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4THE EFFICIENCY ANALYSIS OF BUSINESS SOLUTIONS IN CONDITIONS OF UNCERTAINTY BY MEANS OF MODELING OF PRICE RISKS ASSESSMENT OF ETA ON THE BASIS OF PROBABILISTIC MODELS AND HEDGING
Abstract
The paper is devoted to development of price risks assessment tools of ETAusing hedging and probabilistic models for efficiency increase of business solutions of the organizations participating in international trade.
Keywords
efficiency, external trade activity, hedging, future contract, exchange asset, Markov process, final probabilities, Kolmogorov system of differential equations,
marked graph of system state
AUTHOR Olga Martyanova
Phd in Economics Oryol State Institute of Economy and Trade Oryol, Russia 1263m@mail.ru
The President of Russia addressed his message to the Federal Assembly on December 03, 2015 (Message of the President to Federal Assembly of 03.12.2015), where he stated strengthening of economic positions as one of strategic reference points for business contrary to complication of a situation around our country. The state is ready to support all types of organizations showing high efficiency to win the world markets.
The difficult geopolitical situation, falling of staple prices, weakening of ruble exchange rate demands organizations to develop own techniques of efficiency assessment, including external trade, because of high risk and uncertainty. The risk arises when the person making the decision (here and below - PMD), knows that the situation can have some possible outcomes as his experience allows to predict degree of probability for each further possible event. Uncertainty takes place in case if PMD has lack of experience or statistical data, has no basis for formation forecasts concerning result of business solution.
We consider that one of the ways for efficiency increase of ETAof organization is hedging, which purpose is achievement of optimum structure of risk. The economic uncertainty of the present situation connected with changes of world economy, positions of the countries in global division of labor formation of new trade blocks gives the chance to organizations participating in external economic activity (here and below - EEA) to solve current problems using tendencies of global development and to enter the future markets as highly liquid trade mechanisms.
The goods, which are the objects of exchange trade, have to possess such properties as uniformity and interchangeability, have accurate standard characteristics (Forexaw.com). Premium class beer meets the requirements of exchange goods therefore there is high probability that it would become trade subject at exchange, having allowed the organization, which is carrying out export-import transactions to work at an organized platform and to have the guarantor of the external trade transactions. The resolution of the government of the Russian Federation of November 1, 2008 N 803 "About the approval of Rules of granting the state guarantees of the Russian Federation in external currency
for rendering the state support of export of an industrial output (goods, works, services)" (in an edition of 02.12.2015) emphasizes the importance of the reliable guarantor for the external trade activities organizations.
The organizations, which are carrying out the ETA(here and below - ETA), are the subject for such factors, as change of exchange rates, goods prices, raw materials, established external suppliers. Therefore financial risks can be classified the following way (Figure 1).
ETA financial risks
Market risks Loan risks System risks Marketability risks
Qualitative and quantitative risks assessment
Sensitivity analysis for each type of market risks Analysis of - supply; - repayment; - ban quality Complex system of risk assessment and its group analysis Analysis of financial obligations for repayment period
Currency risk
Price risk
Percent risk
Risk of price change on goods, raw materials
Risk of early repayment
FIGURE 1. CLASSIFICATION OF ETA FINANCIAL RISKS
The most significant for the ETA organizations are market risks connected with uncertainty of future dynamics of the prices in the markets, leading to change of future cash flows cost. However, business owners do not consider hedging not because this service is rather young, but because of misunderstanding of consequences of arising risks, on the one hand, and validity of hedging cost, on the other hand. Absence of desire to show losses from financial instruments use by economic subjects is explained by the tax authorities attitude towards them.
In our opinion, an important factor at making decision on hedging risks accompanying ETA is the assessment of losses, which the organization can receive at refusal hedging. The optimum structure of risk has to establish a compromise between hedging cost and benefits.
Operations with financial instruments supplement financial strategy of organization. Data from Table 1 confirm it and present information on number of the organizations using hedging for reduction of potential losses. The analysis of data shows that organizations having annual turnover more than 2,5 billion US dollars apply hedging in eight transactions from ten (Hedging).
Thus, the organizations can recommend to use future contracts for optimization of risks from instability of goods prices, raw materials, which are planned to put or ship under the external trade contracts in the future.
TABLE 1. HEDGING IN NON-FINANCIAL ORGANIZATIONS
Indicator Measure unit Revenue, billion US dollars Total
<0,25 0,25-0,5 0,5-1,0 1,0-2,5 2,55,0 > 5,0 %
Germany
Total number 0/ % 9,5 8,7 19,8 19,1 14,3 28,6 100
- apply 0/ % 50,0 54,5 84,0 87,5 94,4 75,0 74,2
- do not apply 0/ % 50,0 45,5 16,0 12,5 5,6 25,0 25,8
The USA
Total number 0/ % 19,3 16,2 22,9 14,2 12,2 15,2 100
- apply 0/ % 18,4 43,8 64,4 57,1 72,9 90,0 57,8
- do not apply 0/ % 81,6 56,2 35,6 42,9 27,1 10,0 42,2
Besides parameters of contract parties define liquidity of exchange goods and the existing threats of execution failure, i.e. risks.
Hedging represents set of the tools allowing the participant to protect the asset from price fluctuations, which can reduce its cost. The seller of exchange goods tries to be protected from prices decrease, and the buyer - from their increase (Hedging). Protecting the organization from daily fluctuations of the market, hedging allows the economic subject to increase efficiency of the external trade strategy.
The following types of price risks are inherent for the external trade operations:
- sale and purchase of goods, raw materials, materials under the external trade contracts;
- possession of financial instruments or obligations of their delivery;
- possession of external currency or obligations on its purchases;
- financial obligations, which cost is connected with market indexes.
In our opinion, the risks taking place at implementation of the ETAnot always should be leveled by means of hedging.
Methods of risk decrease are not favorable to ETA organizations for the following reasons:
- stocks of inventory items cannot be sold or bought quickly at adverse dynamics of
prices;
- sale of stocks of goods, materials, raw materials does not exempt the organization from transfer of a rent to the owner of warehouses, which is the highest now;
- it is difficult to cancel the obligations acquired by the organization at the conclusion of the forward contract at the fixed price at market condition change;
- it is difficult to estimate and analyze credit risks, which attract the forward contracts signed by principals.
Therefore the method of ETA risks decrease has to meet the following requirements:
- easy in use;
- not expensive;
- not to break elasticity of organizational management;
- not to substitute price risk for credit risk.
These criteria are answered by hedging, which is a highly marketable tool providing a flexible way of risk decrease, arising during external trade operations.
Future contracts can be two types - commodity and financial. Premium class beer is commodity futures because it has expression in a natural form, for example, grain, oil-bearing crops, different types of metals and consist of the actual delivery of goods. At pricing of the future contract, we estimate basis, which represents a difference between the spot price of exchange asset and the price of the future contract. The price of exchange asset acts as the spot price by its immediate delivery (Degtyareva, 2015).
Therefore, it is important for organization to define basis for the asset reflecting communication of the future price and level of the spot price of the market, at which it functions (Degtyareva, 2015).
The final price of an exchange asset is target price, i.e. the buyer is ready to pay it, plus or minus basis change. The hedging problem is the authentic forecast of value of basis at the concrete size of the target price, which definition is carried out by means of the CVP analysis.
As pricing practice impacts on formation of the exchange market on concrete goods, the technique of risks optimization has to contain procedure of the profitability analysis. Together with hedging, it would allow to estimate influence of expenses changes, prices of realization, quantity and range of exchange goods of future profit of the business solution.
Let us consider the situation connected with decision-making based on the CVP analysis. The organization makes four types of beer, which is delivered under export contracts. According to the draft budget for 2016 (the extract is presented in table 2), constant production expenses are qualified as the general constant expenses relating on the made production and absorbed at the rate defined on the basis of number of machine-hours. Whereas constant administrative expenses are not interfaced to any concrete product and carried on production at the rate of absorption of overhead costs defined on the basis of quantity of the made production. The business owner asks to calculate the total amount of profit, which would give the offered draft budget and to estimate the following offer: to unite dark and light beer of a premium class in a set and to sell it as a gift set that would lower total variable expenses to 169 US dollars for a set. Thus, separately these types of beer would not be sold. The commercial department plans to sell each of 1170 gift sets for 169 US dollars.
TABLE 2. AN EXTRACT FROM THE DRAFT BUDGET FOR 2016
Parameter Measure unit Light beer Dark beer Nonalcoholic beer Beer of cold intoxication
Demand quarrystone. 1 300,00 390,00 585,00 325,00
Realization price US dollars/bottle 117,00 78,00 91,00 117,00
Variable expenses US dollars/bottle 71,50 26,00 65,00 104,00
Constant expenses
including
production US dollars/bottle 32,50 19,50 19,50 32,50
administrative US dollars/bottle 6,50 6,50 6,50 6,50
The financial department made calculations, which results are presented in table 3.
TABLE 3. TOTAL AMOUNT OF PROFIT ON THE BUDGET PROJECT FOR 2016
Parameter Measure unit Light beer Dark beer Nonalcoholi c beer Beer of cold intoxication Parameter
Revenue US dollar 152 100,00 30 420,00 53 235,00 38 025,00 273 780,00
Variable expenses US dollar 92 950,00 10 140,00 38 025,00 33 800,00 174 915,00
Marginal profit US dollar 59 150,00 20 280,00 15 210,00 4 225,00 98 865,00
Constant expenses
including
production US dollar 42 250,00 7 605,00 11 407,50 10 562,50 71 825,00
administrative US dollar 8 450,00 2 535,00 3 802,50 2 112,50 16 900,00
Profit US dollar 10 140,00
Cumulative rate of return % 36,11
Revenue in profitability point US dollar 245 700,00
The assessment results of the business owner carried out by financial department are presented in table 4.
TABLE 4. TOTAL AMOUNT OF PROFIT UNDER THE ALTERNATIVE BUDGET FOR 2016
Parameter Measure unit Gift set Nonalcoholic beer Beer of cold intoxication Total
Revenue US dollar 197 730,00 53 235,00 38 025,00 288 990,00
Variable expenses US dollar 111 033,00 38 025,00 33 800,00 182 858,00
Marginal profit US dollar 86 697,00 15 210,00 4 225,00 106 132,00
Constant expenses
including
the production US dollar 49 855,00 11 407,50 10 562,50 71 825,00
the administrative US dollar 10 985,00 3 802,50 2 112,50 16 900,00
Profit US dollar 17 407,00
Cumulative rate of return % 36,73
Revenue in a profitability point US dollar 241 591,96
Sale of light and dark beer as a gift set would promote growth of sale, having the small size of variable costs of unit that is the positive moment for the organization. Change in assortment line is followed by change of profit, which growth would make $7267 that is true for over 1170 sets.
The cumulative rate of return would slightly change towards increase for 0,62% that would lead to falling of sales proceeds in a profitability point to $241591.96 from $245700.00. As a result, the price of sale of a gift set can be reduced to $162.79. The analysis of sensitivity of the alternative budget to the price of sale of a gift set is low and makes 3,67%.
Thus, business owner make decision on change of assortment line of goods and prices, as upon purchase of light and dark beer in the form of gift sets the economy of buyers would make $26 concerning purchase of these goods separately. Is this economy essential to 780 buyers, who gave the preference to purchase of light beer, to start buying dark beer?
There is a probability that some buyers would refuse this purchase. Therefore not to lose these buyers, it is necessary for the organization to develop price policy on the medium-term prospect providing such discounts for dark beer, which would pay attention of adherents of light beer.
The operational analysis allows the organization to determine goods price, taking into account its volume necessary to delivery by export contracts. It is one of income
sources, when the economic subject would defray expenses taking into account specifics of the ETAthat gives the chance to estimate price risks and to increase efficiency.
However, uncertainty of the market dictates need of protection against price risk, which can provide hedging consisting in use of the future market for decrease in price risk in the off-exchange market. The future bargain concluded when hedging acts as a temporary replacement for the transaction, which would be made in the future in the offexchange market. Thus, the future position is an opposite assessment net-positions in the off-exchange market and is directed on reduction of its risk that is possible in case of equality of position in the off-exchange and cash markets by quantity of goods and identity of terms. Hedging is possible only in the presence of communication between the prices of the future and off-exchange market. Their correlation is more, the efficiency of hedging is higher (Hedging).
The method based on measurement of VAft-parameter is widely used for risk assessment nowadays. It reflects such size of losses, which would not be exceeded by losses at the set probability for a certain period of time. For definition of VAR, function of distribution of financial portfolio profitability owned by organization has to be set for the analyzed time interval. The method of parameters determination of function of distribution - historical, analytical, method of simulation or combination of these methods - remains behind the organization, taking into account merits and demerits (Hedging). The concrete model is used for VAR assessment, so there would be a model risk at calculations. Therefore, it is necessary to test the applied analysis model for receiving adequate results.
Let us consider a situation on optimization of risk when hedging. The organization, which is carrying out the ETA in conditions of economic uncertainty, faced risk of price change for premium class beer. The organization have been exporting this sort of beer for a year. The financial department chose VAR assessment technique for risk assessment. The future contract is the instrument of hedging. The organization carries out the transactions through the future broker, which services makes 15 euros for a contract. The temporary cost of money is not considered. Let us develop a hedging model for this organization for January, 2016. The planned indicators are presented in table 5.
We would define value assessment of risk (VAR) for the financial portfolio consisting of one export contract, which was not hedged by the organization at the set level of reliability (Hedging):
VAR = 1,96xqxPxa, (1)
where q - premium class beer volume subjected to market risk, P - cash price of one liter of premium class beer,
a - beer price volatility, taken for 25% that corresponds to time interval in one month for which VAR pays off.
TABLE 5. THE PLANNED INDICATORS FOR 2016
Indicator Measure Unit Total
Export volume in a year one million l / year 3,80
Proceeds from export in a one million euros/year 34,2
year
Variable expenses one million euros/year 3,76
Constant expenses one million euros/year 26,33
Goods price volatility % 25
Number of the working days dn. 247
On 11.01.2016 for a financial portfolio, not hedged by the economic subject, at the current price in the cash market in 13.7 Euros/l. and the level of reliability of 95%, the cost assessment of risk would make:
VAR95 = 1,96 x 15384,62 x 13,7 x 0,25 = 103276,95 euro.
It means, within a month with probability of 95% the price of exporter's financial portfolio would not change more than for 103276.95 Euros. Realization volume in 15384.62
I./dn. is exposed to high value of risk in a month. Therefore, it is necessary to be protected from cost risk.
Using tools of the CVP analysis, we would calculate the marginal income, as follows
34,2 — 3,16 = 30,44 million euros.
Then the profitability point would be equal in value terms to:
26,33
34,2 x —) = 29,58 million euros.
The price for one liter of premium class beer, which would allow the organization to come to profitability level, would make
29,58/3,8 = 1,18 euro/1.
In case the organization takes the price of 7,78 euros/l as a basis, it is possible to protect from price risk all volume of exported premium class beer. However, if the price at the exchange is higher, it is expedient to organization to be insured for the sum equivalent to the daily volume of realization in value terms that would make 119692,31 euros. Having accepted as the target price the current price of beer in the cash market of
II.01.2016, equal to 13,7 euros/l., and operating with that the price of the future contract signed for one month makes 14,35 euros/l., the organization counted expedient to hedge only 8341 l. The results of calculations for one liter of beer are presented in table 6.
The financial result from hedging of 10.02.2016 at repayment of the obligation under the future contract by means of its repayment is equal to
/119692,31\ //3800000\ /119692,31\\
(-n35r) x (—0,38) + ({-21-)— H^H) x (1Z56 —131
= —11199,36 euro.
At refusal of the organization of hedging, the financial result of its activity would be the following
/3800000 . „ /3800000 . _ „\ . _ r _ . .
(-x 12,56) — (-x 13,1) = —11538,46 euro.
\ 247 ) \ 247 )
Thus, hedging allowed the organization to reduce loss by 1,6 times or by 36% concerning realization of volume of beer at the target price. However if organization needs big degree of security from price fluctuations, then variation margin needs to be hedged by any of known methods, which are carrying out the ETA that considerably would increase efficiency of hedging.
TABLE 6. HEDGING RESULTS ON THE BASIS OF FUTURE CONTRACT OF ONE LITER OF PREMIUM CLASS BEER
Date of the Off-exchange market Future market Basis
economic operation target price operation future price
fact euro/l. euro/l. euro/l.
Transactio Sale of the future
11.01.2016 ns are not presented 13,7 contract 14,35 (0,65)
10.02.2016 Beer sale 12,56 Closing of position through purchase of the future contract 13,59 (1,03)
Final price 13,32 Profit 0,76
Net - result (0,38)
We consider that hedging of variation margin, i.e. daily profit or loss under open future contracts, is expedient to carry out by method of positions of incomplete hedging,
which mentions secondary positions opposite to initial futures. If primary futures are open for purchase, secondary - for sale. In ideal, the profit on secondary or "tail" positions has to cover loss on initial positions.
The quantity of secondary positions is defined by the following ratio (Hedging)
n = -NxWMx—, (2)
360 v '
where n - number of futures for secondary positions or for "tail";
N - number of future contracts in initial position;
WM -credit rate;
d - period of contract validity.
If the organization exports 8341 l. of premium class beer per day, at sale of future contracts in amount 83 on 100 l. and at a rate of the credit of 23%, the quantity of secondary positions would make on a formula (2)
29
n = -83 x 0,23 x —— = -1,537 « 2 positions.
360
In our opinion, the method of incomplete hedging is very convenient for price risks protection as it can be used by any participant of the future market irrespective to type of the contract and their number. Inconvenience for the person making the decision can cause the necessity of continuous revision of the contracts carried to secondary positions for the purpose of efficiency increase of risk assessment.
The hedging results of variation margin are presented in table 7.
Generalization of the results allows to draw a conclusion that when market prices fall, hedging of a variation margin gives a loss of 152 euros.
The hedging financial of day volume of export beer realization is loss concerning sale of these goods at the target price of 11.01.2016,
3800000
8140,93 x (-0,38) + (——-- 8140,53) x (12,56 - 13,7) - 152 = -11503,36 euro.
The financial result from hedging 10.02.2016 would make
3800000
(8140,93 x 13,32) + (——-- 8140,93) x 12,56 - 152 = 199265,88 euro.
TABLE 7. HEDGING RESULTS OF VARIATION MARGIN 11 .01.201 6
Date of the economic fact Off-exchange market Future market Basis operat ion
operation target price operation future price
euro/l. euro/l.
11.01.2016 Bargains were not negotiated 13,7 Purchase of two future contracts 14,35 (0,65)
10.02.2016 Bargains were not negotiated 12,56 Closing of position through sale of two future contracts 13,59 (1,03)
Financial result:
loss: (0,76) x 2 x 100 = (152) euros
Thus, income gained from 10.02.2016hedging exceeded the sum determined for daily insurance in money equivalent for 79573,57 euros. The financial result is higher than profit (which the organization could get without hedging) on 6035,11 euros.
Along with financial result from hedging, the economic subject received information on future cash flows used for justification of actions directed on efficiency increase of
ETA of the organization and costs optimization of financing export-import transactions. Together with the CVP analysis, hedging would protect the organization and yield desirable result only when the principle of rationality is carried out, i.e. benefits from future contracts have to be more than expenses.
On the established practice, a person, specializing on management of financial portfolios, wants to receive the data on risks only in the form of concrete figures reflecting losses. In our opinion, it is disputable as the risk is connected with uncertainty, which can be considered when forecasting only by means of probabilistic model. For receiving concrete results at risk analysis, it is expedient to use Markov processes (Labsker, 2014).
Let us consider a situation for risks assessment at the external trade market by means of probabilistic modeling. Financial department of the ETA organization, carrying out the analysis of the world market of premium class, revealed the following tendency: export contracts, in which high prices are specified, replace contracts with low prices. The can be few changes of export prices, so it is possible to neglected them. The conditional probabilities reflecting the corresponding condition of the export market of premium class beer are specified in matrix of transitional probabilities Re :
/0,2 0,3 0,5\ Pe = ( 0,4 0,6 0,2 ). (3)
\0,1 0,1 0,8/
Having received this information, the business owner asks financial department to estimate condition of export market of premium class beer in the short term.
The financial department needs to find the final probabilities characterizing uniform Markov process. Final probabilities are probabilities of system conditions in the final stationary mode, at which probabilities of system conditions do not depend neither on time, nor on their initial distribution (Labsker, 2014).
The financial department chose the market, on which the organization carries out export supply of beer in the corresponding segment, as S system. The marked state graph of S system is presented in figure 2.
FIGURE 2. THE MARKED GRAPH OF THE EXPORT MARKET STATE
The system can be in one of three states, proceeding from primary data: s1 - decrease of prices; s2 - prices are invariable; s3 - increase of prices,
The process is qualified as discrete. Thus, time points t1, t2, t3 between states are so small that the system S does not change the state that allows treating the analyzed process as process with discrete time.
The forthcoming condition of S system, into which it would pass, depends only on a present state, but does not depend on last state. Therefore, the process is Markov process.
Labsker (Labsker, 2014) proved that if uniform Markov process with final number of states is regular, there are final probabilities px, ...,pn. All elements of matrix fte are positive, the S system is regular and therefore there are limit pi,p2,p3probabilities of si,s2,s3 conditions.
Work (Labsker, 2014) proved that if there are final probabilities, (p1, ...,pn) final vector can be found by the following equation
(Pl,...,Pn) = (Pi,...,Pn)P, (4)
where P -matrix of transitional probabilities.
Then n = 3 from the equation (4) and using the matrix (3)
/0,2 0,3 0,5\
(Pi,P2,P3) = (Pi,P2,P3)x(0,4 0,6 0,2 ). (5)
\0,1 0,1 0,8/
Having multiplied vector line on matrix in the right part of equality, expression (5) would be the following
(Pi,P2,P3) = (0,2pi + 0,4p2 + 0,1p3; 0,3pi + 0,6P2 + 0,1P3; 0,5pi + 0,2P2 + 0,8P3).
From where
pi = 0,2pi + 0,4p2 + 0,1p3; P2 = 0,3pi + 0,6p2 + 0,1p3; P3 = 0,5pi + 0,2p2 + 0,8p3,
or
0,8pi - 0,4p2 - 0,1p3 = 0; -0,3pi + 0,4p2 - 0,1p3 = 0; -0,5pi - 0,2p2 + 0,2p3 = 0.
Having carried out transformation, we would receive
0,8pi - 0,4p2 - 0,1p3 = 0;
0,52p2 - 0,22p3 = 0; Pi = -0,4p2 + 0,4p3.
From where
0,8pi - 0,4p2 - 0,1p3 = 0; P2 = 0,42p3; (6)
Pi = 0,57p3.
The common solution of t equation (5) depending on any p3 parameter is the vector (0,57p3; 0,42p3; p3) . Having replaced in (6) the first equation with normalizing condition, we would receive the system
Pi + P2 + P3 = 1; P2 = 0,42p3; Pi = 0,57p3,
We would find the final vector of probabilities of S system
(Pi, P2, P3) = (0,29; 0,21; 0,5).
Thus, the forecast of the beer export market for a short-term outlook shows that the price on premium class segment would grow more likely(p3 = 0,5 > pi,p2). Thus, they do not depend on an initial condition of the market.
However, if the business owner demands to provide the detailed forecast, its modeling can be carried out with use of Markov processes. Let information received by financial department at research of the premium class beer export market showed that market price of one liter of beer of the analyzed segment can be in range from 9 euros up to 23 euros. The business owner asks to estimate expediency of the conclusion of contracts on export beer supply at the price of 9 euros for liter.
The financial department considers premium class beer in the volume of one liter as S system and estimates its states, which are characterized by the market price of beer, which is in the following limits: s1 - from 9 to 11 euros; s2 - from 11 to 16 euros; s3 - from 16 to 19 euros; s4 - from 19 to 23 euros.
Market price of one liter of beer of this segment significantly depends only on its current price at present time. The change in price of goods in the market can result from casual influences of the market in any casual time point. Transitions of S system from a state to another are carried out with density of probabilities not changing in time, which values are specified in the matrix (7)
P
(0 3 1 2
4 0 4 1
5 0 0 5
{? 1 1 0
(7)
Proceeding from primary data, discrete uniform Markov process with continuous time takes place in S system. It means the streams of events causing transition of S system from one state to another are simple. The marked state graph is given in figure 3.
FIGURE 3. STATE GRAPH OF THE STUDIED SYSTEM
The analysis of the graph shows that for final number of steps from any state the S system can pass into any other state, i.e. it is ergodic. Work (Labsker, 2014) proved that if number of S system conditions is terminal, the S system is ergodic and all streams of events causing transition of S system from one state in another are simple, there are final probabilities of states (pt), defined as
Pi = lim pi(t), i = l,...,n (8)
t^+m
where pi(t) is probability of conditions of S system in t time point.
To define final probabilities, it is expedient to use the system of the differential equations of Kolmogorov
=-(£]=!.Aij)pi(t)+Y11}=1^ijpj(t), i = 1.....n; t>0. (9)
If in the equation (9) to pass to a limit at t ^ + to, it would be transformed to system of the uniform algebraic linear equations concerning n unknown pui = 1, ...,n, of the following type (Martyanova, 2015)
-(X1j=i^ij)pi + lU^ijPj = 0, i = 1.....n (10)
as the probability of a continuous random variable pt(t) at t ^ + to aspires to pt constant, and the derivative of a constant is equal to zero.
Based on the above, we would create system of the equations
-6pi + 4p2 + 5p3 = 0;
3Pi - 9P2 + P4 = 0; (U)
Pi + 4P2 - 10P3 + P4 = 0; ( )
,2pi + P2 + 5p3 - 9p4 = 0.
Having carried out transformations of the equations system (11), we would receive
-6pi + 4p2 + 5p3 = 0; P4 = -3pi + 9p2; Pi = -4p2 + 10p3 - P4; P2 = -2pi - 5p3 + 9p4
or
-6pi + 4p2 + 5p3 = 0; P4 = 1,45p3; Pi = 3,38p3; P2 = 1,29p3.
Therefore, the common solution of the system (11) depending on any p3 e [0,1] parameter is the vector.
(Pi = 3,38p3; P2 = 1,29p3; P3; P4 = 1,45p3).
Having replaced the first equation with normalizing condition, we would receive the system allowing to find the solution which meets the demanded conditions:
Pi + P2 + P3 + P4 = 0; P4 = 1,45p3; Pi = 3,38p3; P2 = 1,29p3.
From where
Pi = 0,47; P2 = 0,18; P3 = 0,14; p4 = 0,20.
Thus, the forecast of financial department at the market price of premium class beer in is as follows: after sufficient time most likely the price on one liter of premium class beer would be ranging from 9 euros to 11 euros; it does not strongly exceed the profitability point calculated on the basis of the CVP analysis. Therefore, the organization can have export contracts for delivery of premium class beer with the price 9 euros, being exposed to minimum risk level of.
Systematization of the results of the carried-out analysis allows to draw the following conclusions:
1. Implementation of external trade activities is interfaced to operational and financial risks that causes the necessity to search optimum structure of the risk establishing a compromise between the hedging cost and benefits that promotes efficiency increase of ETA.
2. Increase of ETA efficiency at the organization and optimization of expenses on financing can be reached when using hedging in total with probabilistic modeling. It would allow not only to improve reliability and quality of forecasts of future cash flows and to be protected from price fluctuations, but also to reveal sources of short-term financing of business solutions in the sphere of international trade.
3. Hedging would allow the organization not to reconstruct policy of formation of stocks in the conditions of economic instability, to keep elasticity in planning, reasonably to raise borrowed funds for financing of export-import transactions.
4. The risks connected with hedging are estimated on the basis of probabilistic models, in which the uncertainty accompanying ETA in values of the probabilities characterizing information on risk of a financial portfolio in the form of the size of real monetary losses is considered. It promotes stability of external trade activities of the economic subject, minimizes the fluctuations of profit caused by the change in price for goods.
5. Application of Markov processes for ETA risks assessment would allow to avoid the model risk accompanying VAR parameter assessment, determined by the model chosen for its calculation. The assessment of price risks by means of the CVP analysis allows the organization to estimate ETA efficiency.
REFERENCES
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