KR102103578B1 - Method for Selecting Asset Portfolio - Google Patents

Abstract

The present invention relates to a portfolio asset selection method. More specifically, the method is to perform portfolio proposal by selecting a combination with respect to high-return and low-risk assets constituting multiple assets in a financial market. To that end, portfolio asset selection is performed by application of Monte Carlo method-based sampling and a genetic algorithm. As a result, a sub-optimal portfolio close to an optimal portfolio is proposed. The method includes: a step of generating m c*k-asset portfolios by Monte Carlo method-based sampling (c > 1, k being the number of portfolio assets); a step of calculating the Sharpe ratio with respect to each of the m c*k-asset portfolios; a step of selecting an r% c*k-asset portfolio in which the Sharpe ratio corresponds to top r%; a step of generating p k-asset portfolios by r% c*k-asset portfolio and calculating the Sharpe ratio with respect to each; a step of performing a unit selection in the order of the Sharpe ratio for turning into a higher k-asset portfolio; and a step of selecting b k-asset portfolios as recommended portfolios in the order of the Sharpe ratio.

Description

How to select portfolio assets using Monte Carlo genetic algorithm {Method for Selecting Asset Portfolio}

The present invention relates to a method for selecting a portfolio asset, and more specifically, a sampling and gene of the Monte Carlo method to select a combination of high-yield and low-risk assets among multiple assets in the financial market and present them as a portfolio. It is about a method of presenting a sub-optimal portfolio approximating an optimal portfolio by applying an algorithm to selecting portfolio assets.

Theory of Portfolio Selection, one of the strategies for effective asset investment, is a theory structured by optimal allocation decisions based on a model developed by Harry Max Markowitz. The theory is that creating a portfolio can reduce risk more than before diversified investment. According to portfolio theory, it is possible to select a product combination of an asset type group with less risk if the expected return is the same, and a product of an asset type group with a higher expected return if the risk is the same. .

이며, 포트폴리오의 위험(Portfolio Variance, 분산)

가 될 때 Sharpe ratio는

가 되므로 포트폴리오는

가 최대화 되는 조합을 선택하는 것이다. 이 때 동일 기대 수익을 제공하는 포트폴리오들이 주어질 때, 낮은 리스크를 가진 것을 선택해야 바람직하므로 Portfolio Selection은

을 최소화하는 Quadratic Programming으로 찾는 것이다. 그리고 포트폴리오로 선택된 자산들에 대한 배분비율을 균등배분(Equally Weighted, 1/k 배분)을 하는 방법이 있고, Markowitz의 Mean Variance모델에 의해 최적의 배분을 결정할 수도 있다.The problem of finding the optimal portfolio in the financial market, that is, selecting a certain number (k) of a number of assets in the financial market to form a portfolio, maximizes profit and minimizes risk (risk) ratio It is to combine assets so that (yield / risk, sharp index) is the highest. Sharpe ratio by Markowitz model is expected return of portfolio

And portfolio risk (Portfolio Variance)

Sharpe ratio

So the portfolio is

Is to choose the combination that maximizes. In this case, when portfolios that provide the same expected return are given, it is desirable to select the one with low risk, so Portfolio Selection

Looking for Quadratic Programming to Minimize In addition, there is a method of equally weighting (1 / k distribution) the distribution ratio of assets selected as a portfolio, and it is also possible to determine the optimal distribution by Markowitz's Mean Variance model.

However, the problem of finding a portfolio combination consisting of a certain number (k) among a large number of assets in the financial market is too many cases for the combination, so it is practically impossible to find a portfolio with the 'best combination with the highest Sharpness Index'. . For example, if you want to find a portfolio of 10 asset combinations out of _3,000 , the number of possible combinations is ₃₀₀₀ C _{10, which} is as much as 1.6 x 10 ²⁸ . Therefore, it is not possible in time under limited computing resources to search for all possible combinations and compare the Sharpness index for them to find the optimal portfolio. Therefore, it is necessary to find a suboptimal portfolio that approximates an optimal portfolio by applying methods such as reducing the search space or reducing the target asset. In the present invention, a sampling and genetic algorithm of the Monte Carlo method is used as a method capable of providing such a suboptimal solution.

Here, the Monte Carlo Method (MC) is a term that refers to an algorithm that calculates the value of a desired function using randomly extracted random numbers. It is a statistical method that includes optimization, numerical integration, and extraction from probability distribution. It is used for simulation. It is often used in mathematics or physics, and is widely used when calculating approximate solutions, i.e. suboptimal solutions, in cases where the degree of freedom is high, the value to be calculated is not expressed in a closed form, or is complex. In this Monte Carlo method, more accurate results can be obtained as the number of randomly selected random numbers increases, but it should be taken into account that it takes more time. Also, it is not to find the optimal solution, but because it is a method to find an approximate solution based on simulation, it should be considered that there may always be some error, unlike the analytical method.

과 1을 비교하여 원에 속한 점인지 아닌지를 판단하고, 이를 반복함으로써 원에 속한 점의 개수와 원의 밖에 속한 점의 개수를 파악할 수 있게 되는데, [1 , 0] x [0, 1]의 영역에서 반지름이 1인 원(4등분 된 원)의 면적은 π/4이므로 ‘전체 점의 개수 대비, 원에 속한 것으로 판단되는 점의 개수’의 비율에 4를 곱한 값이 π의 근사 값이 된다. 이 때 표집된 점의 개수를 늘려갈 수록 실제 π값에 다가가게 된다. 즉 몬테카를로 방법에서는 무작위로 표집된 개수가 늘어날수록 더 정확한 결과를 얻을 수 있게 된다.For example, the circumferential rate can be calculated by the Monte Carlo method. To do this, a point (x, y) is sampled using random numbers randomly extracted from a region of [1, 0] x [0, 1], and the sampled point is' Whether the center is at (0,0) and belongs to a circle with a radius of 1, according to the definition of the circle

By comparing and 1 and determining whether it belongs to a circle or not, and repeating it, it is possible to determine the number of points belonging to a circle and the number of points belonging to a circle outside of [1, 0] x [0, 1]. The area of a circle with a radius of 1 (quadrant circle) in the area is π / 4, so the ratio of 'the number of points determined to belong to the circle to the total number of points' multiplied by 4 is the approximate value of π. do. At this time, as the number of points collected increases, the actual value of π approaches. In other words, in the Monte Carlo method, more accurate results can be obtained as the number of random samples increases.

On the other hand, genetic algorithms (or genetic algorithms) are based on the basic theory of bio genetics in nature, and are a parallel and global search algorithm based on Darwin's theory of survival of the fittest. This genetic algorithm expresses possible solutions to the problem to be solved in a defined data structure, and then gradually transforms them to produce better solutions. Here, the data structures representing the solutions are expressed as genes, and the process of creating better and better solutions by modifying them can be expressed as evolution. In other words, the genetic algorithm can be said to be a simulated evolution search algorithm to find a solution x that optimizes some unknown function Y = f (x). In other words, the genetic algorithm is close to an approach to solving a specific problem, and it can be applied to all problems that can be expressed by converting it into a format that can be used in the genetic algorithm.

In general, if a problem is too complex to be impossible to calculate, it can be approached through a genetic algorithm as a method to obtain an answer close to the optimal solution even though an actual optimal solution is not obtained. In this case, it does not perform better than an algorithm that is optimized to solve the problem, but it can show an acceptable level of solution in most cases. Various types of theories and techniques, such as evolutionary strategies and genetic programming, have been actively studied in recent years as algorithms that mimic the process of evolution of organisms, that is, natural selection and genetic laws. Genetic algorithm is the most basic and representative algorithm among them, and it is widely applied to solve nonlinear or non-computable complex problems in natural science, engineering, and humanities and social science.

The portfolio asset selection method using the Monte Carlo genetic algorithm according to the present invention, created from the above technical background, selects combinations of multiple assets in the financial market and finds combinations of assets with high returns and low risks. It aims to provide a method of presenting a sub-optimal asset portfolio with a performance that approximates an optimal portfolio in a short time using the Monte Carlo method and genetic algorithm.

The portfolio asset selection method using the Monte Carlo genetic algorithm according to the present invention in order to achieve the above object is a portfolio asset selection method performed by an information system, based on n assets, the number of assets to be selected as a portfolio (k) generating a c * k-asset portfolio consisting of the number of assets of c times (c> 1), but generating m c * k-asset portfolios by sampling with the Monte Carlo Method; Calculating a Sharpe ratio for each of the m c * k-asset portfolios; Selecting an r% c * k-asset portfolio whose Sharpe ratio corresponds to the top r% among the m c * k-asset portfolios; Based on the assets included in each of the r% c * k-asset portfolios, a k-asset portfolio consisting of the number of assets (k) to be selected as the portfolio is generated, but the r% c * k-asset portfolio is generating p k-asset portfolios to calculate Sharpe ratios for each; For each of the r% c * k-asset portfolios, selecting a each of the p-k-asset portfolios in order of highest Sharpe ratio to make a top k-asset portfolio; And selecting b k-asset portfolios as a recommended portfolio by arranging in order of high Sharpe ratio for all of the top k-asset portfolios. It is preferably characterized in that it comprises a.

In addition, the p pieces are characterized by the number of k-asset portfolios for all cases that can be generated for each of the r% c * k-asset portfolios, or the p pieces are the r% c * k- For each asset portfolio, it is also possible to use the Monte Carlo genetic algorithm as a portfolio asset selection method, characterized in that it is the number of k-asset portfolios that are generated until the closing condition using a genetic algorithm.

As described above, the portfolio asset selection method using the Monte Carlo genetic algorithm according to the present invention rationalizes the search space by using the Monte Carlo method and the genetic algorithm by selecting a combination of assets with a high return rate among low assets. By reducing it, it is possible to present a sub-optimal portfolio with performance close to the optimal portfolio in a short time.

FIG. 1 shows the concept of calculating the Sharpe ratio by selecting the c * k-asset portfolio when c = 2 through sampling of the Monte Carlo method.
Figure 2 shows the concept of finding the c * k-asset portfolio of the top r% of the c * k-asset portfolio when c = 2.
FIG. 3 illustrates the concept of recommending a k-asset portfolio with a high Sharpe ratio after generating a k-asset portfolio from a c * k-asset portfolio when c = 2.
4 is a flow chart illustrating a process in which a portfolio asset selection method using a Monte Carlo genetic algorithm according to the present invention is performed by an information system.
FIG. 5 shows a histogram distribution chart of the Sharpness index for 25,200 five-asset portfolios randomly generated from 100 stocks when n = 100, k = 5, and c = 2.
6 shows the composition and sharpness index (some cases) of a 10-asset portfolio generated from 100 stocks when n = 100, k = 5, and c = 2.
FIG. 7 shows a histogram of sharp indexes for 2,000 10-asset portfolios when n = 100, k = 5, and c = 2.
8 to 15 show the sharpness index histogram (some cases) of the sharpness index for each of the 10-asset portfolios and the five-assets portfolio generated from them when n = 100, k = 5, and c = 2 will be.
FIG. 16 shows the maximum and minimum sharpness distributions of the 5-asset portfolios generated from 2,000 10-asset portfolios when n = 100, k = 5, and c = 2.
FIG. 17 shows the ratio distribution of a 5-asset portfolio with a sharp index greater than the 10-asset portfolio among the 5-asset portfolios generated from the 10-asset portfolio beam when n = 100, k = 5, and c = 2 It is done.
FIG. 18 shows the Sharpness index statistics and distribution for the top 1.3% (1 million) portfolio obtained in Step 0 when n = 100, k = 5, and c = 2.
FIG. 19 shows the Sharpness index statistic and histogram distribution for the entire portfolio of Case A and Case B (25,200 each) obtained in Step 1 when n = 100, k = 5, and c = 2.
20 is a case of n = 100, k = 5, c = 2, the sharp index statistics and histogram distribution for the top 1% portfolio of Case A and Case B (each 252), obtained in Step 2 and Step 3 It is shown.
FIG. 21 shows that in the case of n = 100, k = 5, c = 2, the total top 1.3% (1 million) obtained from Step 0 among the entire portfolio of Case A and Case B (25,200 each) obtained in Step 1 The figure shows the numbers and ratios included in the 5-asset portfolio.

Hereinafter, the present invention will be described in detail so that the above-described objects and features become clear, and accordingly, a person skilled in the art to which the present invention pertains can easily implement the technical spirit of the present invention. In addition, in describing the present invention, among the known technologies related to the present invention, it is already well known in the technical field, and when it is determined that the detailed description of the known technology may unnecessarily obscure the subject matter of the present invention, the detailed description will be given. It will be omitted.

In addition, the terms used in the present invention have been selected as general terms that are currently widely used as much as possible, but in certain cases, there are also terms that are arbitrarily selected by the applicant. It is intended to clarify that the present invention should be understood as a meaning of a term rather than a name of. Terms used in the description of the embodiments are only used to describe specific embodiments, and are not intended to limit the embodiments. Singular expressions include plural expressions unless the context clearly indicates otherwise.

The embodiments may be modified in various forms and may have various additional embodiments, in which specific embodiments are shown in the drawings and detailed descriptions related thereto are described. However, it is not intended to limit the embodiments to a specific form, it should be understood that it includes all changes or equivalents or substitutes included in the spirit and scope of the embodiments.

In the description of various embodiments, expressions such as “first”, “second”, “first”, or “second” may modify various components of the embodiments, but do not limit the components. For example, the above expressions do not limit the order and / or importance of the components. The above expressions can be used to distinguish one component from another component.

Hereinafter, the present invention will be described with reference to the accompanying drawings. FIG. 1 shows the concept of calculating the sharpe ratio by selecting a c * k-asset portfolio when c = 2 through sampling of the Monte Carlo method, and FIG. 2 shows a c * k-asset portfolio when c = 2 Among them, the concept of finding the c * k-asset portfolio of the top r% is shown, and FIG. 3 shows a high-sharp-e ratio after generating a k-asset portfolio from the c * k-asset portfolio when c = 2. It illustrates the concept of recommending an asset portfolio. As described above, the present invention is a portfolio asset selection method performed by an information system. After the information system constructs a combination of asset portfolios, it searches for an asset portfolio with a high sharpe ratio, but has an approximate value to the optimal portfolio. It's about how to find a suboptimal portfolio. As described above, selecting all the portfolios of combinable assets among all financial assets and selecting the optimal portfolio with the highest sharpe ratio is due to too many cases, due to calculation time problems or computing resource limitations. The reality is that it is almost impossible to find a suboptimal portfolio.

Therefore, in the present invention, first, as shown in FIG. 1, 'm c * k-portfolios' are generated. That is, among the n assets in the financial market, a 'c * k-asset portfolio' consisting of c * k assets corresponding to a number greater than the 'number to be composed of portfolios (k)' is generated. Here, it is preferable to configure c * k to be a multiple of c (c> 1) of numbers (k) to be composed of the portfolio. Since the value of c varies in computing power, the optimal value is determined experimentally. It is desirable to lose. If you try to create a c * k-asset portfolio where c = 2 for all cases that can be composed of n assets, you will get too many cases, for example, about 200 assets in the financial market. Even if there is only one, 2 * k becomes 20 when trying to construct a portfolio of 10 (k), so the number of possible combinations is ₂₀₀ C ₂₀ , so the number of possible combinations in the portfolio is as many as 1.6 x 10 ²⁷ . . Therefore, it is desirable to randomly sample c * k-asset portfolios for n assets using the Monte Carlo Method and limit them to m. Here, it is desirable to maximize m within the limits that can be realistically implemented in consideration of the total number of assets (n), the number of portfolios (k), the limitations of computing resources, and the time required. This is because the higher the number, the closer the optimal portfolio can be obtained.

) 에 대비한 기대수익(Expected Return,

) 즉,

가 되는데, 포트폴리오의 기대수익은

이며, 포트폴리오의 위험은

가 된다. 그리고 도 2에서 보는 바와 같이 정보시스템은 c=2인 경우에 상기 m개의 c*k-자산 포트폴리오 중에서 상기 Sharpe ratio가 상위 r%에 드는 c*k-자산 포트폴리오를 선택하여 이를 ‘r% c*k-자산 포트폴리오’로 하게 되는데, 여기서 r%의 범위는 m의 크기, 포트폴리오의 숫자, 컴퓨팅자원의 한계, 후술하게 되는 k-자산 포트폴리오 생성에 따른 소요시간 등을 감안하여 현실적으로 구현 가능한 한도 내에서 하는 것이 바람직하다.In the case of c = 2, after generating 'm c * k-asset portfolios', the information system calculates the Sharpe ratio for each of the m c * k-asset portfolios. Here, the Sharpe ratio is the portfolio risk (Portfolio Variance,

Expected Return ()

) In other words,

The expected return of the portfolio is

And the risk of the portfolio

Becomes And as shown in Figure 2, the information system selects c * k-asset portfolio whose sharpe ratio falls in the top r% among the m c * k-asset portfolios when c = 2, and selects' r% c * k-asset portfolio ', where the range of r% is within the limits that can be realistically implemented considering the size of m, the number of portfolios, the limitations of computing resources, and the time required for the creation of the k-asset portfolio, which will be described later. It is desirable to do.

Next, as shown in FIG. 3, when c = 2, from each of the r% c * k-asset portfolios, it consists of k assets among 2k assets included in the r% c * k-asset portfolio. It is desirable to create a 'k-asset portfolio', where all the numbers of each k-asset portfolio that can be created in each of the r% c * k-asset portfolios are _2k C _k . For example, if k is 10 and 2k is 20, it becomes ₂₀ C ₁₀ , so a total of 184,756 k-asset portfolios can be generated for each r% c * k-asset portfolio. If 40 is set, 1,378 billion k-asset portfolios can be created. Therefore, in the case of generating the k-asset portfolio, if the _2k C _k is a small number, the k-asset portfolio can be generated in all cases, but when the _2k C _k is increased, the computing resource limit or the time required accordingly Considering that, in all cases, the k-asset portfolio cannot be realistically created. Therefore, when _2k C _k is too large compared to the limit of computing resources, it is desirable to generate a k-asset portfolio by limiting to a certain number (p) using Genetic Algorithm.

As an example of the process of generating a k-asset portfolio using Genetic Algorithm, first, a population of a plurality of k-asset portfolios consisting of k assets among the assets constituting the r% c * k-asset portfolio After randomly constructing, a random pair of two genetic objects is selected from the population, and k having another asset combination through cross-crossing and mutation modification of two randomly selected two pairs of k-asset portfolios, that is, two genetic object pairs. -Create asset portfolio descendants, and evaluate the fit to be high if the Sharpe ratio is high for the generated descendants. Among the many genes generated, a gene having a high degree of fitness is evaluated to increase the probability of forming the next generation. This is because even if the fitness is low in the current generation, the probability of having a high fitness in the next generation is not zero. In this way, the generation is repeated, and the offspring are generated, but until the specified termination condition is reached. Here, the termination condition may be until the distribution of the fitness evaluation value exceeds a certain level, or it may be the number of advanced households, or it may be used as the calculation time. Therefore, even if the _2k C _k is too large to limit to the whole case using the Genetic Algorithm, good genes are selected through cross-crossing and mutagenesis, etc., and good genes are inherited by the child generation. Descendants are created, and k-asset portfolio descendants with higher Sharpe ratios are generated as generations are repeated.

That is, even if a limited number of k-asset portfolios are generated, the descendants of the generated k-asset portfolio inherit and evolve the inheritance of the parent's superior gene, so the subsequent process, the sharpe ratio for each of the r% c * k-asset portfolios In the process of screening a portfolio of k assets with high a, the accuracy can be increased by selecting a portfolio of k-asset portfolios with a high Sharpe ratio, similar to the case of generating a total portfolio of k-asset.

After k-asset portfolios are created for each r% c * k-asset portfolio, the information system selects a piece from the k-asset portfolio for each r% c * k-asset portfolio in order of highest sharpe ratio. It is desirable to put it together as a 'top k-asset portfolio'. Then, after sorting all of the top k-asset portfolios selected from all of the r% c * k-asset portfolios in order of high Sharpe ratio, selecting b top k-asset portfolios in order of high Sharpe ratio It is desirable to make them a recommended portfolio. Here, b is an arbitrary number and may be changed according to the needs of portfolio designers.

Meanwhile, FIG. 4 is a flowchart illustrating a process in which a portfolio asset selection method using a Monte Carlo genetic algorithm according to the present invention is performed by the information system. Hereinafter, a process of the present invention will be described with reference to FIG. 4. As shown in FIG. 4, the information system first generates m c * k-asset portfolios when c = 2 for n assets (s100 to s120). That is, the c * k-asset portfolio including 2k assets among the n assets is generated by sampling by the Mote Carlo Method. To this end, after generating a random number (s100), one c based on the generated random number Create a * k-asset portfolio (s110) and generate another number of c * k-asset portfolios by generating a random number again. This process is repeated until the c * k-asset portfolio becomes m. It becomes (s120).

After generating m c * k-asset portfolios in steps s100 to s120, it is preferable to perform a process of calculating a Sharpe ratio for each of the m c * k-asset portfolios (s130). The method for calculating the sharpe ratio has been described above and will be omitted. After the Sharpe ratio calculation for each of the m c * k-asset portfolios is completed, select the c * k-asset portfolio whose Sharpe ratio falls within the r% among the m c * k-asset portfolios to r% c * It is desirable to select a k-asset portfolio (s140). At this time, the number of r% c * k-asset portfolios will be m x r%.

Then, a process of generating p k-asset portfolios for each of the r% c * k-asset portfolios is performed (s160), wherein the k-asset portfolio is among the assets included in each of the r% c * k-asset portfolios. A portfolio containing k sub-assets. In addition, it is preferable to vary the method of generating the k-asset portfolio according to the calculated result value (number) of _2k C _k for the above-described reasons. In the case where the _2k C _k is less than a certain size, for all cases It is preferable to generate a k-asset portfolio (s160a), and when _2k C _k is greater than or equal to the predetermined size, it is preferable to generate a limited number of k-asset portfolios using the Genetic Algorithm (s160b). Therefore, the number p of k-asset portfolios for each of the r% c * k-asset portfolios is a result of calculating _2k C _k when _2k C _k is less than a certain size, and _2k C _k is greater than or equal to the predetermined size. In this case, p is preferably equal to the predetermined size.

After performing the process of generating p k-asset portfolios for each of the r% c * k-asset portfolios (s160), Sharpe for each of the p k-asset portfolios for each r% c * k-asset portfolio The ratio is calculated (s170), and the top a-k portfolio with high sharpe ratio for each r% c * k-asset portfolio is selected as the 'top k-asset portfolio' (s180). Then, all the “top k-asset portfolios” selected from each of the r% c * k-asset portfolios are sorted in the order of highest sharpe ratio (s190). At this time, the total number of 'top k-asset portfolios' will be m x r% x a.

In addition, after sorting is finished for all of the top k-asset portfolios, it is desirable that the information system selects b k-asset portfolios in the order of highest sharpe ratio among the top k-asset portfolios and presents them as a recommended portfolio. (s200).

Hereinafter, the validity of the present invention is verified through experimental examples of the above-described method.

<Experimental Example 1>

(theory)

When P and Q are respective portfolios, and sp is the Sharpe ratio of P and sq is the Sharpe ratio of Q, for any P, there are enough P ⊃ Q and Q with sp <sq. (P: c * k-asset portfolio, Q: k-asset portfolio)

(Experiment method)

-Step 1: Randomly generate 25,200 5-asset portfolios from 100 stocks, calculate the Sharpness Index for each 5-asset portfolio and display it as a histogram distribution

-Step 2: Randomly generate 2000 10-asset portfolios (2k-asset portfolios) from 100 stocks, and create a 5-asset portfolio (k-asset portfolio) out of 10 assets for each randomly selected 10-asset portfolio. Displays the histogram distribution by calculating the Sharpness index for the number of all selected cases

-Step 3: Verify hypothesis from the result of Step 2

(Experiment data)

-Period: 2016.01.01. ~ 2017.01.02.

-Number of assets: 100

(Experiment result)

-The histogram distribution of the Sharp index for 25,200 5-asset portfolios randomly generated from 100 stocks is shown in FIG. 5.

-The composition of the 10-asset portfolio and the sharp index (some cases) by 10-asset portfolio are shown in Figure 6.

-The histogram of the Sharp index for 2,000 10-asset portfolios was shown in FIG. 7.

-The sharp index for each 10-asset portfolio and the histogram of the five-asset portfolio generated from the corresponding 10-asset portfolio were shown in FIGS. 8 to 15 (in some cases).

The maximum and minimum distributions of the Sharpness index of the 5-asset portfolios generated from each of the 2,000 as 10-asset portfolios are shown in FIG. 16.

The ratio distribution of the 5-asset portfolio with a sharp index greater than the 10-asset portfolio among the 5-asset portfolios generated from each of the 10-asset portfolios is shown in FIG. 17.

(Analysis of experimental results)

-As shown in Figs. 8 to 15, a significant number of 5-asset portfolios having a high sharp index were present compared to the sharp index of each 10-asset portfolio.

-As shown in Figs. 16 and 17, a significant number of 5-asset portfolios with a high Sharpness index existed compared to the Sharpness index of the entire 10-Asset portfolio.

Therefore, for any P, the hypothesis that P ⊃ Q, Q with sp <sq is sufficiently present has been demonstrated.

<Experimental Example 2>

(Experiment contents)

-Step 0: Find all possible portfolios-> After obtaining the total number of 5-asset portfolios for 100 assets, the ranking for the top 1% was saved ( ₁₀₀ C ₅ = 75,287,520, top 1.3%: 1 million) .

-Step 1: 25,200 5-asset portfolios were obtained from 100 assets by Monte Carlo Method (MC) (Case A), and 2,000 10-asset portfolios were obtained from 100 assets by MC (Case B).

-Step 2: In Case A, the maximum (max), minimum (min), average (average) and standard deviation (sd) of the whole are calculated and replaced with 75,287,520 distributions in total, max, 252 for the top 1% min, average, and sd were respectively obtained.

-Step 3: In Case B, a 5-asset portfolio (252x100 = 25,200) for the top 5% (100) was obtained, followed by max, min, average, and sd for the top 1% of 252.

-Comparison of the results of Step 2 and Step 3 (max, min, average, sd and histogram distribution)

(Experiment result)

-The Sharp index statistics and distribution for the top 1.3% (1 million) portfolio obtained in Step 0 were as shown in FIG. 18.

-The Sharp index statistics and histogram distribution for the entire portfolio of Case A and Case B (25,200 each) obtained in Step 1 were as shown in FIG. 19.

-Sharp index statistics and histogram distribution for the top 1% portfolios of Case A and Case B (252 each) obtained in Step 2 and Step 3 were as shown in FIG. 20.

-The numbers and ratios included in the 5-asset portfolio of the top 1.3% (1 million) of the entire portfolio of Case A and Case B (25,200 each) obtained in Step 1, obtained in Step 0, are as shown in FIG. 21.

(Analysis of experimental results)

-Compared to Case A (5-asset portfolio), Case B (10-asset portfolio-> 5-asset portfolio) has significantly improved the overall sharpness index and histogram distribution.

-Compared to Case A, the top 1% Sharp Index statistics and histogram distribution of Case B also improved significantly.

-The number included in the top 1.3% (1 million) was significantly higher in Case B than in Case A.

Although the present invention has been described in various examples, the present invention is not necessarily limited to these examples, and may be variously modified without departing from the spirit of the present invention. Therefore, the examples disclosed in the present invention are not intended to limit the technical spirit of the present invention, but to explain, and the scope of the technical spirit of the present invention is not limited by these examples. The scope of protection of the present invention should be interpreted by the claims below, and all technical thoughts within the equivalent range should be interpreted as being included in the scope of the present invention.

Claims (3)

As a method of selecting portfolio assets performed by an information system,
Based on n assets, a c * k-asset portfolio consisting of the number of assets (c> 1) times the number of assets (k) to be selected as a portfolio is created, but m c * k-assets are sampled by Monte Carlo Method Creating a portfolio;
Calculating a Sharpe ratio for each of the m c * k-asset portfolios;
Selecting an r% c * k-asset portfolio whose Sharpe ratio corresponds to the top r% among the m c * k-asset portfolios;
Based on the assets included in each of the r% c * k-asset portfolios, a k-asset portfolio consisting of the number of assets (k) to be selected as the portfolio is generated, but the r% c * k-asset portfolio is generating p k-asset portfolios to calculate Sharpe ratios for each;
For each of the r% c * k-asset portfolios, selecting a each of the p-k-asset portfolios in order of highest Sharpe ratio to make a top k-asset portfolio; And
Selecting b k-asset portfolios as a recommended portfolio by arranging them in order of high Sharpe ratio for all of the top k-asset portfolios; Characterized in that it comprises, Monte Carlo genetic algorithm portfolio asset selection method using According to claim 1,
The p number is the number of k-asset portfolios for all cases that can be generated for each of the r% c * k-asset portfolios, the method of selecting portfolio assets using the Monte Carlo genetic algorithm According to claim 1,
Wherein p, the r% c * k-asset portfolio for each of the portfolio using a genetic algorithm, characterized in that the number of k-asset portfolio generated until the closing condition, Monte Carlo genetic algorithm portfolio asset selection method using

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