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methods and models of assets management of not state pension funds


The purpose of assets management NPF consists in their gain at the expense of investment of these assets in securities and other financial instruments. The management company incurs responsibilities of distribution of means on various asset classes (to the share, bonds and other tools); investment management with allowance for risks of investments; active management of portfolios: tracing and realisation of arbitration possibilities.
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From the point of view of the theory portfelnogo investments begins possible to evaluate, as private management companies dispose of assets NPF, they would like to have what parity of shares of different kinds, bonds and other kinds of securities, and also cash and savings and other assets in the portfolio.
This part of dissertational work is devoted research of models and methods which are required for parity definition between risk and expected level of yield of investments and for management of pension reserves. The basic idea what even in the presence of a number of common rules of formation of a portfolio there is no uniform model of a portfolio or uniform strategy of its formation of a choice which could use UK and NPF
For construction of models of assets management NPF we use a problem named as a problem of optimisation of G.Markovitsa.
Still in the early fifties of the XX-th century the American economist G.Markovits [124, with. 77-91] has mortgaged science bases about the effective investment, named portfelnoj the theory. Results Markovitsa have been developed and added by works in J. Tobina, U.Sharpa of [124] and other researchers.
For the decision of a problem of formation of the personalised investment portfolio for NPF from the point of view portfelnoj it is offered to theory to use a problem a finding of effective set of investment portfolios on G.Markovitsa's model.
Investment in G.Markovitsa's model is understood as an investment of money in various financial instruments, such, as shares, bonds, bank bills. A major principle portfelnoj theories is so-called portfelnyj type of investments when the capital is put simultaneously in different assets and (whenever possible) different branches of economy. So that with the maximum benefit to use mutual price range of these assets with the course of time. G.Markovits has defined a mathematical measure of risk of investments. The concept of investment risk for the whole set of the financial instruments united in a portfolio, acquires new properties. In particular, changing a mutual parity of assets of an investment portfolio and their types begins possible to operate risk of a portfolio. Though G.Markovitsa's classical model bases on the assumptions limiting its use in a classical kind, nevertheless allows to receive quite good results: All investment decisions starting only for one period; brave assets are considered only; assets entering into a portfolio are assumed infinitely by dividends, that is there is a possibility of acquisition of l of sale of financial instruments in any volume; for each financial instrument it is possible to predict expected yield, srednekvadraticheskoe a deviation, and also kovariatsiju yields of any pair the assets entering into a portfolio; srednekvadraticheskoe the deviation of yield of each asset completely characterises risk from its acquisition, that is normal distribution of yields is supposed.
Appeal of investments into separate brave assets or an investment portfolio is defined exclusively by their expected yield and risk size, in shape srednekvadraticheskogo deviations; from any two portfolios characterised by identical risk, but different yields, the investor will prefer that which yield is more. And, on the contrary: From any two portfolios characterised by identical yield, but different risks, the investor will prefer that, which risk menytse (it is supposed, that the investor is not inclined to risk); taxes and operational costs are not considered.
G.Markovitsa's approach begins with the assumption, that the management company at the moment time has a concrete amount of money for investment. This money will be invested on a certain space of time which is called as a holding period. Thus, G.Markovitsa's approach can be considered as the discrete approach at which has begun the period is designated t = 0, and the period end is designated t = 1. During the moment t = 0 management company should accept the purchasing decision of concrete securities which will be in its portfolio till the moment t = 1. As the portfolio represents a set of various securities, this decision is equivalent to a choice of an optimum portfolio from a set of possible portfolios.
Making of the decision during the moment t = 0, the management company should mean, that yield of securities (and thus yield of a portfolio) in a forthcoming holding period is unknown. However the management company can evaluate expected yield of various securities, being based on some assumptions and then to invest means in papers with the greatest expected yield. G.Markovits notices, that it will be in general the unreasonable decision as typical the management company though wishes that yield was high, but simultaneously wants, that yield would be so defined, how much it is possible. It is meant, that by a management company, aspiring simultaneously to maximise expected yield and to minimise uncertainty (i.e. the risk), has two inconsistent one another the purposes which should be balanced at decision-making on purchase during the moment t = 0. Approach Markovitsa to decision-making gives the chance to consider adequately both these purposes.
Indicator which can be used with reference to any investment. He allows to state an estimation of a paper by comparison of its cost received in the end of a holding period, with an acquisition cost. This relative value can be transformed to yield for a holding period if to take away from it unit:
^ _ Cost on the holding period end ^ (21)
Nr Cost on the holding period beginning ’
Where rv-profitableness for a holding period.
At an alternative method of calculation indicators are defined as similar sizes for the separate periods:
-Hell. (2.2)
V V V vo ch to
Where V0 - an acquisition cost,
V? - Cost in the end of the first period,
V2 - Cost in the end of the second period.
Moreover, there is no necessity to increase number of shares from one period to other as the given factor is simply reduced in the parities concerning by the subsequent periods. Each period can be analysed separately, to calculate the corresponding size, and then them to multiply.
As the portfolio represents set of various securities, its yield can be calculated similarly: where W0 - an aggregate exercise price of purchase of all securities entering into a portfolio during the moment t = 0;
- Cumulative market value of these securities during the moment t = 1 and, besides the cumulative money income of possession the given securities since the moment / = 0 till the moment / = 1.
The management company should make of the decision concerning what portfolio to purchase during the moment / = 0. Doing it, the management company does not know, what will be presumable significance of size for the majority of various alternative portfolios as he does not know with what will be level of yield of the majority of these portfolios. Thus, on Markovitsu, the management company should consider the level of yield connected with any of these portfolios, a casual variable. The characteristics, one of them - expected significance, and other - a standard deviation have such variables.
The management company should evaluate expected yield and a standard deviation of each portfolio, and then to choose best of them, being based on a parity of these two parametres. The intuition thus plays a part. Expected yield can be presented as the measure of compensation connected with a concrete portfolio, and a standard deviation - as the measure of the risk connected with the given portfolio. Thus, after each portfolio has been investigated in sense of potential compensation and risk, a management company should choose a portfolio which is for it the most suitable.
Calculation of expected yield of a portfolio includes calculation of expected yield of a portfolio as average expected yields of the securities which are components of a portfolio. Relative market quotations of securities of a portfolio are used as scales. In the form of symbols the general rule of calculation of expected yield of the portfolio consisting from N of securities, looks as follows:
gr = Y, õin = hf + X 2Ã2 +... + X NrN, (2.4)
/ = ³
Where 7ð - expected yield of a portfolio,
X, - a share of original cost of the portfolio, invested in a valuable paper/,
g, - expected yield of a valuable paper/,
N - quantity of securities in a portfolio.
Now we will consider a standard deviation of portfolios. The useful measure of risk should consider to some extent probability of possible bad results and their size. Instead of measuring probabilities of various results, the risk measure should evaluate to some extent degree of a possible deviation of the valid result from the expected. The standard deviation is the measure, allowing it to make, as it is an estimation of a probable deviation of actual yield from expected.
For a portfolio consisting from N of securities, the formula looks as follows:
¦ * and - "p
YLxgt; xj°gt; j
-1=1 J, (2.5)
Where - kovariatsija yields of securities ' and/,
With •
1 - the share of a portfolio invested in a valuable paper 1,
X. •
3 - a share of the portfolio invested in a valuable paper 3.
Kovariatsija - a statistical measure of interaction of two casual variables. That is it is a measure of that, how much two casual variables, such as yields of two securities / and j, depend from each other. Positive significance kovariatsii shows, that yields of these securities tend to be changed in one party, for example the best, than expected, yield of one of securities should, possibly to cause the best, than expected, yield of other valuable paper. Negative kovariatsija shows, that yields tend to compensate one another, for example the best, than expected, yield of one valuable paper is accompanied, as a rule, by the worst, than expected, yield of other valuable paper. Rather small or zero significance kovariatsii shows, that communication between yield of these securities is weak or is absent in general.
If there is an infinite number of possible investment portfolios the management company should consider only a subset of possible portfolios, the explanation of this fact contains in the theorem of effective set.
The management company will choose the optimum portfolio from set of portfolios each of which: Supplies the maximum expected yield for some risk level. Supplies minimum risk for some significance of expected yield.
The set of the portfolios, satisfying to these two conditions, is called as effective set.
We can define a site of effective set. At first we will allocate sets of the portfolios, satisfying to the first condition of the theorem of effective set. If to look at fig. 2.6 it is possible to notice that there is no less brave portfolio, than j's portfolio if to conduct through E a vertical straight line any point of achievable set will not lay more to the left of the given straight line. Thus there is no more brave portfolio, than a portfolio
J if to conduct through N a vertical line any point of achievable set will not lay more to the right of the given straight line.

Fig. 2.6. Achievable and effective set
Thus, set of the portfolios supplying the maximum expected yield at the changed risk level, the part of the top border of the achievable set, possessed between points E and N.Rassmatrivaja the second condition is further, it is possible to notice, that there is no the portfolio supplying the big expected yield, than portfolio S because any of points of achievable set does not lay above the horizontal straight line which is passing through S. Similarly, there is no the portfolio supplying smaller expected yield, than portfolio G because any of points of achievable set does not lay below the horizontal straight line which is passing through G. Thus, set of the portfolios supplying minimum risk at changed level of expected yield, the part of the left border of the achievable set, possessed between points S and G is.
Considering that both conditions should take into consideration at definition of effective set, we will notice, that us satisfies only the portfolios laying on the top and left border of achievable set between points E and S. Accordingly these portfolios make effective set, and the management company will choose from this set of effective portfolios optimum for itself. All other achievable portfolios are inefficient portfolios.
Conclusions to CHAPTER 2
During the carried out research necessity of working out of methodical bases of assets management NPF for Russia is confirmed.
The purpose of assets management NPF consists in their gain at the expense of investment of these assets in securities and other financial instruments. The management company incurs responsibilities of distribution of means on various asset classes (to the share, bonds and other tools); investment management with allowance for risks of investments; active management of portfolios: tracing and realisation of arbitration possibilities.
Sources of formation of pension reserves are specified and it is offered to understand set of pension reserves which can be formed for the account as assets NPF: voluntary pension instalments of physical persons, the size and which periodicity by the law it is not regulated, and it is defined on the basis of the agreement between its participants; voluntary pension instalments of legal bodies, the size and which periodicity by the law it is not regulated, and it is defined also on the basis of the agreement between its participants;
- The accumulated part of the state pension of those persons which have expressed desire to direct the memory part in NPF.
Thus, pension reserves - set of the means being in the property of fund and intended for performance by fund of obligations to participants according to pension agreements, and pension payments - not state pension in the form of the money resources regularly paid to the participant subject to the conditions of the pension agreement. The object of management - assets NPF fixed in this or that pattern of ownership for NPF, and also for PFR regarding the accumulated part of the state pension of those persons which have expressed desire to direct the memory part in NPF is chosen, the primary goal of their efficient control - maintenance and effective development of a property complex fixed for NPF so that not to suppose mixture of the property intended for maintenance of authorised activity of fund, and the property making pension reserves is formulated. Criteria of formation of optimum structure of assets NPF where the basic criterion is maintenance of the guaranteed yield, and also change of degree and (or) forms of sharing of the state in assets management are formulated. The state role sees in stimulation of active sharing of funds, citizens and employers in a voluntary provision of pensions by granting of privileges by it on tax payment and taxes. We consider, that assets management NPF in strategic aspect should be directed on an establishment and change connected with them financial and organizational-legal relations, and in flowing - on increase of productivity of all elements of assets. From the point of view of the theory portfelnogo investments begins possible to evaluate, as private management companies dispose of assets NPF, they would like to have what parity of shares of different kinds, bonds and other kinds of securities, and also cash and savings and other assets in the portfolio.
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A source: GUSEV Polina Aleksandrovna. ASSETS MANAGEMENT of not STATE PENSION FUNDS In Russia. 2006

More on topic methods and models of assets management of not state pension funds:

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