

Average absolute growth:

Average growth rate:

Average absolute value of 1% increase:

Thus, the average growth rate accounts payable organizations (excluding small businesses) in the Russian Federation for 2003-2015 amounted to 118.1% or 2803.5 billion rubles, which is determined by an average growth of 18.1% per year.

One of the main tasks of studying the series of dynamics is to identify the main tendency (pattern) in the change in the levels of the series, called a trend. To determine the trend based on Table 9, we will apply the analytical alignment method using the equation. Calculations of the required values in table 12.

Table 12 - Calculation of values for determining the trend

Financial and economic indicators of PJSC "Sberbank of Russia"

The total capital of the Bank, calculated in accordance with the Regulation of the Bank of Russia dated December 28, 2012 No. 395-P "On the methodology for determining the amount of equity (capital) of credit institutions (Basel III)", increased as compared to January 1, 2016 by 117.2 billion rubles, up to 2,775.3 billion rubles. Earned profit became the source of capital growth. The return on assets increased from 0.8% to 2.0%, which was due to an increase in the volume of net profit.

Return on equity for the 1st half of 2016 increased from 8.0% to 18.9% due to an increase in the volume of net profit.

· Net assets decreased as compared to January 1, 2016 by 3.7%, or by 0.8 trillion. rubles, up to 21.9 trillion. rubles. The dynamics of net assets was strongly influenced by the negative revaluation of foreign currency balance sheet items as a result of the strengthening of the ruble. Thus, the net loan debt compared with the beginning of the year decreased by 0.7 trillion. rubles, or by 4.0%, which was a consequence of the revaluation of foreign currency loans to legal entities and non-resident banks. Also, the dynamics of net loan debt was influenced by the investment of part of the funds previously placed in loans to banks in more profitable instruments, in particular, in securities... Net investments in securities and others financial assets available-for-sale increased by 16.1%, or $ 0.4 trillion. rubles to 2.7 trillion. rubles. The growth in investments in subsidiaries and affiliates is associated with the pre-capitalization of subsidiaries. Reduction of cash balances from the beginning of the year by 0.3 trillion. rubles, or 34.4%, which took place mainly in January, is explained by the seasonal decrease in the demand for cash compared to the period of the New Year holidays. 12

· The basis of the Bank's resource base remains customer funds. Since the beginning of the year, their balance has decreased by 0.7 trillion. rubles, or 3.9%, to 17.0 trillion. rubles. The dynamics of customer funds was affected by the negative revaluation of foreign currency balances.

· The financial result (including other comprehensive income from the revaluation of securities for sale) amounted to 295.1 billion rubles, which is 89.3 billion rubles, or 43.4%, more than the same indicator of the previous year.

Liquidity indicators of Sberbank of Russia are presented in Table 2. commercial Bank deposit

In the first half of 2016, the total assets of Sberbank of Russia decreased by 831 billion rubles and amounted to 21,876 billion rubles in the second quarter (against 22,707 billion rubles at the beginning of the year).

The main factors that determined the dynamics of assets were:

· Decrease in the amount of net loan debt (decrease over the year by 682 billion rubles to the level of 16,188 billion rubles);

· A decrease in the amount of cash by 252 billion rubles due to a decrease in demand for cash on the part of customers;

Revaluation of assets by fair value through profit or loss (for 2015 - by 155 billion rubles),

· An increase in investments in securities and other financial assets available for sale, as well as an increase in investments in subsidiaries and affiliates (by 598 billion rubles in total over six months).

Indicators	Units	Deviations, RUB bln	Rate of change,%

Key figures of the income statement
Net interest income	in billion rubles
Net fee and commission income	in billion rubles
Operating income before provisions	in billion rubles
Operating income	in billion rubles
Allowance for loan impairment	in billion rubles
Operating expenses	in billion rubles
Profit before tax	in billion rubles
Net profit	in billion rubles
Key balance sheet indicators
Loans and advances to customers	in billion rubles
Funds in other banks	in billion rubles
Loan portfolio before provisions for impairment losses	in billion rubles
Loan impairment allowance	in billion rubles
	in billion rubles
Client funds	in billion rubles
Private deposits	in billion rubles
Funds of legal entities	in billion rubles
	in billion rubles
Key quality indicators
Share of non-performing loans in the loan portfolio
Share of provision for loan impairment in the loan portfolio
Ratio of provision for loan impairment to non-performing loans	Meaning
Net interest margin

Ratio of expenses to operating income (before reserves)
Loans / Deposits
Return on assets (ROAA)
Return on Equity (ROAE)
Earnings per share, in rubles per share (EPS)
Earnings per share, recalculated, in RUB per share (adj. EPS)
Share price on MICEX at the end of the period (in rubles)
Actual number of employees
Average number of shares for the period
Capital Adequacy Ratios
Capital Adequacy Ratio (Tier 1)
Total Capital Adequacy Ratio (Tier 1 and Tier 2)

Analysis of technical and economic indicators of PJSC "Sberbank" of Russia. Analysis of financial results and profitability of sberbank of russia pjsc Main economic indicators of sberbank pjsc

Theoretical foundations of banking statistics. Analysis of the structure of the loan portfolio. Determination of the concentration index of financial flows. Calculation of dynamics indicators and trend detection. Study of the dependence of bank assets on the amount of deposits of individuals.

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2.2 Calculation of relative values

2.3 Averages and indices of variation

2.4 Application of the sampling method

2.5 Calculation of dynamics indicators and trend detection

To calculate the absolute and relative indicators of dynamics, we will use the formulas from Table 10.

Table 10 - Formulas for absolute and relative indicators of dynamics

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Financial and economic indicators of PJSC "Sberbank of Russia"