JP2006350949A - Fund configuration determining device, fund configuration determining method and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a fund configuration determining device, a fund configuration determining method and a computer program for constituting an index fund that can ensure an investment interest not less than the growth of a market index over a long period of time while following the fluctuation locus of the market index. <P>SOLUTION: The fund configuration determining device that specifies the configuration of the index fund capable of following the fluctuation locus of the market index, based on one or more restriction conditions, stores the fluctuation locus of the market index in a storage part, computes a differential value at an optional point of time based on the stored fluctuation locus of the market index, creates a virtual fluctuation locus in which the differential value at the optional point of time is larger than the computed differential value while following the stored fluctuation locus of the market index, and determines the configuration of the index fund following the created virtual fluctuation locus. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a fund configuration determination apparatus, a fund configuration determination method, and a computer program that can configure an index fund that exceeds the expected return on investment by following the fluctuation trajectory of a market index.

  An index fund is a fund whose purpose is to follow the fluctuation trajectory of indexes that represent the market, such as the Nikkei Average Stock Price Index (Nikkei 225) and the TSE First Stock Price Index (TOPIX). By following the fluctuation trajectory of the index that represents the market, it is a fund that can surely earn an investment profit as long as the market rises.

  When configuring an index fund, the complete method or sampling method is used. The complete method is a method of forming a fund by combining all stocks constituting a market index in the same composition ratio as the market index. The full law is highly linked to the market index, and can ensure a certain return on investment if the market is expanding rapidly.

  However, with the full law, the number of stock issues that make up an index fund increases, so management costs such as fees increase. Therefore, the sampling method is a method for reducing the management cost by reducing the number of stocks constituting the index fund. The sampling method can reduce the management cost, but the linkage with the market index is not perfect, and the risk that the expected investment profit cannot be secured depending on the stock stock and the composition ratio to be sampled. Exists.

  For example, Non-Patent Document 1 describes an index fund that can specify stock stocks and constituent ratios to be sampled in order to maintain the linkage with the market index at the same level as the complete method. A knitting method is disclosed. The index fund formation method of Non-Patent Document 1 is an improved surrogate constraints method disclosed in Non-Patent Document 2 as a solution to the multi-dimensional nonlinear knapsack problem (hereinafter referred to as the MNK problem). method (hereinafter referred to as ISC method) is applied to the index fund problem (see Non-Patent Document 3).

In general, a multidimensional nonlinear knapsack problem (MNK problem) in which there are a plurality of constraints and each variable is related in a nonlinear manner can be efficiently solved by using the ISC method. For example, a very large MNK, such as a problem with 3 constraints and 20 substitutions for 1000 variables each, or a problem with 8 constraints and 50 substitutions for 500 variables each. It is possible to obtain an exact solution for the problem. In Non-Patent Document 1, it has been confirmed that when 50 stocks that follow the fluctuation trajectory of the market index are selected from the Nikkei 225 stocks, they follow the fluctuation trajectory of the market index with the same accuracy as the complete method.
Tabata et al., “Minimum Tracking Error and Index Fund”, Finance Research Institute, 1993, No. 16, p. 55-69 Yuji Nakagawa, “An improved surrogate constraints method for separable nonlinear integer programming”, Journal of Operations Research Society of Japan, 2003, 46th Volume, p. 145-163 Kai et al., "Application of improved proxy constraint method to non-separable non-convex programming problems", IEICE Transactions, April 2005.

  However, since the conventional index funds described above only follow the fluctuation trajectory of the market index, it is not possible to expect an excessive return on investment on the assumption that the market is expanding rapidly. It is only possible to secure a solid return on investment. Therefore, there is a problem that it is not possible to expect an investment profit exceeding the growth of the market index.

  Index funds that expect an investment profit exceeding the growth of the market index are also composed of many products, but whether to generate an investment profit exceeding the growth of the market index depends on the ability of the fund manager and is uncertain It was a product with a high sex factor. Therefore, there is a problem that it is practically difficult to construct an index fund that can secure an investment profit exceeding the growth of the market index over a long period of time.

  The present invention has been made in view of such circumstances, and constitutes an index fund capable of ensuring an investment profit exceeding the growth of the market index over a long period of time while following the fluctuation trajectory of the market index. An object of the present invention is to provide a fund configuration determination device, a fund configuration determination method, and a computer program.

  The present invention also provides a fund composition determination apparatus, a fund composition determination method, and a computer that configure an index fund based on past fluctuation trajectories of market indexes so as to suggest an index in which the fluctuation of the current trajectory is higher than the fluctuation trajectory. The purpose is to provide a program.

  A fund composition determination device according to a first aspect of the present invention is a fund composition determination device that determines the structure of an index fund that can follow the fluctuation trajectory of a market index based on one or more constraints, and stores the fluctuation trajectory of the market index. Based on the stored market index fluctuation trajectory, the derivative value calculating means for calculating the differential value at an arbitrary time point, and following the stored market index fluctuation trajectory, A virtual fluctuation trajectory generating means for generating a virtual fluctuation trajectory that has a differential value greater than the calculated differential value, and a configuration determining means for determining the configuration of an index fund that follows the generated virtual fluctuation trajectory. .

  In the fund configuration determining apparatus according to the second invention, in the first invention, the virtual fluctuation trajectory generating means generates a virtual fluctuation trajectory obtained by correcting a past fluctuation trajectory downward at a predetermined rate from the time point. It is characterized by.

  The fund composition determination device according to a third aspect of the present invention is characterized in that, in the first or second aspect, the time point is a latest time point of a stored market index fluctuation trajectory.

  A fund configuration determination method according to a fourth aspect of the present invention is a fund configuration specifying method for determining an index fund configuration that can follow a fluctuation trajectory of a market index based on one or a plurality of constraints using a computer. Store the fluctuation trajectory in the storage unit, calculate the derivative value at an arbitrary time point based on the stored market index fluctuation trajectory, follow the stored market index fluctuation trajectory, and differentiate at an arbitrary time point A virtual fluctuation trajectory having a value larger than the calculated differential value is generated, and a configuration of an index fund that follows the generated virtual fluctuation trajectory is determined.

  A fund configuration specifying method according to a fifth invention is characterized in that, in the fourth invention, a virtual fluctuation trajectory is generated by downwardly correcting a past fluctuation trajectory at a predetermined rate from the time point.

  The fund configuration specifying method according to a sixth aspect of the present invention is characterized in that, in the fourth or fifth aspect, the time point is the latest time point of the stored market index fluctuation trajectory.

  A computer program according to a seventh aspect of the present invention is a computer program that can be executed by a fund configuration determination device that specifies the configuration of an index fund that can follow the fluctuation trajectory of a market index based on one or more constraints. The fund composition determining device includes means for storing a market index fluctuation trajectory in a storage unit, a differential value calculating means for calculating a differential value at an arbitrary time point based on the stored market index fluctuation trajectory, Determines the configuration of the virtual fluctuation trajectory generating means that follows the fluctuation trajectory of a certain market index and generates a virtual fluctuation trajectory that has a differential value that is greater than the calculated differential value, and the index fund that follows the generated virtual fluctuation trajectory. It is made to function as a structure determination means to do.

  The computer program according to an eighth invention is the computer program according to the seventh invention, wherein the pseudo fluctuation trajectory generating means generates a virtual fluctuation trajectory obtained by correcting a past fluctuation trajectory downward at a predetermined rate from the time point. And

  According to a ninth aspect of the present invention, there is provided the computer program according to the seventh or eighth aspect, wherein the time point is a latest time point of a stored market index fluctuation locus.

  In the first invention, the fourth invention, and the seventh invention, the fluctuation trajectory of the market index is stored in the storage unit, and based on the stored fluctuation trajectory of the market index, a differential value at an arbitrary time point is calculated, Following the stored market index fluctuation trajectory, a virtual fluctuation trajectory is generated in which the differential value at an arbitrary time is greater than the calculated differential value. Because fluctuations in the market index are continuous, if the index fund is configured to follow a virtual fluctuation trajectory where the differential value at any point in time is greater than the calculated differential value, it is greater than the expected performance of the market index. Expect to get performance. Therefore, by determining the composition of the index fund that follows the generated virtual fluctuation trajectory in the same way as before, it is possible to obtain performance that is greater than the performance of the market index, and because it follows the market index, It is possible to configure an index fund that can continuously obtain a performance that is greater than the performance of the market index over a long period of time. In order to construct a portfolio (index fund) that accurately follows the generated virtual fluctuation trajectory, the time series gain rate ((stock price at an arbitrary time-stock price at a base time) / stock price at a base time) It will be matched to the virtual fluctuation trajectory.

  In the second invention, the fifth invention, and the eighth invention, a virtual fluctuation trajectory is generated by correcting a past fluctuation trajectory downward at a predetermined rate from an arbitrary time point. As a result, the differential value of the virtual fluctuation trajectory at an arbitrary point in time is larger than the derivative value of the past fluctuation trajectory at an arbitrary point in time, and is expected to obtain a performance that is greater than the expected performance of the market index. It becomes possible to configure an index fund that can continuously obtain performance that is greater than the performance of the market index over a period of time.

  In the third invention, the sixth invention, and the ninth invention, the latest differential value of the stored market index fluctuation trajectory is calculated. Therefore, it is possible to generate a virtual fluctuation trajectory that can obtain a performance that is larger than the expected performance of the market index based on the fluctuation history of the market index to date, and that is larger than the performance of the market index over a long period of time. It becomes possible to configure an index fund that can continuously obtain performance.

  According to the first invention, the fourth invention, and the seventh invention, the structure of the index fund that follows the generated virtual fluctuation trajectory is determined by the same method as before, thereby obtaining performance that is greater than the performance of the market index. Since it follows the market index, it is possible to configure an index fund that can continuously obtain performance that is larger than the performance of the market index over a long period of time.

  According to the second invention, the fifth invention, and the eighth invention, the differential value of the virtual fluctuation trajectory at an arbitrary time becomes larger than the differential value of the past fluctuation trajectory at the arbitrary time, and the expected performance of the market index It is possible to construct an index fund that is expected to obtain a greater performance than the market index over a long period of time.

  According to the third invention, the sixth invention, and the ninth invention, it is possible to generate a virtual fluctuation trajectory that can obtain performance larger than the expected performance of the market index based on the fluctuation history of the market index up to now. Therefore, it is possible to configure an index fund that can continuously obtain a performance larger than the performance of the market index over a long period of time.

  Hereinafter, a fund configuration determining apparatus according to an embodiment of the present invention will be specifically described with reference to the drawings. FIG. 1 is a block diagram showing a configuration of a fund configuration determining apparatus according to an embodiment of the present invention. In FIG. 1, the fund configuration determining apparatus 1 includes at least a CPU (central processing unit) 11, a storage unit (storage unit) 12, a ROM 13, a RAM 14, an input unit 15, an output unit 16, a communication unit 17, and the like described above. It is composed of an internal bus 18 for connecting the wear.

  The CPU 11 is connected to the hardware components as described above of the fund configuration determination apparatus 1 via the internal bus 18, and controls the hardware components described above, and also stores the processing program stored in the storage unit 12 or the ROM 13. For example, various software functions are executed according to a virtual fluctuation locus calculation program, a fund configuration determination program, or the like. The storage unit 12 may be a portable storage medium such as a ROM, DVD, or CD-ROM in addition to a built-in fixed storage device (hard disk). In addition, the storage unit 12 stores a market index fluctuation trajectory storage unit 121 that stores fluctuation trajectories of market indexes such as the Nikkei Average Stock Price Index (Nikkei 225) and the Tokyo Stock Exchange First Section Stock Price Index (TOPIX).

  The RAM 14 includes an SRAM, a flash memory, and the like, and stores an execution program, temporary data generated when the software is executed, and the like. The communication means 17 is connected to an internal bus 18 and acquires a market index fluctuation locus via an external computer by connecting to the network 2 such as the Internet. The input means 15 is a data input medium such as a keyboard and a mouse, and the output means 16 is a display device such as a CRT monitor or LCD.

  The auxiliary storage unit 19 uses a portable storage medium 2 such as a CD or a DVD, and downloads a program, data, or the like to be processed by the CPU 11 to the storage unit 12. It is also possible to write the data processed by the CPU 11 for backup.

  A method for determining the configuration of an index fund using the fund configuration determination apparatus 1 having the above-described configuration will be described. In the present embodiment, the market index is a Nikkei 225 stock price index, and 225 stocks constituting the Nikkei 225 stock price index are a population. The problem to be solved using the ISC method in this embodiment is to select 50 stocks from the population that follow the fluctuation trajectory of the Nikkei Stock Average, and whose expected performance exceeds the Nikkei Stock Price Index. The resource allocation rate to the selected 50 brands and individual brands is obtained.

When the problem described above is formulated, the objective function S can be expressed as (Equation 1). In (Equation 1), the Nikkei average stock index is R ₀ , the number of selected issues is q (= 50), and the rate of return of the portfolio of 50 issues is R. Μ _i represents the average of the brand i, and σ _ij represents the covariance of the brands i and j.

  FIG. 2 is a flowchart showing a processing procedure of the CPU 11 of the fund configuration determining apparatus 1 according to the embodiment of the present invention. The CPU 11 of the fund composition determination device 1 receives, via the input device 15, the arbitrary 50 issues constituting the fund and the individual resource allocation ratios to the selected 50 issues as a provisional solution (step S201). The CPU 11 reads the fluctuation trajectory of the Nikkei Stock Average (hereinafter referred to as Nikkei 225) stored in the market index fluctuation trajectory storage unit 121 (step S202), and the fluctuation trajectory of the Nikkei 225 that goes back for a predetermined period, for example, one year from the present time. Based on the above, a virtual fluctuation trajectory is calculated (step S203).

  Hereinafter, an example of a method for calculating a virtual fluctuation locus will be described. FIG. 3 is a view showing an example of the fluctuation locus of the read Nikkei 225 over the past year. The fluctuation trajectory of Nikkei 225 over the past year is indicated by a triangle. In FIG. 3, assuming that the current time is March 1997 (199703), the Nikkei 225 for each month is plotted with the current performance as 100 until April 1996.

  The CPU 11 calculates a differential value at an arbitrary time. In the example of FIG. 3, the differential value is obtained as the inclination angle between the plotted points. Then, the CPU 11 calculates a virtual fluctuation locus having a differential value larger than each differential value. For example, 99% of the plot value one month ago, 98% of the plot value two months ago, and so on. A virtual fluctuation trajectory having a differential value larger than the differential value can be specified. Note that the method of calculating the virtual fluctuation trajectory is not limited to this, and it is possible to calculate a virtual fluctuation trajectory having a differential value at an arbitrary point in time in Nikkei 225, particularly a differential value larger than the current differential value. Any method is possible. By doing in this way, since the differential value at the present time of the virtual fluctuation locus is larger than the differentiation value based on the Nikkei 225, it always has an upwardly inclined angle with respect to the fluctuation locus of the Nikkei 225.

  In FIG. 3, the virtual fluctuation trajectory is plotted with a circle. As is apparent from FIG. 3, it can be seen that the virtual fluctuation trajectory always has an upwardly inclined angle with respect to the fluctuation trajectory of Nikkei 225.

  The CPU 11 substitutes the received provisional solution into the objective function that follows the calculated virtual fluctuation trajectory, and the provisional value obtained based on the provisional solution, that is, the value of the objective function shown in (Expression 1) based on the selected 50 issues. S1 is calculated (step S204) and stored in the RAM 12.

  The CPU 11 calculates an optimal solution using the ISC method (step S205), and determines whether or not the objective function value S2 into which the calculated optimal solution is substituted is larger than the stored provisional value S1 (step S206). . When the CPU 11 determines that the value S2 of the objective function is equal to or less than the provisional value S1 (step S206: NO), the CPU 11 ends the process. That is, the provisional solution is the optimal solution. When the CPU 11 determines that the objective function value S2 is larger than the provisional value S1 (step S206: YES), the CPU 11 sets the optimum solution and the objective function value S2 as the new provisional solution and provisional value S1 ( In step S207), the data is stored in the RAM 12, and the process returns to step S204 to repeat the above-described processing.

  FIG. 4 is a diagram illustrating the relationship between the objective function value S2 for the optimal solution calculated by the above-described processing and the virtual variation trajectory. Similar to FIG. 3, the fluctuation trajectory of Nikkei 225 in the past year is indicated by Δ and the virtual fluctuation trajectory is indicated by ○. The value S2 of the objective function is indicated by □. As can be seen from FIG. 4, the value S2 of the objective function follows the virtual fluctuation trajectory before the current time of March 1997 (199703).

  FIG. 5 is an illustration of the optimal solution finally determined. As an optimal solution, 50 brands from 225 brands of Nikkei 225 to 50 brands from A company to Po company, and respective distribution rates are determined. The distribution ratio is determined so that the total distribution ratio of the 50 issues is ‘1’.

  FIG. 6 is a diagram showing the fluctuation locus of the objective function value S2 and the actual fluctuation locus of the actual Nikkei 225 after the current March 1997 (199703). As apparent from FIG. 6, the fluctuation locus of the objective function value S2 always exceeds the fluctuation locus of the actual Nikkei 225. In other words, it is nothing but an index fund composed of 50 stocks that can always obtain higher performance than that of Nikkei 225. Therefore, by determining the index fund configuration by the above-described method, it is possible to configure an index fund that can obtain a performance that is greater than the performance of the Nikkei Stock Average (Nikkei 225) over a long period of time.

  In the present embodiment, the index fund configuration determining apparatus 1 has been described with respect to a configuration using one computer having one CPU 11, but is not particularly limited to this, and a plurality of CPUs 11 , 11,... May be used, or a plurality of computers each having a CPU may be connected to each other. The present invention can also be applied to a parallel computer using a plurality of CPUs or a plurality of computers, and can solve an index fund configuration determination problem, which is a kind of discrete optimization problem, at a higher speed.

It is a block diagram which shows the structure of the fund structure determination apparatus which concerns on embodiment of this invention. It is a flowchart which shows the process sequence of CPU of the fund structure determination apparatus which concerns on embodiment of this invention. It is an illustration figure of the fluctuation locus | trajectory of the Nikkei 225 of the past 1 year read. It is a figure which shows the relationship between the value of the objective function with respect to the calculated optimal solution, and a virtual fluctuation locus. It is an illustration figure of an optimal solution. It is a figure which shows the fluctuation locus | trajectory of the value of the objective function and the actual fluctuation | variation locus | trajectory of the actual Nikkei 225 after March, 1997 (199703) which is the present.

Explanation of symbols

1 Fund configuration determination device 2 Storage medium 11 CPU
12 Storage means (storage unit)
13 ROM
14 RAM
15 Input means 16 Output means 17 Communication means

Claims (9)

In a fund configuration determination device that determines the configuration of an index fund that can follow the fluctuation trajectory of a market index based on one or more constraints,
Means for storing the fluctuation trajectory of the market index in the storage unit;
Differential value calculating means for calculating a differential value at an arbitrary point of time based on the stored fluctuation trajectory of the market index;
A virtual fluctuation trajectory generating means for following a fluctuation trajectory of a stored market index and generating a virtual fluctuation trajectory that has a differential value greater than a calculated differential value at an arbitrary time point;
A fund configuration determination apparatus comprising: a configuration determination unit that determines a configuration of an index fund that follows the generated virtual fluctuation trajectory. The virtual variation trajectory generating means is
2. The fund configuration determining apparatus according to claim 1, wherein a virtual fluctuation trajectory is generated by downwardly correcting a past fluctuation trajectory at a predetermined rate from the time point.   3. The fund configuration determining apparatus according to claim 1, wherein the time point is a latest time point of a stored market index fluctuation trajectory. In a fund configuration determination method for determining the configuration of an index fund that can follow a fluctuation trajectory of a market index using a computer based on one or more constraints,
Store the fluctuation track of the market index in the storage unit,
Based on the stored market index fluctuation trajectory, calculate the derivative value at any point in time,
Follow the memorized market index fluctuation trajectory, generate a virtual fluctuation trajectory that is greater than the calculated differential value at any point in time,
A fund configuration determination method, comprising: determining a configuration of an index fund that follows a generated virtual fluctuation trajectory.   5. The fund configuration determination method according to claim 4, wherein a virtual fluctuation trajectory is generated by downwardly correcting a past fluctuation trajectory from the time point at a predetermined rate.   6. The fund configuration determining method according to claim 4, wherein the time point is a latest time point of a stored market index fluctuation trajectory. In a computer program that can be executed by a fund configuration determination device that determines the configuration of an index fund that can follow the fluctuation trajectory of a market index based on one or more constraints,
The fund configuration determination device,
Means for storing the fluctuation trajectory of the market index in the storage unit;
Differential value calculating means for calculating a differential value at an arbitrary time point based on the stored fluctuation trajectory of the market index;
A virtual fluctuation trajectory generating means for following the stored fluctuation trajectory of the market index and generating a virtual fluctuation trajectory that has a differential value greater than the calculated differential value at an arbitrary time point, and an index fund that follows the generated virtual fluctuation trajectory A computer program which functions as a configuration determining means for determining a configuration. The pseudo fluctuation trajectory generating means includes:
8. The computer program according to claim 7, wherein a virtual fluctuation trajectory is generated by downwardly correcting a past fluctuation trajectory from the time point at a predetermined rate.   9. The computer program according to claim 7, wherein the time point is a latest time point of a stored market index fluctuation trajectory.

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