Decision device, decision method, and decision program

Abstract

To realize a decision-making system that can efficiently determine portfolios. [Solution] The decision device includes a learning means that creates a model representing the relationship between the portfolio and the target indicator value and an evaluation representing the quality of the portfolio, based on data including a portfolio representing the composition of multiple stocks and a target indicator value representing a target indicator value, and a decision means that uses the model to determine a portfolio that will improve the evaluation, wherein the evaluation includes error information representing the degree to which the indicator and target indicator value deviate from the portfolio and cost information representing the transaction costs required to rearrange the multiple stocks.

Description

[Technical Field]

[0001] This disclosure relates to a decision device, a decision method, and a decision program. [Background technology]

[0002] A technique for determining a portfolio using a computer is known. An example of a technique for determining a portfolio using a computer is the technique described in Patent Document 1. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2001-98699 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] In the technology described in Patent Document 1, calculations using quadratic programming or Markov chain models are performed to determine the portfolio. However, there is a problem in that, for example, the computational cost becomes enormous when the evaluation formula becomes complex.

[0005] This disclosure has been made in view of the above-mentioned issues, and one exemplary purpose thereof is to provide a technique for efficiently determining portfolios. [Means for solving the problem]

[0006] A decision-making device relating to an exemplary aspect of this disclosure includes a learning means for creating a model that represents the relationship between the portfolio and the target indicator value and an evaluation representing the quality of the portfolio, based on data including a portfolio representing the composition of multiple securities and a target indicator value representing a target indicator value, and a decision means for determining a portfolio that improves the evaluation using the model, wherein the evaluation includes error information representing the degree to which the indicator and target indicator value deviate from the portfolio and cost information representing the transaction costs required to rearrange the multiple securities.

[0007] The method for determining an exemplary aspect of this disclosure includes a learning process that creates a model representing the relationship between the portfolio and the target indicator value and an evaluation representing the quality of the portfolio, based on data including a portfolio representing the composition of multiple securities and a target indicator value representing a target indicator value, and a decision process that uses the model to determine a portfolio that will improve the evaluation, wherein the evaluation includes error information representing the degree to which the indicator and target indicator value deviate from the portfolio and cost information representing the transaction costs required to rearrange the multiple securities.

[0008] A decision program relating to an illustrative aspect of this disclosure causes a computer to perform a learning process that creates a model representing the relationship between the portfolio and the target indicator value and an evaluation representing the quality of the portfolio, based on data including a portfolio representing the composition of multiple securities and a target indicator value representing a desired indicator value; and a decision process that uses the model to determine a portfolio that will improve the evaluation, wherein the evaluation includes error information representing the degree to which the indicator and target indicator value deviate from the portfolio, and cost information representing the transaction costs required to rearrange the multiple securities. [Effects of the Invention]

[0009] One illustrative aspect of this disclosure is that it can provide a technique for efficiently determining portfolios. [Brief explanation of the drawing]

[0010] [Figure 1] This is a block diagram illustrating the configuration of the determination device according to the present disclosure. [Figure 2] This is a flowchart illustrating the flow of the determination method according to the present disclosure. [Figure 3] This is a block diagram illustrating the configuration of the determination device according to the present disclosure. [Figure 4] This is a diagram illustrating an example of portfolio management. [Figure 5] This is a flowchart illustrating the flow of the determination method according to the present disclosure. [Figure 6] This is a block diagram illustrating the configuration of the determination device according to the present disclosure. [Figure 7] This is a diagram for explaining portfolio selection by the determination device according to the present disclosure. [Figure 8] This is a block diagram illustrating the configuration of the determination device according to the present disclosure. [Figure 9] This is a graph illustrating the results of the determination method according to the present disclosure. [Figure 10] This is a graph illustrating the results of the determination method according to the present disclosure. [Figure 11] This is a graph illustrating the results of the determination method according to the present disclosure. [Figure 12] This is a graph illustrating the results of the determination method according to the present disclosure. [Figure 13] This is a block diagram illustrating the configuration of a computer that functions as the determination device according to the present disclosure. [Mode for Carrying Out the Invention]

[0011] The following are examples of embodiments of the present invention. However, the present invention is not limited to the exemplary embodiments shown below, and various modifications are possible within the scope of the claims. For example, embodiments obtained by appropriately combining some or all of the technologies (things or methods) employed in each of the exemplary embodiments shown below may also be included in the scope of the present invention. Furthermore, embodiments obtained by appropriately omitting some of the technologies employed in each of the exemplary embodiments shown below may also be included in the scope of the present invention. In addition, the effects mentioned in each of the exemplary embodiments shown below are examples of effects that can be expected in that exemplary embodiment and do not define the scope of the present invention. That is, embodiments that do not produce the effects mentioned in each of the exemplary embodiments shown below may also be included in the scope of the present invention.

[0012] [First Exemplary Embodiment] A first exemplary embodiment, which is an example of an embodiment of the present invention, will be described in detail with reference to the drawings. This exemplary embodiment is the basic form for each of the exemplary embodiments described later. The scope of application of each technology adopted in this exemplary embodiment is not limited to this exemplary embodiment. That is, each technology adopted in this exemplary embodiment can also be adopted in other exemplary embodiments included in this disclosure, to the extent that no particular technical problems occur. Furthermore, each technology shown in the drawings referenced to explain this exemplary embodiment can also be adopted in other exemplary embodiments included in this disclosure, to the extent that no particular technical problems occur.

[0013] (Configuration of the decision-making device) The configuration of the decision device 1 will be explained with reference to Figure 1. Figure 1 is a block diagram showing the configuration of the decision device 1. As shown in Figure 1, the decision device 1 comprises a learning unit 11 and a decision unit 12.

[0014] The learning unit 11 creates a model that represents the relationship between the portfolio and target indicator values ​​and the evaluation of the portfolio's quality, based on data including a portfolio representing the composition of multiple stocks and target indicator values ​​representing the desired indicator values.

[0015] The decision unit 12 uses the model created by the learning unit 11 to determine a portfolio that will improve the evaluation.

[0016] A "portfolio" refers to the composition of multiple securities. A "security" refers to an individual financial product such as stocks, insurance, or low-liquidity assets. For example, in the case of stocks, it refers to shares issued by a specific company, which are identified by the company name, code, etc. The "composition of multiple securities" refers to the combination of multiple securities included in the portfolio and the number of units of each security.

[0017] "Market value" refers to the value of an index that serves as a benchmark for the market. For example, well-known indices such as TOPIX® and Nikkei 225® may be used, or a proprietary index derived from the average or weighted average of a specific combination of stocks may be used. "Target benchmark value" refers to the benchmark value among the benchmark values ​​that the portfolio's rate of return will track.

[0018] An "assessment of the strengths of a portfolio" is an evaluation of the portfolio from one or more perspectives, and includes at least error information and cost information.

[0019] Error information, also known as tracking error, represents the degree to which a portfolio's performance indicators and target performance indicators deviate from each other. A portfolio's performance indicator is, for example, the portfolio's rate of return. The degree to which a portfolio's performance indicators and target performance indicators deviate is represented, for example, by the difference between the portfolio's rate of return and the target performance indicator's rate of return over a given period. A portfolio is considered "good" if its rate of return closely tracks the target performance indicator's rate of return.

[0020] Cost information represents the transaction costs required to rebalance securities from the current portfolio to construct the (next) portfolio. “Transactions required for rebalancing” means selling existing securities and purchasing securities from the market. “Transaction costs” include fees paid to brokerage firms, etc. A portfolio is rated “better” if the transaction costs for rebalancing securities from the current portfolio are low.

[0021] The learning unit 11 can use data including the current portfolio and target indicator values ​​to calculate error information representing the degree of deviation from the target indicator values, and cost information related to rebalancing from the current portfolio. This allows the learning unit 11 to calculate an evaluation including the error information and cost information, and to create a model representing the relationship between the portfolio, target indicator values, and the evaluation. The decision unit 12 can use this model to determine a portfolio that will improve its evaluation.

[0022] (Effect of the decision-making mechanism) As described above, the decision device 1 employs a configuration that creates a model representing the relationship between the portfolio, target indicator values, and the evaluation of the portfolio, and uses this model to determine the portfolio that will improve its evaluation. Therefore, the decision device 1 has the effect of efficiently determining the portfolio.

[0023] (Decision-making process) The flow of decision method S1 will be explained with reference to Figure 2. Figure 2 is a flowchart showing the flow of decision method S1. As shown in Figure 2, decision method S1 includes a learning process S11 and a decision process S12.

[0024] In the learning process S11, the decision device 1 creates a model that represents the relationship between the portfolio and the target indicator value and the evaluation that represents the quality of the portfolio, based on data including a portfolio representing the composition of multiple stocks and a target indicator value representing the desired indicator value.

[0025] In decision processing S12, the decision device 1 uses the model created by the learning unit 11 to determine a portfolio that will improve its evaluation. This evaluation includes error information and cost information. The error information represents the degree to which the portfolio deviates from the index and target index values. The cost information represents the transaction costs required to rearrange the multiple securities that make up the portfolio.

[0026] (Effect of the decision method) As described above, the determination method S1 employs a structure in which a model is created that represents the relationship between the portfolio and target indicator values ​​and the evaluation of the portfolio, and this model is used to determine the portfolio that will improve its evaluation. Therefore, the determination method S1 has the effect of efficiently determining the portfolio.

[0027] [Second exemplary embodiment] A second exemplary embodiment, which is an example of an embodiment of the present invention, will be described in detail with reference to the drawings. Components having the same function as those described in the above-described exemplary embodiment are denoted by the same reference numerals, and their descriptions are omitted as appropriate. The scope of application of each technology adopted in this exemplary embodiment is not limited to this exemplary embodiment. That is, each technology adopted in this exemplary embodiment can also be adopted in other exemplary embodiments included in this disclosure, to the extent that no particular technical problems arise. Furthermore, each technology shown in the drawings referenced to describe this exemplary embodiment can also be adopted in other exemplary embodiments included in this disclosure, to the extent that no particular technical problems arise.

[0028] (Configuration of the decision-making device) The configuration of the decision device 1A will be explained with reference to Figure 3. Figure 3 is a block diagram showing the configuration of the decision device 1A. In addition to the learning unit 11 and decision unit 12 of the decision device 1, the decision device 1A includes an annealing machine 13 and an output unit 16, and stores data 14 and a learning model 15.

[0029] The annealing machine 13 is an operating unit that performs calculations to find the ground state of the Hamiltonian of the Ising model. The annealing machine 13 is a vector computer with a pseudo-quantum annealing method implemented, or a quantum computer with a quantum annealing method implemented. The annealing machine 13 is not limited to a vector computer or a quantum computer, but may also be a parallel computer, a graphics card, etc.

[0030] Data 14 is data that includes the portfolio and target index values. For example, Data 14 may include information showing the composition of the current portfolio and information showing the target index values. Data 14 may also include information showing the historical value fluctuations of all securities being traded and the historical value fluctuations of all index values.

[0031] The learning model 15 is a machine learning model trained to create a model that represents the relationship between the portfolio and target indicator values ​​and the evaluation of the portfolio's quality. Any machine learning model that can output a model convertible to an Ising model is acceptable, such as a factorization machine, restricted Boltzmann machine, ensemble learner, or linear regression learner.

[0032] The output unit 16 outputs the portfolio determined by the determination unit 12. The output unit 16 may display the portfolio determined by the determination unit 12 on a display unit (not shown), save it to a storage device (not shown), or transmit it to another device via a communication unit (not shown).

[0033] (Uses of decision-making devices) Figure 4 shows an example of portfolio management. In this example, the portfolio may be rebalanced periodically (the composition of the portfolio may be changed). In the example shown in Figure 4, T sThe initial portfolio is determined annually, and rebalancing is performed every year. The rebalancing cycle is not particularly limited, and rebalancing may be performed aperiodically. The decision device 1A is used to determine the next portfolio or its candidates during rebalancing.

[0034] (Explanation of terms) Next, before explaining the operation of the decision device 1A, let's explain some terminology. In the following, error information may be referred to as "tracking error," cost information as "rebalancing cost," and target indicator values ​​as "index."

[0035] First, let's explain tracking error (error information). Tracking error should represent the degree to which a portfolio deviates from its indicators and indices, but it can be calculated as follows, for example.

[0036] In one example, the tracking error can be defined as the standard deviation of the difference between the logarithm of the index's return and the logarithm of the portfolio's return. Such a tracking error can be calculated as follows:

[0037] First, the index return "R" in week t. i,t " is "I t If we let "" be the value of the index at week t, it can be expressed as shown in equation (1) below.

[0038]

number

[0039] Note that "return" represents the logarithm of the rate of return (the ratio of the value in week t to the value in week t-1).

[0040] Also, the portfolio return "R v,t " is "V t", as the value of the portfolio in week t (the sum of the values of each issue included in the portfolio), can be expressed as the following formula (2).

[0041]

Math.

[0042] Here, "V t " can be expressed as the following formula (3).

[0043]

Math.

[0044] "c" is a predetermined constant. "M" is a set of issues to be considered. "m" denotes an issue. "P m(t) " denotes the value of issue m in week t. "P r " denotes a vector indicating the constituent ratio of each issue in the portfolio. The constituent ratio "P of issue m r,m " can be expressed as the following formula (4).

[0045]

Math.

[0046] "a i " denotes the number of units of the issues included in the portfolio. One unit can be, for example, 100. "a i " can be selected from N a types of options. A set A of selectable options is expressed in the following formula (5).

[0047]

Math.

[0048] This practice of allowing users to choose the purchase quantity for each stock from a set of predefined options, rather than freely setting it, is also known as an "encoding constraint."

[0049] "S m,i "The portfolio has stock m a i Units (e.g., 100a) i This is a decision variable (binary variable) that is "1" if it contains the specified value, and "0" otherwise.

[0050] In one example, the function "E(P)" is used to calculate the tracking error of a portfolio. r The tracking error can be expressed as shown in equation (6) below. In equation (6) below, the tracking error is expressed as the standard deviation of the difference between the index and portfolio returns.

[0051]

number

[0052] "T" represents the set of weeks for which value data for each stock exists.

[0053] Next, we will explain rebalancing costs (cost information). Rebalancing costs, which are the costs associated with rebalancing a portfolio, are generally proportional to the trading amounts of the securities being rebalanced. Therefore, rebalancing costs can also be calculated based on trading amounts. In this case, the portfolio will be determined in a way that minimizes trading amounts, which has the effect of discouraging changes from the current portfolio.

[0054] In one example, the function "C(p a )" can be expressed as shown in equation (7) below.

[0055]

number

[0056] "p a This shows the purchase amount vector for the portfolio. The purchase amount of stock m "P a,m This can be expressed by the following formula (8).

[0057]

number

[0058] "q a " indicates the number of units for each security included in the current portfolio. The number of units for security m is "q a,m This indicates "abs()". "abs()" represents the absolute value.

[0059] Next, we will explain how to evaluate the quality of a portfolio. The evaluation can be based on tracking error and rebalancing costs, but in one example, the evaluation can be a weighted sum of tracking error and rebalancing costs.

[0060] Here, the function used to calculate the evaluation is called a black-box function. The black-box function f can be expressed as shown in equation (9) below.

[0061]

number

[0062] α and β are positive constants that represent weights. When determining the initial portfolio, β By setting it to 0, we can disregard the rebalancing cost.

[0063] Demand for index funds is increasing among investors. There is a need to manage index funds in a way that tracks the index while also keeping rebalancing costs down. Tracking error relative to an index indicates the degree to which a portfolio's rate of return deviates from the index's rate of return (a higher tracking error is considered to indicate greater investment risk). When tracking error increases, it can be reduced by rebalancing the portfolio with more appropriate assets. However, larger portfolio rebalancing increases costs (rebalancing costs). Therefore, to solve the conflicting problems of reducing tracking error and controlling rebalancing costs, an evaluation that includes both tracking error (error information) and rebalancing costs (cost information) is used.

[0064] The "cardinality constraint" is a constraint that limits the number of securities that make up a portfolio. The "encoding constraint" and "cardinality constraint" are constraints for adjusting computational costs and should be set appropriately according to the computational power of the annealing machine used.

[0065] (Operation of the decision-making device) Figure 5 is a flowchart showing the flow of the decision method S2 executed by the decision device 1A. As shown in Figure 4, the decision method S2 includes a training data generation process S21, a training process S22, a model creation process S23, an Ising model creation process S24, an annealing process S25, a termination condition determination process S26, an additional training data generation process S27, and a portfolio determination process S28 that improves the evaluation.

[0066] In the training data generation process S21, the learning unit 11 generates the initial training data. For example, the learning unit 11 first generates one or more portfolios x0. The one or more portfolios x0 may be predetermined portfolios or may be generated randomly. Then, the learning unit 11 refers to the data 14 and calculates the evaluation y0 for each portfolio x0 using a black box function f. Then, the learning unit 11 generates pairs (x0, y0) of each portfolio x0 and its evaluation y0 as the initial training data.

[0067] Next, in the learning process S22, the learning unit 11 trains the learning model 15 using the training data. For example, if the learning model 15 is a factorization machine, the model parameters w and v are determined.

[0068] Next, in the model creation process S23, the learning unit 11 uses the learning model 15 to create a model that represents the relationship between the portfolio and target indicator values ​​and the evaluation that indicates the quality of the portfolio. For example, if the learning model 15 is a factorization machine, the learning model 15 outputs a function "y(s)" that approximates the black box function f related to the target indicator values ​​as the model. Note that the function y(s) is used in place of the black box function f in the annealing described later, and is therefore also referred to as the "proxy function" below. The proxy function y(s) can be formulated as shown in equation (10) below.

[0069]

number

[0070] Next, in the Ising model creation process S24, the decision unit 12 creates an Ising model by converting the model created by the learning unit 11 into an Ising model. The decision unit 12 may also reflect constraints such as cardinality constraints and encoding constraints in the Ising model. This allows the constraints to be applied to the annealing machine 13.

[0071] In one example, a cardinality constraint where the number of securities in a portfolio is k can be formulated as shown in equation (11) below.

[0072]

number

[0073] In one example, the number of units to be purchased for each stock is N. aThe encoding constraint that requires selection from a set of options can be formulated as shown in equation (12) below.

[0074]

number

[0075] Next, in the annealing process S25, the decision unit 12 inputs the Ising model to the annealing machine 13, thereby obtaining the solution (portfolio) obtained by the annealing machine 13.

[0076] In the termination condition determination process S26, the determination unit 12 determines whether the solution (portfolio) obtained in the preceding annealing process S25 satisfies predetermined termination conditions. Examples of predetermined termination conditions include, but are not limited to, the following conditions or combinations thereof. • The annealing process has been repeated more than the specified number of times. • The evaluation calculated from the obtained solution (portfolio) is above a predetermined level.

[0077] In the termination condition determination process S26, if it is determined that the termination condition is not met, the additional training data generation process S27 is executed. In the additional training data generation process S27, the learning unit 11 refers to the data 14 and uses the black box function f to calculate the evaluation y' for the solution (portfolio) x' obtained in the preceding annealing process S25. The learning unit 11 then generates pairs of portfolio x' and evaluation y' as additional training data. The process then returns to the learning process S22 and is repeated.

[0078] In the termination condition determination process S26, if it is determined that the termination condition is met, the portfolio determination process S28, which determines the portfolio with an improved evaluation, is executed. In the portfolio determination process S28, the determination unit 12 determines the solution (portfolio) obtained in the preceding annealing process S25 as the portfolio with an improved evaluation.

[0079] The output unit 16 then outputs the portfolio whose evaluation has been determined by the decision unit 12.

[0080] (Effect of the decision-making mechanism) Currently, the development of index portfolio products typically uses the beta index, a parameter that weights the index correlation coefficient with a risk coefficient. However, the beta index does not calculate the correlation between the selected stocks or the overall difference from the target index, so it is a fairly rough approximation. Furthermore, the correlation between the selected stocks is a combinatorial optimization problem, and the overall difference from the index has a nonlinear objective function. Combining these two aspects results in a complex model, making it difficult to create an approximate model in some cases.

[0081] In contrast, in the decision device 1A, the learning unit 11 can efficiently create approximate models through machine learning, even for complex models.

[0082] As described above, the decision device 1A employs a configuration in which a portfolio is determined by inputting an Ising model, which is based on a model representing the relationship between the portfolio and target indicator values ​​and the evaluation that indicates the quality of the portfolio, into the annealing machine. Therefore, the decision device 1A has the effect of efficiently determining portfolios that will improve in evaluation.

[0083] Furthermore, decision device 1A employs a configuration in which a constraint limiting the number of securities constituting the portfolio is applied to the annealing machine. Therefore, decision device 1A offers the advantage of being able to adjust the computational cost.

[0084] Furthermore, in the decision device 1A, the error information is configured to represent the standard deviation of the difference between the logarithm of the rate of return of the target indicator value and the logarithm of the rate of return of the portfolio. Therefore, in addition to the effects of decision device 1, decision device 1A provides the effect of being able to determine the portfolio based on a more appropriate evaluation.

[0085] [Third Exemplary Embodiment] A third exemplary embodiment, which is an example of an embodiment of the present invention, will be described in detail with reference to the drawings. Components having the same function as those described in the above-described exemplary embodiments are denoted by the same reference numerals, and their descriptions are omitted as appropriate. The scope of application of each technology adopted in this exemplary embodiment is not limited to this exemplary embodiment. That is, each technology adopted in this exemplary embodiment can also be adopted in other exemplary embodiments included in this disclosure, to the extent that no particular technical hindrance occurs. Furthermore, each technology shown in the drawings referenced to describe this exemplary embodiment can also be adopted in other exemplary embodiments included in this disclosure, to the extent that no particular technical hindrance occurs.

[0086] (Configuration of the decision-making device) The configuration of the decision device 1B will be explained with reference to Figure 6. Figure 6 is a block diagram showing the configuration of the decision device 1B. The decision device 1B stores reference information 17 and differs from the decision device 1A in that the decision unit 12 includes a change unit 121 and a selection unit 122.

[0087] The variable unit 121 changes the weighting of cost information to error information in the evaluation, causing the learning unit 11 and the decision unit 12 to execute the decision method S2 described above. For example, if the evaluation is obtained by the following equation (9) described above, the variable unit 121 changes the values ​​of α and β, causing the learning unit 11 and the decision unit 12 to execute the decision method S2. As a result, the decision unit 12 can determine multiple portfolios. Each determined portfolio has a different balance of emphasis on either tracking the target indicator value or the cost required for rebalancing. By determining multiple portfolios with the variable unit 121, it is possible to search for multiple optimal solutions (multi-objective optimal solutions) that can achieve both a reduction in rebalancing costs and a reduction in tracking errors.

[0088] The selection unit 122 selects one portfolio from a plurality of portfolios determined by the decision unit 12, based on reference information 17 that shows a predetermined ratio of error information to cost information.

[0089] Figure 7 illustrates the selection process performed by the selection unit 122. In Figure 7, the solid line plots the error information and cost information in the evaluation of multiple portfolios determined by the decision unit 12 (Pareto frontier of the multi-objective optimal solution). The dotted line represents the ratio indicated by the reference information 17. The selection unit 122 selects a portfolio from among the multiple portfolios determined by the decision unit 12 in which the ratio of error information and cost information in the evaluation of each portfolio is close to the ratio indicated by the reference information 17 (a portfolio close to the intersection of the solid and dotted lines in Figure 7). This allows for the selection of an appropriate portfolio.

[0090] Here, the reference information 17 only needs to show a predetermined ratio between error information and cost information, but it is preferable that it shows a ratio calculated based on portfolios created in the past. For example, it may show the average ratio of error information to cost information in the evaluation of one or more past portfolios that performed well in terms of investment returns. Alternatively, the reference information 17 may be a collection of portfolios created in the past, and the selection unit 122 may calculate the average ratio of error information to cost information in the evaluation of one or more past portfolios that performed well in terms of investment returns that are stored in the reference information 17.

[0091] The output unit 16 may output all of the multiple portfolios determined by the decision unit 12, or it may output only the one portfolio selected by the selection unit 122, or it may output all of the multiple portfolios determined by the decision unit 12 and highlight the one portfolio selected by the selection unit 122.

[0092] Note that the determination unit 12 does not necessarily have to include the selection unit 122.

[0093] Furthermore, in the decision device 1B, the decision unit 12 is configured to determine multiple portfolios by changing the weighting of cost information against error information in the evaluation. Therefore, in addition to the effects of the decision device 1A, the decision device 1B provides the effect of determining multiple portfolios and selecting a portfolio according to the purpose.

[0094] Furthermore, in the decision device 1B, the decision unit 12 is configured to select one portfolio from multiple portfolios based on reference information indicating a predetermined ratio of error information to cost information. Therefore, the decision device 1B has the effect of being able to select an appropriate portfolio.

[0095] [Fourth exemplary embodiment] A fourth exemplary embodiment, which is an example of an embodiment of the present invention, will be described in detail with reference to the drawings. Components having the same function as those described in the above-described exemplary embodiments are denoted by the same reference numerals, and their descriptions are omitted as appropriate. The scope of application of each technology adopted in this exemplary embodiment is not limited to this exemplary embodiment. That is, each technology adopted in this exemplary embodiment can also be adopted in other exemplary embodiments included in this disclosure, to the extent that no particular technical hindrance occurs. Furthermore, each technology shown in the drawings referenced to describe this exemplary embodiment can also be adopted in other exemplary embodiments included in this disclosure, to the extent that no particular technical hindrance occurs.

[0096] (Configuration of the decision-making device) The configuration of the decision device 1C will be explained with reference to Figure 8. Figure 8 is a block diagram showing the configuration of the decision device 1C. The decision device 1C differs from the decision device 1A in that the decision unit 12 is equipped with a setting unit 123.

[0097] As described above, the learning unit 11 can efficiently create approximate models using machine learning. Therefore, the following settings are also possible. • Portfolio determination aims for the portfolio's rate of return to be greater than the rate of return of the target indicator. • Portfolio decisions that include specific stocks in a fixed proportion while the portfolio as a whole tracks a target benchmark. The setting unit 123 controls the determination unit 12 to determine a portfolio according to the settings described above.

[0098] In one example, the setting unit 123 may apply a constraint to the annealing machine 13 that the portfolio's rate of return is greater than the rate of return of the target index by a certain threshold. That is, the setting unit 123 may include a constraint that the portfolio's rate of return is greater than the rate of return of the target index by a certain threshold in the constraints reflected when converting the model created by the learning unit 11 into an Ising model. As such a threshold, for example, it could be x% higher than the target index, or y yen (or other currency) higher than the target index.

[0099] Furthermore, the setting unit 123 may apply the constraints to the annealing machine 13 while changing the criteria, determine whether a solution can be obtained from the annealing machine 13, and determine the portfolio corresponding to the criterion that yields the highest possible solution from the annealing machine 13.

[0100] For example, by gradually increasing the criteria and searching for a portfolio that meets those criteria, it is possible to determine a portfolio that maximizes returns while tracking the index.

[0101] In another example, the setting unit 123 may apply a constraint to the annealing machine 13 that certain stocks be included in the portfolio at a fixed percentage.

[0102] [Examples] A portfolio was determined using the decision device according to the embodiment (Example), and its effectiveness was verified. As comparative examples, Comparative Example 1 involved formulating the solution using dynamic external approximation and obtaining the solution, while Comparative Example 2 involved obtaining a model that approximates the black box function using quadratic programming.

[0103] For the validation dataset, we used the Nikkei 225 as the target index value, selected 100 stocks with high contribution from the Nikkei 225 as the target stocks, and prepared data showing weekly price movements for 22 years.

[0104] Using data from the first year, the decision-making system determined the initial portfolio. Only tracking error (error information) was used for evaluation. Rebalancing was performed annually, and the decision-making system determined the portfolio for the following year. Evaluation was performed as the sum of weighted tracking error (error information) and rebalancing costs (cost information), and this process was run multiple times with varying weights.

[0105] The above-mentioned equations (1) to (12) were used in calculating the evaluation and creating the Ising model.

[0106] Cardinality constraints of 10 and 100 were used. Note that a cardinality constraint of 100 is equivalent to no cardinality constraint.

[0107] The weighting coefficient ratios for tracking error (error information) and rebalancing cost (cost information) were 500:1 to 100:5 in the examples, 400:1 to 100:4 in Comparative Example 1, and 100:1 in Comparative Example 2.

[0108] In the Example and Comparative Example 1, the number of units for each stock included in the portfolio could be selected from 0 to 4 units or 0 to 7 units. In Comparative Example 2, the selection was from 0 to 4 units.

[0109] In both the Example and Comparative Example 2, the initial number of training data was 100. In the Example, the training process was repeated 200 times, with 20 additional training data points per iteration. In Comparative Example 2, the training process was repeated 4000 times, with 1 additional training data point per iteration. In both the Example and Comparative Example 2, the total number of training data points was 4000.

[0110] Figure 9 is a graph showing the tracking error and rebalancing cost values ​​when the weight coefficient is changed, with the cardinality constraint set to 10. Figure 10 is a graph showing the tracking error and rebalancing cost values ​​when the weight coefficient is changed, with the cardinality constraint set to 100 (no cardinality constraint).

[0111] As shown in Figures 9 and 10, the embodiment provides a solution that is more faithful to the changes in the weight coefficients compared to Comparative Example 1. Furthermore, the embodiment provides a solution that is even more faithful to the changes in the weight coefficients when there is no cardinality constraint.

[0112] Figure 11 is a graph showing the changes in the number of training data points used for the training process and the evaluation of the obtained solution (portfolio), with a cardinality constraint of 10. Figure 12 is a graph showing the changes in the number of training data points used for the training process and the evaluation of the obtained solution (portfolio), with a cardinality constraint of 100 (no cardinality constraint).

[0113] As shown in Figures 11 and 12, the embodiment shows improved evaluation even at the stage where the amount of training data is small, compared to Comparative Example 2.

[0114] Although the data is not shown, the impact of the choice of unit size for each stock included in the portfolio on accuracy was small.

[0115] As described above, in the embodiment, even when the function for determining the evaluation includes a nonlinear term, as shown in equations (4) to (9) above, a well-balanced solution faithful to the weight coefficients can be obtained, and a good solution can be obtained even when the amount of training data is small.

[0116] [Examples of implementation using software] Some or all of the functions of the decision devices 1, 1A, 1B, and 1C (hereinafter also referred to as "each of the above devices") may be implemented by hardware such as integrated circuits (IC chips) or by software.

[0117] In the latter case, each of the above devices is implemented, for example, by a computer that executes instructions for a program, which is software that realizes each function. An example of such a computer (hereinafter referred to as Computer C) is shown in Figure 13. Figure 13 is a block diagram showing the hardware configuration of Computer C, which functions as each of the above devices.

[0118] Computer C comprises at least one processor C1 and at least one memory C2. Memory C2 stores a program P that causes computer C to operate as each of the above-mentioned devices. In computer C, processor C1 reads program P from memory C2 and executes it, thereby realizing each of the above-mentioned devices.

[0119] For processor C1, for example, a CPU (Central Processing Unit), GPU (Graphic Processing Unit), DSP (Digital Signal Processor), MPU (Micro Processing Unit), FPU (Floating Point Number Processing Unit), PPU (Physics Processing Unit), TPU (Tensor Processing Unit), quantum processor, microcontroller, or a combination thereof can be used. For memory C2, for example, flash memory, HDD (Hard Disk Drive), SSD (Solid State Drive), or a combination thereof can be used.

[0120] Computer C may also be equipped with RAM (Random Access Memory) for loading program P at runtime and for temporarily storing various data. Furthermore, computer C may be equipped with communication interfaces for sending and receiving data with other devices. Additionally, computer C may be equipped with input / output interfaces for connecting input / output devices such as keyboards, mice, displays, and printers.

[0121] Furthermore, program P can be recorded on a non-temporary, tangible recording medium M that is readable by computer C. Such a recording medium M could be, for example, tape, disk, card, semiconductor memory, or programmable logic circuitry. Computer C can acquire program P via such a recording medium M. Program P can also be transmitted via a transmission medium. Such a transmission medium could be, for example, a communication network or broadcast waves. Computer C can also acquire program P via such a transmission medium.

[0122] Furthermore, each of the above functions of each of the above devices may be implemented by a single processor in a single computer, by multiple processors in a single computer working together, or by multiple processors in each of multiple computers working together. In addition, the programs for implementing each of the above functions in each of the above devices may be stored in a single memory in a single computer, distributed and stored in multiple memories in a single computer, or distributed and stored in multiple memories in each of multiple computers.

[0123] [Additional Note 1] This disclosure includes the technologies described in the following appendices. However, the present invention is not limited to the technologies described in the following appendices, and various modifications are possible within the scope of the claims.

[0124] (Note 1) A learning means for creating a model that represents the relationship between the portfolio and the target indicator value and an evaluation of the quality of the portfolio, based on data including a portfolio representing the composition of multiple stocks and a target indicator value representing the desired indicator value. Using the aforementioned model, a decision means for determining the portfolio that will improve the evaluation, Equipped with, The evaluation includes error information representing the degree to which the index and target index values ​​of the portfolio deviate, and cost information representing the transaction costs required to rebalance the multiple securities. decision device.

[0125] (Note 2) The determination means determines the portfolio by inputting the Ising model based on the model into the annealing machine. The decision-making device described in Appendix 1.

[0126] (Note 3) The determination means applies a constraint condition to the annealing machine that the rate of return of the portfolio is greater than or equal to a certain threshold than the rate of return of the target indicator value. The decision-making device described in Appendix 2.

[0127] (Note 4) The determination means applies the constraints to the annealing machine while changing the criteria, and determines the portfolio corresponding to the criterion for which the annealing machine can obtain the largest solution. The decision-making device described in Appendix 3.

[0128] (Note 5) The determination means applies a constraint to the annealing machine that limits the number of securities constituting the portfolio. The decision-making device described in Appendix 2.

[0129] (Note 6) The error information represents the standard deviation of the difference between the logarithm of the rate of return of the target indicator value and the logarithm of the rate of return of the portfolio. The decision-making device described in Appendix 1.

[0130] (Note 7) The determination means determines a plurality of portfolios by changing the weighting of the cost information to the error information in the evaluation. The decision-making device described in Appendix 1.

[0131] (Note 8) The determination means selects one portfolio from the plurality of portfolios based on reference information indicating a predetermined ratio between the error information and the cost information. The decision-making device described in Appendix 7.

[0132] (Note 9) A learning process that creates a model representing the relationship between the portfolio, the target indicator, and an evaluation of the portfolio's quality, based on data including a portfolio representing the composition of multiple stocks and a target indicator value representing the desired indicator value. Using the aforementioned model, a decision process is performed to determine the portfolio that will improve the evaluation. Includes, The evaluation includes error information representing the degree to which the index and target index values ​​of the portfolio deviate, and cost information representing the transaction costs required to rebalance the multiple securities. How to decide.

[0133] (Note 10) On the computer, A learning process that creates a model representing the relationship between the portfolio, the target indicator, and an evaluation of the portfolio's quality, based on data including a portfolio representing the composition of multiple stocks and a target indicator value representing the desired indicator value. Using the aforementioned model, a decision process is performed to determine the portfolio that will improve the evaluation. Make it run, The evaluation includes error information representing the degree to which the index and target index values ​​of the portfolio deviate, and cost information representing the transaction costs required to rebalance the multiple securities. Decision program.

[0134] [Additional Note 2] This disclosure includes the technologies described in the following appendices. However, the present invention is not limited to the technologies described in the following appendices, and various modifications are possible within the scope of the claims.

[0135] (Note 1) It comprises at least one processor, and the at least one processor is A learning process that creates a model representing the relationship between the portfolio, the target indicator, and an evaluation of the portfolio's quality, based on data including a portfolio representing the composition of multiple stocks and a target indicator value representing the desired indicator value. Using the aforementioned model, a decision process is performed to determine the portfolio that will improve the evaluation. Execute, The evaluation includes error information representing the degree to which the index and target index values ​​of the portfolio deviate, and cost information representing the transaction costs required to rebalance the multiple securities. decision device.

[0136] The decision-making device may also include a memory. Furthermore, the memory may store a program that causes at least one processor to execute each of the aforementioned processes.

[0137] (Note 2) In the decision process, the at least one processor determines the portfolio by inputting an Ising model based on the model to an annealing machine. The decision-making device described in Appendix 1.

[0138] (Note 3) In the decision process, the at least one processor applies a constraint to the annealing machine that the rate of return of the portfolio is greater than or equal to a certain threshold than the rate of return of the target indicator value. The decision-making device described in Appendix 2.

[0139] (Note 4) In the decision process, the at least one processor applies the constraints to the annealing machine while changing the criteria, and determines the portfolio corresponding to the criterion for which the annealing machine can obtain the largest solution. The decision-making device described in Appendix 3.

[0140] (Note 5) In the decision process, the at least one processor applies a constraint to the annealing machine that limits the number of securities constituting the portfolio. The decision-making device described in Appendix 2.

[0141] (Note 6) The error information represents the standard deviation of the difference between the logarithm of the rate of return of the target indicator value and the logarithm of the rate of return of the portfolio. The decision-making device described in Appendix 1.

[0142] (Note 7) In the decision process, the at least one processor determines a plurality of portfolios by changing the weighting of the cost information to the error information in the evaluation. The decision-making device described in Appendix 1.

[0143] (Note 8) In the decision process, the at least one processor selects one portfolio from the plurality of portfolios based on reference information indicating a predetermined ratio of the error information and the cost information. The decision-making device described in Appendix 7. [Explanation of Symbols]

[0144] 1,1A,1B,1C...Decision device 11 ···Learning Department 12 ···Decision Section 121 ···Change section 122 ···Selection section 123 ···Settings Section 13. Annealing machine 14 ···Data 15 ···Learning Model 16 ··· Output section 17...Reference information

Claims

1. A learning means for creating a model that represents the relationship between the portfolio and the target indicator value and an evaluation of the quality of the portfolio, based on data including a portfolio representing the composition of multiple stocks and a target indicator value representing the desired indicator value. Using the aforementioned model, a decision means for determining the portfolio that will improve the evaluation, Equipped with, The evaluation includes error information representing the degree to which the index and target index values ​​of the portfolio deviate, and cost information representing the transaction costs required to rebalance the multiple securities. decision device.

2. The determination means determines the portfolio by inputting the Ising model based on the model into the annealing machine. The determination device according to claim 1.

3. The determination means applies a constraint condition to the annealing machine that the rate of return of the portfolio is greater than or equal to a certain threshold than the rate of return of the target indicator value. The determination device according to claim 2.

4. The determination means applies the constraints to the annealing machine while changing the criteria, and determines the portfolio corresponding to the criterion for which the annealing machine can obtain the largest solution. The determination device according to claim 3.

5. The determination means applies a constraint to the annealing machine that limits the number of securities constituting the portfolio. The determination device according to claim 2.

6. The error information represents the standard deviation of the difference between the logarithm of the rate of return of the target indicator value and the logarithm of the rate of return of the portfolio. The determination device according to claim 1.

7. The determination means determines a plurality of portfolios by changing the weighting of the cost information to the error information in the evaluation. The determination device according to claim 1.

8. The determination means selects one portfolio from the plurality of portfolios based on reference information indicating a predetermined ratio between the error information and the cost information. The determination device according to claim 7.

9. A learning process that creates a model representing the relationship between the portfolio, the target indicator, and an evaluation of the portfolio's quality, based on data including a portfolio representing the composition of multiple stocks and a target indicator value representing the desired indicator value. Using the aforementioned model, a decision process is performed to determine the portfolio that will improve the evaluation. Includes, The evaluation includes error information representing the degree to which the index and target index values ​​of the portfolio deviate, and cost information representing the transaction costs required to rebalance the multiple securities. How to decide.

10. On the computer, A learning process that creates a model representing the relationship between the portfolio, the target indicator, and an evaluation of the portfolio's quality, based on data including a portfolio representing the composition of multiple stocks and a target indicator value representing the desired indicator value. Using the aforementioned model, a decision process is performed to determine the portfolio that will improve the evaluation. Make it run, The evaluation includes error information representing the degree to which the index and target index values ​​of the portfolio deviate, and cost information representing the transaction costs required to rebalance the multiple securities. Decision program.

Images