Index tracking method and device based on mixed integer linear programming, and electronic equipment
Through an exponential tracking method based on mixed integer linear programming, the value information of the pre-constructed target index and benchmark index is used to construct an objective function to balance tracking errors and transaction costs, solving the problem of difficult to effectively balance tracking errors and transaction costs in the existing technology, and improving the practicality and accuracy of index tracking.
Patent Information
- Application Number
- CN202510143506.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-10
- Publication Date
- 2025-05-13
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
Existing index tracking strategies are difficult to effectively balance tracking errors and transaction costs, and pay more attention to the synchronization of the overall value of the investment portfolio rather than matching single-term returns, resulting in poor practicality.
Using an exponential tracking method based on mixed integer linear programming, an objective function is constructed to balance tracking errors and transaction costs by pre-constructing target indexes with the same rate of return as the benchmark index but with different levels of possible fluctuations.
With the guarantee of consistent returns, we can balance the value trajectory of the tracking portfolio more flexibly, so that it is not only similar to the benchmark index overall, but also better cope with the impact of transaction costs, thereby improving practicality and tracking accuracy.
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Figure CN119991300A_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates to the field of financial technology, and in particular to an index tracking method, device and electronic device based on mixed integer linear programming. Background Art
[0002] Index tracking is a passive investment strategy that aims to replicate the performance of a specific financial index (such as the S&P 500, Dow Jones Industrial Average, CSI 500, etc.) as accurately as possible by constructing a portfolio of stocks similar to those in the index. Index fund products are widely popular due to their low cost, high transparency and relatively stable risk-return characteristics.
[0003] In the process of managing and operating index tracking products, fund companies face multiple business and technical challenges in achieving high-precision index tracking. The main technical challenges include:
[0004] 1) Transaction Costs: Frequent buying and selling operations will generate fixed and proportional transaction costs, which will erode the fund's assets and reduce the ultimate tracking accuracy;
[0005] 2) Market Frictions: Factors such as bid-ask spreads and market slippage make it difficult to achieve the theoretical effect of fully replicating the index in practice;
[0006] 3) Portfolio Size: When there are many index constituents, replicating the entire index will result in a portfolio that is too large, increasing management complexity and transaction costs;
[0007] 4) Constraints: such as minimum trading unit, position limit, prohibition of short selling, etc., which limit the freedom of the investment portfolio and thus affect the tracking accuracy.
[0008] In response to the above technical challenges, existing technologies usually calculate the optimal index tracking strategy by constructing various mathematical models to achieve high-precision index tracking. Currently, there are two main types of mathematical models used to calculate index tracking strategies, namely return-based models and value-based models.
[0009] However, the index tracking strategies calculated by the above mathematical models either cannot balance tracking errors and transaction costs well, or focus more on the synchronization of the overall value of the investment portfolio rather than matching single-period returns, resulting in poor practicality of existing index tracking strategies. Summary of the invention
[0010] It would be advantageous for the present disclosure to provide a mechanism to mitigate, alleviate or eliminate at least one of the problems discussed above.
[0011] In a first aspect, an index tracking method based on mixed integer linear programming is provided. The method includes: obtaining a value function of a tracking investment portfolio; obtaining a value function of a pre-constructed target index, wherein the value return of the target index in each investment cycle is the same as that of a benchmark index, and the initial value point of the target index is the same as or different from the initial value point of the benchmark index; obtaining tracking error information of the tracking investment portfolio based on the value function of the tracking investment portfolio and the value function of the target index, and obtaining transaction cost information of the tracking investment portfolio based on the value function of the target index and the value information of the benchmark index; determining an objective function of a tracking investment portfolio model based on mixed integer linear programming based on the tracking error information and transaction cost information of the tracking investment portfolio; and obtaining an index tracking result of the tracking investment portfolio based on the objective function.
[0012] In a second aspect, an index tracking device based on mixed integer linear programming is provided. The device includes: a first acquisition unit, used to acquire the value function of the tracking investment portfolio; a second acquisition unit, used to acquire the value function of a pre-constructed target index, the value return of the target index in each investment cycle is the same as that of the benchmark index, and the initial value point of the target index is the same as or different from the initial value point of the benchmark index; a first calculation unit, used to acquire the tracking error information of the tracking investment portfolio based on the value function of the tracking investment portfolio and the value function of the target index, and to acquire the transaction cost information of the tracking investment portfolio based on the value function of the target index and the value information of the benchmark index; an objective function determination unit, used to determine the objective function of the tracking investment portfolio model based on mixed integer linear programming based on the tracking error information and transaction cost information of the tracking investment portfolio; and a second calculation unit, used to acquire the index tracking result of the tracking investment portfolio based on the objective function.
[0013] In a third aspect, an electronic device is provided. The electronic device includes: one or more processors; and one or more memories coupled to the one or more processors and storing instructions thereon, and when the instructions are executed by the one or more processors individually or collectively, the electronic device executes an exponential tracking method based on mixed integer linear programming.
[0014] In a fourth aspect, a non-transitory computer-readable storage medium storing machine-executable instructions is provided. The machine-executable instructions, when executed individually or collectively by one or more processors of a machine, cause the machine to perform an exponential tracking method based on mixed integer linear programming.
[0015] In a fifth aspect, a computer program product is provided comprising machine executable instructions, which, when executed individually or collectively by one or more processors of a machine, cause the machine to perform an exponential tracking method based on mixed integer linear programming.
[0016] Different from the prior art that directly uses the value information of the benchmark index as a reference, the embodiment of the present disclosure pre-constructs a target index that has the same rate of return as the benchmark index but may have a different volatility level, so as to more flexibly balance the tracking investment portfolio while ensuring consistent returns; then, the objective function is constructed using the value information of the tracking investment portfolio, the target index and the benchmark index. Since the objective function introduces the target index, the value trajectory of the tracking investment portfolio is not only similar to the benchmark index as a whole, but can also better cope with the impact of transaction costs, thereby improving practicality and tracking accuracy.
[0017] It should be understood that the invention summary is not intended to identify the key or essential features of the embodiments of the present disclosure, nor is it intended to limit the scope of the present disclosure. Other features of the present disclosure will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS
[0018] The above and other objects, features and advantages of the present disclosure will become more apparent through a more detailed description of some embodiments of the present disclosure in the accompanying drawings, in which:
[0019] Figure 1 A flow chart of an exponential tracking method based on mixed integer linear programming according to some embodiments of the present disclosure is shown;
[0020] Figure 2 A structural block diagram of an exponential tracking device based on mixed integer linear programming according to some embodiments of the present disclosure is shown;
[0021] Figure 3 A simplified block diagram of a device suitable for implementing the exemplary embodiments of the present disclosure is shown. DETAILED DESCRIPTION
[0022] The principle of the present disclosure will now be described with reference to some embodiments. It should be understood that the description of these embodiments is only for illustrative purposes, and helps those skilled in the art to understand and implement the present disclosure, without any limitation to the scope of the present disclosure. The disclosure described herein can be implemented in a manner different from that described below.
[0023] In the following description and claims, unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
[0024] References in this disclosure to "one embodiment," "an embodiment," "an exemplary embodiment," etc. indicate that the described embodiment may include a particular feature, structure, or characteristic, but not every embodiment necessarily includes the particular feature, structure, or characteristic. Moreover, such phrases do not necessarily refer to the same embodiment. In addition, when a particular feature, structure, or characteristic is described in conjunction with an exemplary embodiment, whether or not explicitly described, those skilled in the art will recognize that such feature, structure, or characteristic affects incorporation into other embodiments.
[0025] It should be understood that although the terms "first" and "second" etc. may be used to describe various elements herein, these elements should not be limited by these terms. These terms are only used to distinguish one element from another element. For example, without departing from the scope of the exemplary embodiments, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element. The term "and / or" as used herein includes any and all combinations of one or more of the listed terms.
[0026] The terms used herein are only for describing specific embodiments, rather than for limiting exemplary embodiments. The singular forms "one", "an", and "the" used herein also include plural forms, unless the context clearly indicates otherwise. "A group of elements" or "element set" used herein is intended to include one or more elements. It should also be understood that the terms "include", "comprise", "have", "have", "include" and / or "include", when used herein, specify the presence of the features, elements and / or parts, etc., but do not exclude the presence or addition of one or more other features, elements, parts and / or combinations thereof.
[0027] As mentioned above, the optimal index tracking strategy is currently calculated mainly through return-based models and value-based models. The return-based model mainly optimizes the construction of the tracking portfolio by minimizing the return difference between the tracking portfolio and the benchmark index during the historical period. This type of model usually assumes that the weight of the tracking portfolio remains unchanged in each historical investment cycle, thereby converting the return difference into a convex optimization problem, which is easy to solve. For example, Canakgoz and Beasley proposed in 2009 that through regression analysis, the regression intercept of the tracking portfolio is made zero and the slope is 1, thereby achieving the tracking goal. However, the method proposed by Canakgoz and Beasley mainly controls the tracking error through regression analysis and linear constraints, and the balancing effect on tracking error and transaction costs is general, resulting in poor results in practical applications.
[0028] The value-based model optimizes the tracking portfolio by minimizing the difference in value trajectory between the tracking portfolio and the benchmark index during the historical period. This type of model focuses more on the synchronization of the overall value of the tracking portfolio rather than the matching of single-period returns. For example, Konno and Wijayanayake proposed in 2001 to use the mean absolute deviation (MAD) as a measure of tracking error to minimize the absolute difference between the value trajectory of the tracking portfolio and the benchmark index during the historical period. This method emphasizes the minimization of the historical value trajectory, ignores the returns of a single period, and has poor practicality.
[0029] Based on the above problems, the embodiments of the present disclosure provide an index tracking method, index tracking device, electronic device, non-transient computer-readable storage medium and computer program product based on mixed integer linear programming. Different from the prior art that directly uses the value information of the benchmark index as a reference, the embodiments of the present disclosure pre-construct a target index with the same rate of return as the benchmark index but with a different level of volatility, so as to balance the tracking investment portfolio more flexibly while ensuring consistent returns; then, the target function is constructed using the value information of the tracking investment portfolio, the target index and the benchmark index. Since the target function introduces the target index, the value trajectory of the tracking investment portfolio is not only similar to the benchmark index in general, but also can better cope with the impact of transaction costs, thereby improving practicality and tracking accuracy.
[0030] In order to make the purpose, features and beneficial effects of the technical solution more obvious and easy to understand, the following first introduces the parameter definitions and decision variables related to the embodiments of the present disclosure:
[0031] (I) Parameter definition:
[0032] T is the last investment cycle in the historical period;
[0033] n is the number of constituent stocks in the tracking portfolio;
[0034] J is the set of constituent stocks of the tracking portfolio, J = {1, 2, ..., n};
[0035] q jt is the closing price of component stock j at the end of period t;
[0036] I t is the value of the benchmark index at the end of period t;
[0037] ΔC T is the cash change in period T, deposits are positive and withdrawals are negative;
[0038] Y jT is the number of units of the constituent stock in the tracking portfolio before rebalancing;
[0039] C T-1 The excess cash amount of the previous investment cycle;
[0040] r T is the excess cash rate during the investment period T;
[0041] C T is the total capital of the fund, calculated as
[0042] and is the minimum and maximum investment proportion of constituent stock j when it is included in the investment period T;
[0043] and is the ratio of the minimum and maximum transaction values of constituent stock j in investment period T;
[0044] k is the maximum number of constituent stocks in the tracking portfolio;
[0045] is the fixed transaction cost of component stock j;
[0046] and is the proportional transaction cost of buying and selling constituent stock j.
[0047] (II) Decision variables:
[0048] X jT is the number of units of constituent stock j in the tracking portfolio after rebalancing;
[0049] G jT is the total transaction cost of constituent stock j in investment period T;
[0050] and is the buying and selling value of component stock j in investment period T;
[0051] is a binary variable. If constituent stock j is included in the investment period T, then Otherwise, 0;
[0052] and Binary variables, indicating whether to buy or sell constituent stock j.
[0053] Reference now Figure 1 . Figure 1A flow chart of a mixed integer linear programming based exponential tracking method 100 according to some embodiments of the present disclosure is shown, and the method 100 can be implemented on one device or on distributed devices. It should be understood that the method 100 may include additional steps not shown and / or may omit some of the steps shown, and the scope of the present disclosure is not limited to this point.
[0054] like Figure 1 As shown, the index tracking method 100 based on mixed integer linear programming includes at least the following steps S110 to S150:
[0055] Step S110, obtaining a value function of the tracking investment portfolio.
[0056] In some embodiments, the closing price of the constituent stocks may be jt The number of units of the constituent stock after rebalancing is X jT Calculate the value function of the tracking portfolio, for example according to the formula t∈{1,2,...,T} calculates the value function Q of the tracking portfolio t (x).
[0057] Step S120, obtaining a value function of a pre-constructed target index, wherein the value return of the target index in each investment cycle is the same as that of the benchmark index, and the initial value point of the target index is the same as or different from the initial value point of the benchmark index.
[0058] A benchmark index refers to a specific financial index, such as the S&P 500, Dow Jones Industrial Average, CSI 500 and other financial indices, while a target index is a virtual index constructed based on the benchmark index. The target index and the benchmark index have the same value return rate in the same investment cycle, but may have different volatility levels.
[0059] It is understandable that, in actual applications, those skilled in the art may first execute step S110 and then execute step S120; or first execute step S120 and then execute step S110; or may execute step S110 and step S120 at the same time. This embodiment does not limit the execution order of step S110 and step S120.
[0060] Step S130, obtaining tracking error information of the tracking investment portfolio according to the value function of the tracking investment portfolio and the value function of the target index, and obtaining transaction cost information of the tracking investment portfolio according to the value function of the target index and the value information of the benchmark index.
[0061] Since the target index has the same value return as the benchmark index in each investment cycle, but the initial value points of the target index and the benchmark index may be different, using the target index to calculate the tracking error information and transaction cost information of the tracking portfolio can more flexibly balance or adjust the tracking portfolio while ensuring consistent returns, so that the value trajectory of the tracking portfolio after rebalancing is similar to the value trajectory of the benchmark index as a whole, and at the same time can better cope with the impact of transaction costs, thereby more effectively balancing tracking error and transaction costs.
[0062] Step S140, determining an objective function of a tracking investment portfolio model based on mixed integer linear programming according to the tracking error information and transaction cost information of the tracking investment portfolio.
[0063] The tracking portfolio model is a mathematical model based on mixed integer linear programming (MILP), which is applicable to different investment scenarios of self-financing and external financing. The tracking portfolio model of this embodiment aims to optimize the construction and rebalancing of the tracking portfolio, especially to balance the tracking error and transaction costs through the target index.
[0064] Step S150, obtaining the index tracking result of the tracking investment portfolio according to the objective function.
[0065] like Figure 1 It can be seen from the index tracking method based on mixed integer linear programming that, unlike the prior art which directly uses the value information of the benchmark index as a reference, the disclosed embodiment pre-constructs a target index that has the same rate of return as the benchmark index but may have a different volatility level, so as to more flexibly balance the tracking investment portfolio while ensuring consistent returns; then, the objective function is constructed using the value information of the tracking investment portfolio, the target index and the benchmark index. Since the objective function introduces the target index, the value trajectory of the tracking investment portfolio is not only similar to the benchmark index as a whole, but can also better cope with the impact of transaction costs, thereby improving practicality and tracking accuracy.
[0066] In some embodiments, the step S120 of obtaining the pre-constructed value function of the target index includes:
[0067] Get the value function Q of the last investment cycle of the tracking portfolio during the historical period T (x) the value of the benchmark index in each investment cycle I t and a preset adjustment coefficient α;
[0068] According to the value function Q of the last investment cycle of the tracking portfolio during the historical period T(x) the value of the benchmark index in each investment cycle I t and a preset adjustment coefficient α, to obtain the value function of the target index in each investment cycle.
[0069] Specifically, according to the value function Q of the last investment cycle of the tracking portfolio during the historical period T (x) and the value of the benchmark index at each investment period I t The product value Q T (x)*I t The value of the benchmark index during the last investment period in the historical period I T Ratio Obtain the initial value function of the target index in each investment cycle; adjust the initial value function of the target index in each investment cycle according to the adjustment coefficient α to obtain the value function of the target index in each investment cycle
[0070] That is to say, according to the formula Get the value function of the target index in each investment cycle, then the value function of the target index in the historical period is
[0071] In some embodiments, obtaining the tracking error information of the tracking investment portfolio according to the value function of the tracking investment portfolio and the value function of the target index in the above step S130 includes:
[0072] Get the value function Q of the tracking portfolio for each investment cycle during the historical period t (x), and the value function of the target index at each investment cycle during the historical period
[0073] Obtain the difference between the tracking investment portfolio and the value function of the target index in each investment cycle
[0074] According to the difference and Get the tracking error information for the tracking portfolio.
[0075] In some other embodiments, the step S130 of obtaining the transaction cost information of the tracking investment portfolio according to the value function of the target index and the value information of the benchmark index includes:
[0076] Get the value function of the target index in each investment cycle during the historical period and the value information of the benchmark index in each investment cycle during the historical period It ;
[0077] Obtain the difference between the value function of the target index and the benchmark index in the same investment period
[0078]
[0079] According to the difference and Transaction cost information for the tracking portfolio is obtained.
[0080] After the tracking error information and transaction cost information of the tracking investment portfolio are obtained through the above embodiment, the objective function of the tracking investment portfolio model is determined according to the tracking error information and transaction cost information of the tracking investment portfolio in the above step S140, including:
[0081] According to the combined information of the tracking error information of the tracking investment portfolio and the transaction cost information, the objective function of the tracking investment portfolio model is obtained, that is, the objective function is:
[0082] In some embodiments, Figure 1 The method 100 further includes obtaining constraints of the tracking portfolio model, wherein the constraints include at least one of the following:
[0083] A capital constraint is used to constrain the value of the tracking portfolio after rebalancing and transaction costs to not exceed the total capital of the fund;
[0084] Transaction value constraints, which are used to constrain the relationship between the buy value and sell value of the constituent stocks of the tracking portfolio and the number of units in the tracking portfolio;
[0085] Trading behavior constraints are used to constrain the constituent stocks of the tracking investment portfolio to only be bought or sold in one investment cycle, but not both at the same time;
[0086] Transaction cost constraints, used to constrain the transaction costs of the constituent stocks of the tracking portfolio;
[0087] Portfolio constraints, used to implement constraints corresponding to investment settings.
[0088] In some possible implementations of this embodiment, the funding constraint can be expressed as The transaction value constraint can be expressed as The transaction behavior constraint can be expressed as The transaction cost constraint can be expressed as Portfolio constraints can be implemented based on specific investment settings. For example, if a stock is not currently in the portfolio, it cannot be sold. The portfolio constraint can be expressed as
[0089] In some embodiments, obtaining the index tracking result of the tracking investment portfolio according to the objective function in the above step S150 includes:
[0090] Obtaining a minimum value of the objective function according to the constraint condition;
[0091] The number of units of each constituent stock of the rebalanced tracking investment portfolio is obtained according to the minimum value of the objective function.
[0092] The optimization goal of the objective function in this embodiment is
[0093] In practical applications, the tracking portfolio model is a mathematical model built based on MILP. It uses a dedicated solver and combines constraints to solve the above objective function. The objective function can simultaneously consider the matching of the value trajectory of each investment cycle and the minimization of transaction costs, thereby more effectively balancing tracking errors and transaction costs and improving the practicality and tracking accuracy of the tracking portfolio model.
[0094] In practical applications, the comparison of calculations based on real business data shows that the tracking error of the tracking portfolio model of the embodiment of the present disclosure is better than that of the existing benchmark model under various investment settings. For example, under self-financing conditions, due to the existence of transaction costs, the value-based model (the model proposed by Konno and Wijayanayake in 2001) may lead to high-frequency rebalancing operations and increase transaction costs in practical applications, while the embodiment of the present disclosure can better cope with the impact of transaction costs and improve practicality and tracking accuracy.
[0095] Reference now Figure 2 . Figure 2 The structure diagram of the index tracking device 200 based on mixed integer linear programming according to some embodiments of the present disclosure is shown. The index tracking device 200 based on mixed integer linear programming can be implemented on one device or on distributed devices. Figure 2 As shown, the index tracking device 200 based on mixed integer linear programming at least includes a first acquisition unit 210, a second acquisition unit 220, a first calculation unit 230, an objective function determination unit 240 and a second calculation unit 250, wherein:
[0096] A first acquisition unit 210 is used to acquire a value function of a tracking investment portfolio;
[0097] A second acquisition unit 220 is used to acquire a value function of a pre-constructed target index, wherein the value return of the target index in each investment cycle is the same as that of the benchmark index, and the initial value point of the target index is the same as or different from the initial value point of the benchmark index;
[0098] A first calculation unit 230 is used to obtain tracking error information of the tracking investment portfolio according to the value function of the tracking investment portfolio and the value function of the target index, and to obtain transaction cost information of the tracking investment portfolio according to the value function of the target index and the value information of the benchmark index;
[0099] An objective function determination unit 240, configured to determine an objective function of a tracking investment portfolio model based on mixed integer linear programming according to the tracking error information and transaction cost information of the tracking investment portfolio;
[0100] The second calculation unit 250 is used to obtain the index tracking result of the tracking investment portfolio according to the objective function.
[0101] In some embodiments, the second acquisition unit 220 is used to obtain the value function of the tracking investment portfolio in the last investment cycle of the historical period, the value of the benchmark index in each investment cycle and a preset adjustment coefficient; based on the value function of the tracking investment portfolio in the last investment cycle of the historical period, the value of the benchmark index in each investment cycle and the preset adjustment coefficient, obtain the value function of the target index in each investment cycle.
[0102] In some embodiments, the second acquisition unit 220 is used to obtain the initial value function of the target index in each investment cycle based on the ratio of the product of the value function of the tracking investment portfolio in the last investment cycle of the historical period and the value of the benchmark index in each investment cycle to the value of the benchmark index in the last investment cycle of the historical period; and adjust the initial value function of the target index in each investment cycle according to the adjustment coefficient to obtain the value function of the target index in each investment cycle.
[0103] In some embodiments, the first calculation unit 230 includes a tracking error calculation module;
[0104] A tracking error calculation module is used to obtain the value function of the tracking investment portfolio in each investment cycle during the historical period, and the value function of the target index in each investment cycle during the historical period; obtain the difference between the value function of the tracking investment portfolio and the target index in each investment cycle; and obtain the tracking error information of the tracking investment portfolio based on the sum of the differences of the value functions corresponding to all investment cycles during the historical period.
[0105] In some embodiments, the first calculation unit 230 further includes a transaction cost calculation module;
[0106] The transaction cost calculation module is used to obtain the value function of the target index in each investment cycle during the historical period, as well as the value information of the benchmark index in each investment cycle during the historical period; obtain the difference between the value functions of the target index and the benchmark index in the same investment cycle; and obtain the transaction cost information of the tracking investment portfolio based on the sum of the differences in the value functions corresponding to all investment cycles during the historical period.
[0107] In some embodiments, the objective function determination unit 240 is configured to obtain the objective function of the tracking investment portfolio model according to the combination of the tracking error information of the tracking investment portfolio and the transaction cost information.
[0108] In some embodiments, the apparatus 200 further includes a constraint condition acquisition unit, configured to acquire a constraint condition of the tracking investment portfolio model, wherein the constraint condition includes at least one of the following:
[0109] A capital constraint is used to constrain the value of the tracking portfolio after rebalancing and transaction costs to not exceed the total capital of the fund;
[0110] Transaction value constraints, which are used to constrain the relationship between the buy value and sell value of the constituent stocks of the tracking portfolio and the number of units in the tracking portfolio;
[0111] Trading behavior constraints are used to constrain the constituent stocks of the tracking investment portfolio to only be bought or sold in one investment cycle, but not both at the same time;
[0112] Transaction cost constraints, used to constrain the transaction costs of the constituent stocks of the tracking portfolio;
[0113] Portfolio constraints, used to implement constraints corresponding to investment settings.
[0114] In some embodiments, the second calculation unit 250 is used to obtain the minimum value of the objective function according to the constraint condition; and obtain the number of units of each constituent stock of the rebalanced tracking investment portfolio according to the minimum value of the objective function.
[0115] It can be understood that the above-mentioned exponential tracking device based on mixed integer linear programming can implement the various steps of the exponential tracking method based on mixed integer linear programming provided in the aforementioned embodiments, and the relevant explanations about the exponential tracking method based on mixed integer linear programming are applicable to the exponential tracking device based on mixed integer linear programming, which will not be repeated here.
[0116] Figure 33 is a simplified block diagram of a device 300 suitable for implementing an embodiment of the present disclosure. Figure 3 As shown, the device 300 includes one or more processors 310 , one or more memories 320 coupled to the processors 310 , and one or more communication modules 340 coupled to the processors 310 .
[0117] The communication module 340 is used for two-way communication. The communication module 340 has at least one antenna to facilitate communication. The communication interface may represent any interface necessary for communicating with other network elements.
[0118] Processor 310 may be of any type suitable for the local technology network, and may include, as non-limiting examples, one or more of: a general purpose computer, a special purpose computer, a microprocessor, a digital signal processor (DSP), and a processor based on a multi-core processor architecture. Device 300 may have multiple processors, such as application specific integrated circuit chips, which are driven in time to a clock that synchronizes a master processor.
[0119] The memory 320 may include one or more non-volatile memories and one or more volatile memories. Examples of non-volatile memories include, but are not limited to, read-only memory (ROM) 324, electrically programmable read-only memory (EPROM), flash memory, hard disk, compact disk (CD), digital video disk (DVD), and other magnetic and / or optical memories. Examples of volatile memories include, but are not limited to, random access memory (RAM) 322 and other volatile memories that do not persist during the duration of a power outage.
[0120] The computer program 330 includes computer executable instructions that are executed by the associated processor 310. The program 330 may be stored in the ROM 324. The processor 310 may perform any appropriate actions and processes by loading the program 330 into the RAM 322.
[0121] The embodiments of the present disclosure may be implemented by a program 330, so that the device 300 may execute the reference Figure 1 Any process discussed. The embodiments of the present disclosure may also be implemented by hardware or by a combination of software and hardware.
[0122] In some embodiments, the program 330 may be tangibly contained in a computer-readable medium, which may be contained in the device 300 (e.g., memory 320) or other storage devices accessible to the device 300. The device 300 may load the program 330 from the computer-readable medium to the RAM 322 for execution. The computer-readable medium may include any type of tangible non-volatile memory, such as ROM, EPROM, flash memory, hard disk, CD, DVD, etc. The computer-readable medium has the program 330 stored thereon.
[0123] Generally, various embodiments of the present disclosure may be implemented in hardware or dedicated circuits, software, logic, or any combination thereof. Certain aspects may be implemented in hardware, while other aspects may be implemented in firmware or software, which may be executed by a controller, microprocessor, or other computing device. Although various aspects of the embodiments of the present disclosure are shown and described as block diagrams, flow charts, or using some other graphical representations, it should be understood that, as non-limiting examples, the blocks, devices, systems, techniques, or methods described herein may be implemented in hardware, software, firmware, dedicated circuits or logic, general hardware or controllers or other computing devices, or some combination thereof.
[0124] The present disclosure also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer executable instructions, such as instructions included in program modules, which are executed in a device on a target real or virtual processor to perform the above-mentioned reference Figure 1 The index tracks 100. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform specific tasks or implement specific abstract data types. In various embodiments, the functionality of program modules can be combined or separated between program modules as needed. Machine executable instructions for program modules can be executed in local or distributed devices. In distributed devices, program modules can be located in local and remote storage media.
[0125] The program code for executing the disclosed method can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer or other programmable data processing equipment so that when the program code is executed by the processor or controller, the function / operation specified in the flow chart and / or block diagram is realized. The program code can be executed completely on the machine as an independent software package, partially on the machine, partially on the machine, partially on a remote machine, partially on a remote machine, or all on a remote machine or server.
[0126] In the context of the present disclosure, computer program codes or related data may be carried by any appropriate carrier to enable a device, apparatus or processor to perform various processes and operations as described above. Examples of carriers include signals, computer readable media, etc.
[0127] The computer readable medium may be a computer readable signal medium or a computer readable storage medium. The computer readable medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared or semiconductor systems, devices or apparatuses, or any suitable combination of the foregoing. More specific examples of computer readable storage media include an electrical connection with one or more wires, a portable computer floppy disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
[0128] In addition, although the operations are described in a specific order, this should not be understood as requiring the specific order or sequence shown to be performed, or performing all the operations shown, to obtain the desired result. In some cases, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these details should not be interpreted as limitations on the scope of the present disclosure, but can be interpreted as descriptions of features specific to a particular embodiment. Certain features described in the context of a separate embodiment may also be implemented in combination in a single embodiment. On the contrary, the various features described in the context of a single embodiment may also be implemented in multiple embodiments individually or in any suitable sub-combination.
[0129] Although the disclosure has been described in language specific to structural features and / or methodological acts, it should be understood that the disclosure defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.
[0130] It should be fully understood that the use of personally identifiable information should be subject to privacy policies and practices generally recognized as meeting or exceeding industry or government requirements for maintaining user privacy. In particular, personally identifiable information data should be managed and processed to minimize the risk of inadvertent or unauthorized access or use, and the nature of authorized use should be clearly indicated to users.
Claims
1. An exponential tracking method based on mixed integer linear programming, characterized in that: The index tracking method includes: Get the value function that tracks the portfolio; Obtaining a value function of a pre-constructed target index, wherein the value return of the target index in each investment cycle is the same as that of a benchmark index, and an initial value point of the target index is the same as or different from an initial value point of the benchmark index; Acquire tracking error information of the tracking investment portfolio according to the value function of the tracking investment portfolio and the value function of the target index, and acquire transaction cost information of the tracking investment portfolio according to the value function of the target index and the value information of the benchmark index; Determining an objective function of a tracking portfolio model based on mixed integer linear programming according to the tracking error information and transaction cost information of the tracking portfolio; An index tracking result of the tracking investment portfolio is obtained according to the objective function.
2. The method according to claim 1, characterized in that: The method of obtaining a value function of a pre-built target index includes: Obtaining the value function of the last investment cycle of the tracking investment portfolio during the historical period, the value of the benchmark index in each investment cycle and a preset adjustment coefficient; The value function of the target index in each investment cycle is obtained based on the value function of the last investment cycle of the tracking investment portfolio in the historical period, the value of the benchmark index in each investment cycle and a preset adjustment coefficient.
3. The method according to claim 2, characterized in that: The step of obtaining the value function of the target index in each investment cycle according to the value function of the last investment cycle of the tracking investment portfolio in the historical period, the value of the benchmark index in each investment cycle and a preset adjustment coefficient comprises: Obtaining an initial value function of the target index in each investment cycle according to a ratio of a product value of the tracking investment portfolio in the last investment cycle of the historical period and the value of the benchmark index in each investment cycle to the value of the benchmark index in the last investment cycle of the historical period; The initial value function of the target index in each investment cycle is adjusted according to the adjustment coefficient to obtain the value function of the target index in each investment cycle.
4. The method according to claim 1, characterized in that: The obtaining tracking error information of the tracking investment portfolio according to the value function of the tracking investment portfolio and the value function of the target index includes: Obtaining the value function of the tracking investment portfolio in each investment cycle during the historical period, and the value function of the target index in each investment cycle during the historical period; Obtaining the difference between the value function of the tracking investment portfolio and the target index in each investment cycle; The tracking error information of the tracking investment portfolio is obtained based on the sum of the differences of the value functions corresponding to all investment cycles in the historical period.
5. The method according to claim 1, characterized in that: The obtaining the transaction cost information of the tracking investment portfolio according to the value function of the target index and the value information of the benchmark index includes: Obtaining the value function of the target index in each investment cycle during the historical period, and the value information of the benchmark index in each investment cycle during the historical period; Obtaining the difference between the value functions of the target index and the benchmark index in the same investment period; The transaction cost information of the tracking investment portfolio is obtained according to the sum of the differences of the value functions corresponding to all investment cycles in the historical period.
6. The method according to claim 1, characterized in that: Determining the objective function of the tracking investment portfolio model according to the tracking error information and transaction cost information of the tracking investment portfolio includes: The objective function of the tracking investment portfolio model is obtained according to the combination of the tracking error information of the tracking investment portfolio and the transaction cost information.
7. The method according to claim 1, characterized in that: The method further includes obtaining constraints of the tracking portfolio model, wherein the constraints include at least one of the following: A capital constraint is used to constrain the value of the tracking portfolio after rebalancing and transaction costs to not exceed the total capital of the fund; Transaction value constraints, which are used to constrain the relationship between the buy value and sell value of the constituent stocks of the tracking portfolio and the number of units in the tracking portfolio; Trading behavior constraints are used to constrain the constituent stocks of the tracking investment portfolio to only be bought or sold in one investment cycle, but not both at the same time; Transaction cost constraints, used to constrain the transaction costs of the constituent stocks of the tracking portfolio; Portfolio constraints, used to implement constraints corresponding to investment settings.
8. The method according to claim 7, characterized in that: The obtaining the index tracking result of the tracking investment portfolio according to the objective function includes: Obtaining a minimum value of the objective function according to the constraint condition; The number of units of each constituent stock of the rebalanced tracking investment portfolio is obtained according to the minimum value of the objective function.
9. An index tracking device based on mixed integer linear programming, characterized in that: The index tracking device comprises: A first acquisition unit is used to acquire a value function for tracking an investment portfolio; A second acquisition unit is used to acquire a value function of a pre-constructed target index, wherein the value return of the target index in each investment cycle is the same as that of the benchmark index, and the initial value point of the target index is the same as or different from the initial value point of the benchmark index; A first calculation unit is used to obtain the tracking error information of the tracking investment portfolio according to the value function of the tracking investment portfolio and the value function of the target index, and to obtain the transaction cost information of the tracking investment portfolio according to the value function of the target index and the value information of the benchmark index; An objective function determination unit, configured to determine an objective function of a tracking investment portfolio model based on mixed integer linear programming according to tracking error information and transaction cost information of the tracking investment portfolio; The second calculation unit is used to obtain the index tracking result of the tracking investment portfolio according to the objective function.
10. An electronic device, characterized in that: The electronic device comprises: one or more processors; and One or more memories coupled to the one or more processors and storing instructions thereon, which, when the instructions are executed individually or collectively by the one or more processors, cause the electronic device to perform the mixed integer linear programming-based exponential tracking method of any one of claims 1 to 8.