Optimal Investment Decision on Open-end Funds

The study of open-end fund is conducted in this paper in terms of the theory of Random process and the theory of Sequential Decision, which based on the benefit of investors and the cost of transaction (commission occurred in the transaction). In addition the thesis introduces the method of factor of random discounting, by which investors can choose the optimal way of investment, which is calculated in an analogue case.


Introduction
In 2001 Open-end fund was introduced into China.The fund is characterized by refund, less risk and more income.But the problem is that in China the fund is only used in few financial products and manipulated in a similar way .The way of investment is all alike.The introduction of the "Securities Investment Fund Law" and QFII (qualified foreign institutional investors scheme) will undoubtedly promote the function of the orderly market, and enforce regulations and law, which provides a good opportunity for fund development.The new variety of fund will emerge continuously; the type of product design will be more varied.The fund companies such as Xiang Cai Hefeng, China Merchants, Jiashi, Cathay Pacific and a number of fund management companies have designed Umbrella Fund that is also adapted to the demand of the market.This problem has been studied previously (Yao Er-qiang, 1998, pp.455).Umbrella Fund refers to a mother in a number of subfunds established under the Fund.They are of independent management.In the conversion between the funds the cost is lower or zero.Of Umbrella funds in Europe, the United States and Hong Kong, the proportion is as high as 60%.It is expected to reach 70% -80% in China.It can meet the demand of different investors in the investing objective, direction and areas.The products under the same brand can appeal to investors with different preferences, enjoy the advantages of the scale of economy and lower the cost of administration.Also will some new types of open-end fund such as (SR recorded as LOF), index funds, secured capital funds, futures funds and other fund come out.Among them, investors have to be faced with the dilemma of choosing to which one is the most profitable.That makes up one of the subjects worth studying.
First, investors can choose fund in terms of its performance.Because Securities Investment Fund has just been introduced into China, the approach of valuation adopted in the west is not suitable in China.And the valuation organizations in China are not yet recognized as the just authorities and performance of fund is so fluctuated that speculation is wild.This problem has been studied previously (Wu Qi-fang,2003, pp.33).Second, the anticipated profit that fund management company promise is not deducted from the proceeds related to the cost which occurs in liquidity of fund which reported by Liu Hailong (2003, pp.217) and Edelen, R. (1999, pp.439-466).Because investors would purchase and redempt fund, conversion and pay higher transaction costs.All fund management companies are competing for rates and take rates progressive decline, back-end fees, the redemption rate or conversion rate of 0, and other measures Managerial experience from Europe and the United States, high-yield can bring in high costs and high costs come from the investors transaction costs.So from a longterm development, competitive rates will be maintained at a certain level.In addition, China's foreign fund compared with the size of a far cry from, but it is closer to the level of rates, leading fund management companies operating difficulties.Therefore, the choice of investment fund investors must consider transaction costs.
In this paper, we make a research on the medium and small investors, because the transactions rates are relatively fixed for them, and transaction costs directly affect the profit number.In the course of the study, with discounts to the sequential theory-based decision-making process, and in accordance with open-end fund investment existence of two rates are different from the past, the discount factor random formula, the establishment of a model, through calculating, the optimal draw more accurate decision-making.

Sequential basic tenets of the decision-making process
Markov process with the assumption that a state of N, fro m the state i to the statej has shifted to step k ways, each way recorded as 1,2 k ... ... K, the probability of occurrence for the k transfer said fro m the beginning i of the transfer n of maximu m profit, and the following recursive relat ionship between Then (1) can be written as q ground state i with the first k form of a transfer of the average profit (profit expectations).

Now considering the process of transfer of part of the loss, the introduction of rando m d iscount factor
. Fro m (3) losses can be divided into two parts: one part state i with the first k form o f a transfer of the average to state j, Have to pay the cost ratio is the ratio recorded as losses means started from the state i that the transfer of the n +1 times.k i α means fro m the state i of the k form of a transfer to loss ratio of j .k j λ is the N-step transfer of the remaining loss ratio.
, this Markov chain is through the state, that is, when the number ∞ → n transfer probability exists Limit The beginning has nothing to do with the state of i , j π meet equations Now considering all the states through the N -state Markov process.Assuming that the transfer process can be long-term, and considering the process depends on the total expected profit frequency of the transfer system, the total number o f transfers n profit with the increase of constantly changing.Because the process is after all the states, there is a probability i π limit state has nothing to do with the in itial state.Basing (3) where each transfer with a way to use the k, can be removed fro m the right side of great symbolic value k max , Anything dealing with the two sides of the Z-transform from the literature available: , which is the approximation line.i v is the approximation line nodal increment on the axis of bank, at present k i g : fro m state i begins to change n times, and average changing under k kinds of metastasis way every time in mansion earns profit when pretty big.k j q : Be that many times we use k kinds of way to begin to change from state j , the transferred average earns profit every t ime.When thinking that process is chain only when one cycles and every state gets through, so it is having same earn ing profit g after all beginning state changes many times suitable, see R. A.

∑
Be that (10) style is write be accomplished ) 10 ( Can use as the checkout number that every state asks to maximization, n in style (4) and style (9) exchange into n + 1,we get Considering the loss part when the process is changing, introducing random discount factor, (11) style become:

Order passes through the decision process algorithm step
Order birthplace decision process algorithm as follows: Solve a set of equations, Second step: order t=2 Calculate the checkout number Have to optimize decision-making the 2nd time As above recursion until the mansion t step, calculate Solve a set of equations , when ε λ ≤ , stop order birthplace iteration, g is to be that the maximu m earns profit.
Otherwise, order t =t +1, shift to the mansion t step.
In the arbit rarily ε is s mall positive number wh ich is being appointed as to shifting to an earlier date in algorith m, (.) expresses the vector model.Reason is demonstrable N v =0 does not affect the person optimizing result in untying set of equations process middle order.And reason is demonstrable, if tactics B earning profit is slap B g , iteration tactics of time as soon as order b irthplace A earn ing profit is slap A g , then A g ≥ B g , wh ich reported by R. A. Howard in 1963.

Open-end funds investment decision calculates an example
Following ascertains the open-ended fund investment decision considering transaction costs according to iteration method of tactics.

Fundamental hypotheses
(1).Assumes that the investor invests in a single day, redeems or changes a fund, but calls back a fund no forever or.
(2).Assumes that the fund management company wants to long range to continue to manage, and every kind of type fund there exists in long range.

Variables explanation
Since our country fund manages lower open-ended fund of company flag great majority at present, that every fund manages the lower fund of company flag only when are one future may be a various type's affirmatively.Think that the event composing condition's has pure probability in the process of Markov.Consider a series of random experiments, at every time the experiment is only limited or countable be the fundamental event more infinitely i Α (i=1,2,3…) may happen.Say system is in state right away i Α .Th is problem moves downwards in fundamental hypothesis premise, we can manage a company being regarded as state with every fund, buying different type fund under the flag being regarded as metastasis way, the stock fund, bond fund, balance fund wait for instance.Then thinking that every fund manages company's every kind of type fund is investment, some funds which the investor is invested in surely manage some co mpany's kind of type funds.Umbrella shape fund is appearing, feasible fund type enriches especially, choice foundation of investor is more.Change probability being able to do estimat ion fro m h istory data, difference of earning profit being able to win front and back two funds avails according to metastasis process asks for.Random d iscount factor k i α representing to buy the kind o f type k fund the mansion i fund manage co mpany mansion buys rate, k j λ representing surplus n changes every step transferred rate, it can give to out from underneath formula When I ≠ j, m i β representing to redeem the i fund managing the m kind of type fund rate, p j α representing to buy the kind of type p fund from the j fund manage company the buying rate.When i=j, m i β representing redeems rate to be 0; (m ≠ p) p j α representing the changing rate which is buying another type of the same co mpany fund, It can be that 0 also can be not 0; (m=p) p j α = m i β =0, Be that the fund not being in progress changes.

Simulation examples are given below
As shown in table 1   .That is a long-term shift, the first fund management co mpany's first type of fund benefit the most, the second fund management co mpany third types of fund profit-largest.To calculate here is simp le, relatively few data is used only on the first iterat ion concluded.Each iteration is in fact resulting in a corresponding transfer rate, which will eventually co me to the fund of the largest fund company profits to every fund co mpany.Such investors can choose one or more funds according to their personal preferences for investment.

4.4
The problem that should be stated (1).Although we do not directly consider the scale of the fund putting its impact on investment decisions, but to some extent transaction costs has been reflected.Table 1.Open-end fund initial investment decision-making data tables (2).In the process of calculating a fund company which has two or more types of funds is optimal strategy, the choice of different types of funds can be the biggest profit.
(3).In considering fund proceeds at the same time, we have to consider the level of risk (risk large returns, but the risks small receipts small).Because of all the different types of risks associated with the fund which is established, investors can be different risks according to their preference which will combine the optimal decision-making for investment.

Conclusion
In this paper the issue of open-end fund issue of the optimal has been analyzed in terms of Sequential Principle investment decision to analyze, and using random discount factor to describe transaction costs, and giving the different random discounts compare to the past with the Markov process model, which is deriving from the decision-making so that more accurate.This paper provides an investment decision-making method for investors, while provides a basis to investment fund management company to increase capacity and improve management to provides, that is, when the fund management company operate only one type of fund in long-term which has the largest profit.It also should strengthen management for other types of funds in order to improve yield rate.
which remove the redemption rate which is the i fund management co mpany m types funds, which is fro m the purchase of the first j fund management company first p types of funds, after the transaction costs of the actual proceeds. data: