KR20210082878A - Method and system for determining investment weight using copula function - Google Patents

Abstract

The present invention relates to a method and a system for determining an investment ratio using a copula function. The method includes: a step in which investment strategies are selected; a step of collecting investment performance data regarding each of the investment strategies; a step of generating investment strategy cluster hierarchies buildable through hierarchical clustering with respect to the investment strategies; a step of performing copula function parameter and likelihood calculation with respect to each of the investment strategy cluster hierarchies generated using a predetermined copula function; and a step of selecting the investment strategy cluster hierarchy with the highest likelihood out of the generated investment strategy cluster hierarchies. According to the present invention, the investment ratio of each investment strategy can be determined based on the selected investment strategy cluster hierarchy.

Description

Method and system for determining investment weight using copula function

The present invention relates to a method and system for determining an investment weight, and more particularly, to a method and system for determining an investment weight for each investment strategy according to a hierarchical structure of an investment strategy cluster tree type selected using a copula function.

Investment is a set of the following five decisions (① what, ② when ③ how much to buy, and ④ when ⑤ how much to sell). For example, buying and holding a specific stock is an investment strategy and is an investment target.

Investment efficiency is greatly affected by the logic of determining the proportion of investment between investment strategies, that is, the logic of distributing funds.

Among the fund allocation logic between investment strategies, there are the following types of allocation logic. After obtaining time-series data of investment returns for each investment strategy, measuring the linearity between each of the time-series data of investment returns, based on the linearity between the measured returns, the proportion of investment between investment strategies is determined according to a predetermined algorithm.

However, one of the limitations of this conventional method is that the proportion of investment between investment strategies is determined based only on “linearity between investment returns”. Therefore, there was a limit to its application to investment activities carried out over time.

Japanese Laid-Open Patent Publication No. 2008-250975 (published date: October 16, 2008)

The technical problem to be achieved by the present invention is to provide a method and system for determining the investment weight for each investment strategy according to the hierarchical structure of the selected investment strategy cluster tree using a copula function.

The method of determining the proportion of investment using a copula function according to an embodiment of the present invention for solving the above technical problem includes the steps of selecting a plurality of investment strategies, collecting investment performance data of each of the plurality of investment strategies; Generating a plurality of investment strategy cluster hierarchical structures that can be established through hierarchical clustering for the plurality of investment strategies, and for each of the generated plurality of investment strategy cluster hierarchies using a predetermined copula function, Calculating a full function parameter and a likelihood (Likelihood), and selecting an investment strategy cluster hierarchical structure having the highest likelihood from among the generated plurality of investment strategy cluster hierarchical structures.

The method may further include determining an investment weight of each of the plurality of investment strategies based on the selected investment strategy cluster hierarchical structure.

The method includes the steps of merging clusters with a degree of similarity or higher preset in advance using the copular function parameter for the selected investment strategy cluster hierarchical structure, and the plurality of investment strategies based on the investment strategy cluster hierarchical structure in which the clusters are merged. It may further include the step of determining each investment weight.

The investment performance data of each of the plurality of investment strategies may be yield time series data of each of the plurality of investment strategies in a predetermined period.

The return time series data may be a return based on the daily closing price of the predetermined period or a return based on the closing price at the end of each week, month, quarter, or year.

The investment weight of each of the plurality of investment strategies is equal to the investment weight between the lower clusters having the same upper investment strategy cluster in the selected investment strategy cluster hierarchy or the investment strategy cluster hierarchy in which the clusters are merged or the amount of risk is determined. It can be determined in a way that equalizes.

The investment performance data of each of the plurality of investment strategies, the investment performance of the investment for a predetermined period in the plurality of investment strategies according to the investment weight determined based on the selected investment strategy cluster hierarchy structure or the investment strategy cluster hierarchy structure in which the clusters are merged After adding to , it is possible to re-create the selected investment strategy cluster hierarchical structure or an investment strategy cluster hierarchical structure in which the clusters are merged.

It may include a computer-readable recording medium in which a program for executing the method in a computer according to an embodiment of the present invention for solving the above technical problem is recorded.

Investment weight determination system using a copular function according to an embodiment of the present invention for solving the above technical problem is a data collection unit that collects investment performance data of each of a plurality of investment strategies, a layer for the plurality of investment strategies A hierarchical structure generating unit for generating a plurality of investment strategy cluster hierarchical structures that can be established through enemy clustering, and for each of the plurality of investment strategy cluster hierarchical structures created above using a predetermined copula function, copula function parameters and likelihood and a hierarchical structure selection unit for calculating (Likelihood) and selecting an investment strategy cluster hierarchical structure having the highest likelihood among the generated plurality of investment strategy cluster hierarchical structures.

The hierarchical structure selection unit may merge clusters having a similarity level higher than or equal to a preset similarity level using the copular function parameter with respect to the selected investment strategy cluster hierarchical structure.

The system determines the investment proportion of each of the plurality of investment strategies based on the selected investment strategy cluster hierarchical structure, or determines the investment proportion of each of the plurality of investment strategies based on the investment strategy cluster hierarchical structure that merges the clusters It may further include an investment weight determining unit.

According to the present invention, it is possible to more accurately grasp the similarity between investment strategies and the hierarchical structure, and to reclassify into a desired number of clusters. In addition, it is possible to improve investment efficiency by accurately classifying various investment targets in the order of similarity, and has the advantage of improving the return on investment in asset management and enabling precise investment risk management and control.

1 is a block diagram of a system for determining investment weight using a copular function according to an embodiment of the present invention.
FIG. 2 shows a dendrogram, which is a tree-shaped structure, indicating an order in which a plurality of individual entities are sequentially and hierarchically combined through hierarchical clustering.
Figure 3 illustrates an investment strategy hierarchical structure in the form of a cluster-tree according to an embodiment of the present invention.
4 is a flowchart illustrating a method of determining an investment weight using a copular function according to an embodiment of the present invention.

Hereinafter, with reference to the accompanying drawings, embodiments of the present invention will be described in detail so that those of ordinary skill in the art to which the present invention pertains can easily implement them. However, the present invention may be embodied in various different forms and is not limited to the embodiments described herein. And in order to clearly explain the present invention in the drawings, parts irrelevant to the description are omitted, and similar reference numerals are attached to similar parts throughout the specification.

Throughout the specification, when a part "includes" a certain component, it means that other components may be further included, rather than excluding other components, unless otherwise stated.

In addition, the terms “…unit” and “…module” described in the specification mean a unit that processes at least one function or operation, which may be implemented as hardware or software or a combination of hardware and software.

1 is a block diagram of a system for determining investment weight using a copular function according to an embodiment of the present invention.

Referring to FIG. 1 , the investment weight determination system 100 using a copula function according to the present invention includes an investment strategy input unit 110 , a data collection unit 120 , a hierarchical structure generation unit 130 , and a hierarchical structure selection unit ( 140) and an investment weight determining unit 150 may be included.

The investment strategy input unit 110 may receive a plurality of investment strategies selected from the user. Here, the investment strategy may be the simplest investment target stock. In other words, buying and holding the relevant investment target stock itself can be an investment strategy. Here, the investment target stock may be a stock traded on a stock exchange, a fund, etc., or various investment product stocks such as a futures trading stock and an option trading stock.

On the other hand, purchasing and holding a plurality of investment target stocks at a certain weight may also be an investment strategy. For example, buying and holding stock A by 60% and stock B by 40% may be an investment strategy.

Also, when to buy and when to sell an investment target may be an investment strategy. For example, one investment strategy may be to buy and hold stock A, then sell stock A and buy stock B when certain conditions are met.

The data collection unit 120 may collect investment performance data of each of a plurality of investment strategies. Here, the investment performance data for each investment strategy may be time series data consisting of a rate of return obtained according to the corresponding investment strategy for a predetermined period. For example, it may be time series data consisting of a return based on the daily closing price of the relevant stock for a certain period or a return based on the closing price at the end of each week, month, quarter, or year. Of course, in the case of two or more stocks, it may be a time-series data consisting of a return based on the daily closing price reflecting the investment weight or a return based on the closing price at the end of each week, month, quarter, or year. Of course, it may be time-series data consisting of returns determined by other criteria other than the daily closing price or weekly, monthly, quarterly, or yearly closing price.

The data collection unit 120 may collect from a database server (not shown) that is constructing a database for the rate of return of each investment target item.

The hierarchical structure generator 130 may generate a plurality of investment strategy cluster hierarchical structures that can be established through hierarchical clustering for a plurality of investment strategies.

FIG. 2 illustrates a dendrogram, which is a tree-shaped structure, indicating an order in which a plurality of individual entities are sequentially and hierarchically combined through hierarchical clustering. Here, hierarchical clustering assumes each of a plurality of investment strategies as the lowest cluster, and repeats the process of merging clusters by merging two clusters to form one upper cluster (pairwise method) to create one uppermost cluster. can be understood as

The hierarchical structure generation unit 130 may generate all the investment strategy cluster hierarchical structures that can be established for the plurality of investment strategies without considering the degree of similarity or similarity of each of the plurality of investment strategies.

The hierarchical structure selection unit 140 uses a predetermined copula function for each of the plurality of investment strategy cluster hierarchical structures generated by the hierarchical structure generation unit 130 to obtain copula function parameters and likelihood. (Likelihood) can be calculated. In addition, the hierarchical structure selection unit 140 may select an investment strategy cluster hierarchical structure having the highest likelihood among a plurality of investment strategy cluster hierarchical structures.

The copula function was proposed by Skalar as a method for understanding the complex structure between several random variables. When it is difficult to mathematically derive the joint probability distribution of two or more random variables, the copula function estimates the function from pseudo observation obtained from the marginal probability distribution of two random variables. do. That is, the copula function refers to a function that connects a set of univariate distributions to a multivariate distribution, and is defined as a joint distribution function of n uniform distributions from 0 to 1.

The copula function can be expressed as Equation 1 below.

[Equation 1]

where, X = (X ₁ , X ₂ , …, X _n ) is a random vector.

U ₌ (u ₁ , u ₂ , …, u _n ) is a uniformly distributed margin of X defined by _{(F 1} (X ₁ ), F ₂ (X ₂ ), …, F _n (X _{n ))} marginals).

F _i is the cumulative distribution function of the random variable X _{i .}

F _i ^{- 1} is the inverse of F _{i .}

The copular function C(u ₁ , u ₂ , …, u _n ) is a joint cumulative distribution of U defined by Equation 1 above.

)를 가진다.Among the copular functions, the Archimedean copular is as shown in Equation 2 below, and the Archimedean copular function is divided into AMH, Clayton, Frank, Gumbel, Joe, etc. generator (generator,

) has

[Equation 2]

Here, θ is a parameter of the copular function, and is calculated and obtained together when calculating the likelihood according to the copula function.

[Table 1]

The hierarchical structure selection unit 140 may calculate the likelihood of each investment strategy cluster hierarchical structure with respect to the observation data of the investment performance data of each of the plurality of investment strategies using the copular function, and parameters can be obtained.

Meanwhile, the hierarchical structure selection unit 140 may selectively merge clusters having a similarity level higher than or equal to a preset similarity level using a copular function parameter with respect to the investment strategy cluster hierarchical structure previously selected as having the highest likelihood.

The investment proportion determining unit 150 may determine the investment proportion of each of the plurality of investment strategies based on the investment strategy cluster hierarchical structure selected by the hierarchical structure selection unit 140 . In addition, when the clusters selected by the hierarchical structure selection unit 140 are merged, the investment proportion determining unit 150 may determine the investment proportion of each of the plurality of investment strategies based on the investment strategy cluster hierarchical structure in which the investment strategy clusters are merged. .

Figure 3 illustrates an investment strategy hierarchical structure in the form of a cluster-tree according to an embodiment of the present invention.

Assuming that the investment strategy cluster hierarchical structure selected by the hierarchical structure selection unit 140 is shown in FIG. 3 , the investment weighting unit 150 may equally distribute 50% to the cluster ABC and 50% to the cluster DC. And you can go down one tier and allocate 50% to cluster ABC, 25% to cluster AB, and 25% to investment strategy C. And as 50% is distributed to cluster DC, 25% can be distributed to investment strategies D and E, respectively. Finally, as 25% is distributed to cluster AB, 12.5% can be distributed to clusters A and B.

Of course, it is also possible to determine the investment weight for each investment strategy while equally matching the risk for each cluster using the risk parity method. For example, it is possible to determine the proportion of investment in a risk parity method, and calculate investment performance data accordingly. For example, if the proportion of investment strategy A determined by the risk parity method is 20% and the proportion of investment strategy B is 80%, a weight of 0.2 is given to the rate of return of investment strategy A and a weight of 0.8 is given to the rate of return of investment strategy B. It is possible to calculate the return data of the cluster A and B are tied together. The risk parity method, which configures the degree of contribution of each asset's return to the overall risk of the portfolio to be the same, is already well known, so a detailed description will be omitted.

Meanwhile, unlike the one illustrated in FIG. 3 , even when an investment strategy cluster hierarchical structure in which investment strategy clusters are merged is selected, the investment weight can be distributed in the same manner.

4 is a flowchart illustrating a method of determining an investment weight using a copular function according to an embodiment of the present invention.

1 and 4 , first, the investment strategy input unit 110 may receive a plurality of investment strategies selected from the user ( S410 ).

Then, the data collection unit 120 may collect investment performance data of each of the plurality of investment strategies input in step S410 (S420). Here, it may be time series data consisting of a rate of return obtained according to a corresponding investment strategy for a predetermined period. For example, it may be time series data such as a return based on the daily closing price obtained according to the corresponding investment strategy or a return based on the closing price at the end of each week, month, quarter, or year.

Next, the hierarchical structure generating unit 130 may generate a plurality of investment strategy cluster hierarchical structures that can be established through hierarchical clustering for a plurality of investment strategies ( S430 ). In step S430 , the hierarchical structure generating unit 130 may generate all possible investment strategy cluster hierarchical structures for the plurality of investment strategies without considering the degree of similarity or similarity of each of the plurality of investment strategies.

Thereafter, the hierarchical structure selection unit 140 uses a predetermined copula function for each of the plurality of investment strategy cluster hierarchical structures generated by the hierarchical structure generation unit 130 to obtain a copula function parameter and Likelihood may be calculated (S440).

In addition, the hierarchical structure selection unit 140 may select an investment strategy cluster hierarchical structure having the highest likelihood among a plurality of investment strategy cluster hierarchical structures ( S450 ).

In step S450 , the hierarchical structure selection unit 140 may selectively merge clusters having a similarity level higher than or equal to a preset similarity level using a copular function parameter with respect to the investment strategy cluster hierarchical structure previously selected as having the highest likelihood.

Thereafter, the investment proportion determining unit 150 may determine the investment proportion of each of the plurality of investment strategies based on the investment strategy cluster hierarchical structure selected by the hierarchical structure selection unit 140 ( S460 ). As described above, when the clusters selected by the hierarchical structure selection unit 140 are merged in step S460 as described above, the investment proportion determining unit 150 is configured to include a plurality of investment strategies based on the investment strategy cluster hierarchical structure in which the investment strategy clusters are merged. It is also possible to determine the proportion of each investment.

Next, it may be invested in a plurality of investment strategies for a predetermined period according to the investment weight determined in step S460 (S470).

In addition, the data collection unit 120 may update the investment performance data of each of the plurality of investment strategies by adding the data collected on the investment performance in step S470 (S480). And the investment weight determination system 100 may repeat steps (S430) to (S460). Of course, if the plurality of investment strategy cluster hierarchical structures generated in step S430 are used as they are, step S430 may be omitted.

The embodiments described above may be implemented by a hardware component, a software component, and/or a combination of a hardware component and a software component. For example, the apparatus, methods and components described in the embodiments may include, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate (FPGA) array), a programmable logic unit (PLU), a microprocessor, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. The processing device may also access, store, manipulate, process, and generate data in response to execution of the software. For convenience of understanding, although one processing device is sometimes described as being used, one of ordinary skill in the art will recognize that the processing device includes a plurality of processing elements and/or a plurality of types of processing elements. It can be seen that can include For example, the processing device may include a plurality of processors or one processor and one controller. Other processing configurations are also possible, such as parallel processors.

The software may comprise a computer program, code, instructions, or a combination of one or more thereof, which configures a processing device to operate as desired or is independently or collectively processed You can command the device. The software and/or data may be any kind of machine, component, physical device, virtual equipment, computer storage medium or device, to be interpreted by or to provide instructions or data to the processing device. , or may be permanently or temporarily embody in a transmitted signal wave. The software may be distributed over networked computer systems, and stored or executed in a distributed manner. Software and data may be stored in one or more computer-readable recording media.

The method according to the embodiment may be implemented in the form of program instructions that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, etc. alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiment, or may be known and available to those skilled in the art of computer software. Examples of the computer-readable recording medium include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic such as floppy disks. - includes magneto-optical media, and hardware devices specially configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine language codes such as those generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

As described above, although the embodiments have been described with reference to the limited drawings, those skilled in the art may apply various technical modifications and variations based on the above. For example, the described techniques are performed in a different order than the described method, and/or the described components of the system, structure, apparatus, circuit, etc. are combined or combined in a different form than the described method, or other components Or substituted or substituted by equivalents may achieve an appropriate result.

100: investment weight determination system
110: investment strategy input unit
120: data collection unit
130: hierarchical structure generator
140; Hierarchy Selection
150: investment proportion determining unit

Claims (15)

A step of selecting a plurality of investment strategies,
collecting investment performance data of each of the plurality of investment strategies;
generating a plurality of investment strategy cluster hierarchical structures that can be established through hierarchical clustering for the plurality of investment strategies;
For each of the generated plurality of investment strategy cluster hierarchical structures by using a predetermined copula function, calculating a copula function parameter and a likelihood (Likelihood); and
selecting an investment strategy cluster hierarchical structure having the highest likelihood among the generated plurality of investment strategy cluster hierarchical structures
A method of determining the proportion of investment using a copula function including In claim 1,
Determining the investment weight of each of the plurality of investment strategies based on the selected investment strategy cluster hierarchy
A method of determining the proportion of investment using a copula function further comprising a. In claim 1,
For the selected investment strategy cluster hierarchical structure, merging clusters with a degree of similarity or higher preset in advance using the copular function parameter; and
Determining the investment proportion of each of the plurality of investment strategies based on the investment strategy cluster hierarchical structure in which the clusters are merged
A method of determining the proportion of investment using a copula function further comprising a. 4. In claim 2 or 3,
The investment performance data of each of the plurality of investment strategies,
A method of determining an investment weight using a copula function that is return time series data of each of the plurality of investment strategies in a predetermined period. In claim 4,
The yield time series data is,
A method of determining an investment weighting ratio using a copula function consisting of a return based on the daily closing price of the predetermined period or a return based on the closing price at the end of each week, month, quarter, or year. In claim 5,
The investment proportion of each of the plurality of investment strategies is,
In the selected investment strategy cluster hierarchy or in the investment strategy cluster hierarchy in which the clusters are merged, the investment weight between the lower clusters having the same upper investment strategy cluster is equally determined or a copula function determined in a way that equalizes the amount of risk How to determine the proportion of investment using In claim 6,
The investment performance data of each of the plurality of investment strategies, the investment performance of the investment for a predetermined period in the plurality of investment strategies according to the investment weight determined based on the selected investment strategy cluster hierarchy structure or the investment strategy cluster hierarchy structure in which the clusters are merged After adding to , the investment weight determination method using a copula function to regenerate the selected investment strategy cluster hierarchy or the investment strategy cluster hierarchy that merges the clusters. A computer-readable recording medium in which a program for executing any one of the methods of any one of claims 1 to 3 is recorded on a computer. A data collection unit that collects investment performance data for each of a plurality of investment strategies;
A hierarchical structure generating unit for generating a plurality of investment strategy cluster hierarchical structures that can be established through hierarchical clustering for the plurality of investment strategies, and
For each of the generated plurality of investment strategy cluster hierarchical structures by using a predetermined copula function, a copula function parameter and likelihood are calculated, and the highest likelihood among the generated plurality of investment strategy cluster hierarchical structures is calculated. Hierarchical structure selection unit that selects the investment strategy cluster hierarchy
Investment weight determination system using a copula function, including 10. In claim 9,
An investment proportion determining unit that determines an investment proportion of each of the plurality of investment strategies based on the selected investment strategy cluster hierarchical structure
Investment weight determination system using a copula function further comprising a. 10. In claim 9,
The hierarchical structure selection unit, for the selected investment strategy cluster hierarchical structure, merges clusters with a degree of similarity or higher preset preset using the copular function parameter,
An investment weight determination unit that determines an investment weight of each of the plurality of investment strategies based on an investment strategy cluster hierarchical structure in which the clusters are merged
Investment weight determination system using a copula function further comprising a. 12. In claim 10 or 11,
The investment performance data of each of the plurality of investment strategies,
An investment weighting system using a copula function that is return time series data of each of the plurality of investment strategies in a predetermined period. In claim 12,
The yield time series data is,
An investment weighting system using a copula function consisting of a return based on the daily closing price of the predetermined period or a return based on the closing price at the end of each week, month, quarter, or year. In claim 13,
The investment proportion of each of the plurality of investment strategies is,
In the selected investment strategy cluster hierarchy or in the investment strategy cluster hierarchy in which the clusters are merged, the investment weight between the lower clusters having the same upper investment strategy cluster is equally determined or a copula function determined in a way that equalizes the amount of risk Investment weight determination system using 15. In claim 14,
The investment performance data of each of the plurality of investment strategies, the investment performance of the investment for a predetermined period in the plurality of investment strategies according to the investment weight determined based on the selected investment strategy cluster hierarchy structure or the investment strategy cluster hierarchy structure in which the clusters are merged After adding to, the investment weight determination system using a copula function to regenerate the selected investment strategy cluster hierarchy or the investment strategy cluster hierarchy that merges the clusters.

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