trading strategies based on bs

• Research
• Open Access
• Published: 25 March 2022

Research on a stock-matching trading strategy based on bi-objective optimization

Frontiers of Business Explore in China volumedannbsp;14, Articledannbsp;number:8 (2020) Cite this clause

Pinch

In recent years, with self-abnegating domestic business enterprise supervision and other policy-oriented factors, some products are becoming increasingly restricted, including substandard products, bank-guaranteed riches management products, and other products that can offer investors with a more stable income. Pairs trading, a type of stabilized strategy that has proved businesslike in many financial markets cosmopolitan, has become the concenter of investors. Based connected the traditional Gatev–Goetzmann–Rouwenhorst (GGR, Gatev et Alabama., 2006) strategy, this paper proposes a unoriginal-coordinated strategy based on atomic number 83-object quadratic programming with quadratic constraints (BQQ) model. Under the precondition of ensuring a long-terminus sense of equilibrium 'tween matched-stock prices, the volatility of stock spreads is increased as much as come-at-able, improving the profitability of the strategy. To verify the effectiveness of the scheme, we expend the natural logs of the daily stock marketplace indices in Shanghai. The GGR model and the BQQ model proposed in this paper are back-reliable and compared. The results show that the BQQ fashion mode can attain a high rate of returns.

Introduction

Since the A-share margin trading system opened in 2010, at that place has been a gradual melioration shortly gross revenue of stock index futures (Wang and Wang 2022) and investors are again favoring prudent investiture strategies, which let in pairs-trading strategies. Atomic number 3 a sort of statistical arbitrage strategy (Bondarenko 2003), the essence of pairs trading (Gatev et alii. 2006) is to discover wrongly priced securities in the market, and to chastise the pricing through trading agency to earn a profit from the spreads. However, with the gain in statistical trading strategies and the gradual improvement of market efficiency (Hu et al. 2022), net profit opportunities using existing trading strategies own become more scarce, driving investors to seek new trading strategies. At attending, academic research on pairs trading has mainly concentrated on the construction of pairing models and the optimization design of trading parameters, with a greater focus on the last mentioned. However, merely rising trading parameters does not guarantee a spiky return for the strategy, and this drives researchers back to the foundations of the pairs-trading model.

There are threesome main methods for screening stocks: the borderline distance method, the cointegration pairing method, and the random spread method. The minimum distance method was proposed by Gatev et al. (2006)—thence its common name, the GGR model. Gatev et al. (2006) used the space of a price series to measure the correlational statistics 'tween the price movements of two stocks. When making a specific transaction, the strategy user determines the trading signal by observing the magnitude of the change in the Euclidean distance 'tween the normalized cost series of two stocks (the sum of the squared deviations, or SSD). Perlin (2007) promoted GGR as a united method rather than a pluralistic nonpareil; testing it in the Brazilian financial market, he found that risk nates be lessened by increasing the number of pairs and carry. Do and Faff (2010) found that the duration of a trading period can buoy feign strategy returns; their study laid the initiation for later search. Jacobs and Weber (2011) found that the GGR model's revenue comes from the divergence in the stop number of paired-stock information diffusion. Chen et al. (2017) revised the mensuration method of the GGR posture, changing the original metre (SSD) to the correlation coefficient, and increased the reliability of the multi-pairing strategy. Shanghai dialect and Cui (2011) first applied the GGR model to the A-share commercialize; conducting a back-test happening the stock markets in Shanghai, they recovered that the GGR model tail generate hefty returns, and its net profit seed from a market's non-validity. Wang and Mai (2014) sounded the return happening stock markets in Impress, Shenzhen, and Hong Kong respectively, and found that improvements to the germinal approach fundament take portfolio construction strategic benefits just can also increase the risk of victimisation of the GGR model.

The cointegration pairing method was first used by Vidyamurthy (2004) to find stock pairs with a cointegral kinship. He old cointegrating vectors every bit the weight of pairs when trading. To solve the trouble of single-stock conjugation risks, Dunis and Ho (2005) elongated the cointegration method from unitarism to pluralism and proposed an enhanced index strategy based on cointegration. By extracting sparse mean–render portfolios from multiple time serial, D'Aspremont (2007) found that bantam portfolios had lower transaction costs and higher portfolio interpretability than the original intensive portfolios. Peters et aluminum. (2010) and Gatarek et al. (2014) applied the Bayesian process to the cointegration test and found that the pairing method stern embody applied to high-frequency information.

The stochastic spread method first appeared in a paper aside Elliott et al. (2005), who used the continuous Gauss–Markov good example to describe the mean return process of paired-strain spreads, thus theoretically predicting stock spreads. Supported the research by Elliott et alibi. (2005). Exercise et al. (2006) first linked the capital asset pricing model (CAPM) with the pairs-trading strategy and achieved a higher strategic benefit than when using the traditional random spread method acting. Bertram (2010), assuming that the price differences of ancestry obey the Ornstein–Uhlenbeck process, derived the expression of the mean and variance of the strategic replication on the put across and found the parameter value when the expected income tax return was maximized.

Based on above approaches, many scholars take over begun to study assorted multistage pairing-trading strategies. Miao (2014) added a correlation screen to the traditional cointegration method acting and found that screening stock-correlation analysis improved the gainfulness of the scheme. Xu et al. (2012) combined cointegration pairing with the stochastic spread model and conducted a back-test on the stock markets in both Shanghai and Shenzhen; they set up that higher returns could be obtained. Following Bertram's (2010) research, Zhang and Liu (2017) examined a pairs-trading strategy supported cointegration and the Ornstein–Uhlenbeck process and found the strategy to atomic number 4 robust and profitable.

In Recent epoch old age, to the highest degree scholars have focused on improving the polysyllabic-full term counterbalance of opposite-store prices in the stock-matching process continuously. Few studies have considered the low-set-term fluctuations of paired-stock spreads, which has light-emitting diode to poor profitableness of the strategy. Therefore, this paper focuses happening the stock matching of pairs trading and constructs a bi-objective optimized stock-matching scheme supported the traditional GGR model. The strategy introduces weight parameters, conducts long-term stock price volatility spreads, and adjusts the equalizer to peer investors' preferences, enhancing the flexibility and practicality of the strategy.

The residue of this paper is reorganised every bit follows. Basic theory and mould section provides the basic theories and models of pairs-trading strategies and double atomic number 83-objective optimisation. Optimized coupling model segment establishes an optimized mating model. Pairing strategy verifiable analysis section provides an empirical analysis of the optimal matching strategy projected in this paper. Finally, Conclusions section presents conclusions and suggests future research direction.

Fundamental theory and model

Based happening theories of pairs trading, stock-mating rules in the minimum distance method, and multi-oblique case computer programing, we purport a strategy to improve profits based on the minimum aloofness method acting.

Pairs trading

Pairs-trading parameters

Using a pairs-trading strategy requires a focalize on the following trading parameters:

• Formation period: the time musical interval for stock-pair cover using the stock-matching strategy.

• Trading period: the time interval in which selected stock pairs are utilized for actualised trading.

• Configuration of opening: the treasure of the portfolio grammatical construction triggered. For example, we can offse a transaction by satisfying the pursual conditions: (1) The drug user is in the abruptly office state; (2) the degree to which the paired-blood line spread deviates from the mean changes; and (3) the degree changes from less than a given standard deviance to more a given standard deviation.

• Final verge: the value of the position closing triggered. For example, when the strategy exploiter is in position and the paired-stock spread hits the mean.

• Stop-release brink: the value of the blockage-loss triggered; that is, when the rules are engaged for exiting an investment after reaching a upper limit acceptable room access of expiration or for re-entering after achieving a specified level of gains.

Minimum distance method

When using the minimum aloofness method to concealment stocks, it is needful to standardize the stock Leontyne Price serial publication maiden. Suppose the monetary value sequence of stock A in period T is \( {P}_i^A\left(i=1,2,3,\dots, T\right) \); \( {r}_t^A \) is the daily rate of return of stock A. By compounding r, we can get the cumulative rate of restitution of stock A in period T, which is recorded as:

$$ C{P}_t^A=\prod \limits_{i=1}^t\left(1+{r}_t^A\right), $$

(1)

where t = 1, 2, 3, …, T. When we record the standardized bloodline price series as \( S{P}_t^A \), the aloofness SSD of to each one two-Malcolm stock normalized monetary value series can atomic number 4 deliberate as follows (Krauss 2022):

$$ SS{D}_{AB}=\sum \limits_{t=1}^n\left(S{P}_t^A-S{P}_t^B\right). $$

(2)

Multi-objective programming

The multi-objective optimisation job was first proposed by economist Vilfredo Pareto (Deb and Sundar 2006). It agency that in an actual problem, there are several objective functions that need to be optimized, and they often conflict with each other. In general, the multi-objective optimization problem can be left-slanting as a plurality of objective functions, and the restraint equation and the inequality can be expressed as follows:

$$ \Min dialect F(x)=\left[{f}_1(x),{f}_2(x),\cdots, {f}_v(x)\right], $$

(3)

$$ s.t.{g}_i(x)\le 0,i=1,2,\cdots, p, $$

(4)

$$ {h}_j(x)=0,j=1,2,\cdots, q, $$

(5)

where, x∈R ^u , f _i  :R ⁿ  →R(i = 1, 2, ...,n) is the objective function; and g _i  :R ⁿ  →R and h _i  :R ⁿ  →R are constraint functions. The feasible domain is given as follows:

$$ X=\left\{x\in {R}^u|{g}_i(x)\le 0,i=1,2,\cdots, p;{h}_j(x)=0,j=1,2,\cdots, q\good\}. $$

(6)

If there is not an x∈X, so much that

$$ f(x)\le f\far left({x}^{\ast}\right), $$

(7)

and then x ^∗ ∈X is called an effective solution (Bazaraa et al. 2008) to the multi-objective optimisation problem.

Optimized coupling model

Previous studies on the GGR model have got mostly focused on similarities available trends and take over cared less almost the excitability of stock spreads. Much studies could not present ways to achieve higher returns. This paper, however, is founded on the traditional GGR model, and posterior thus propose a new pairs-trading model, namely bi-object number programming with quadratic constraints (BQQ) fashion mode. By adjusting the weights between maintaining a long-term equipoise of paired-stockpile prices and accretionary the volatility of stock spreads (James Abbott McNeill Whistler 2004), we can attain equilibrium.

Mean-variance minimization space modeling

Bear that there are m stocks in the alternative stock pool, and the formation period of the stock pairing is n days. Take the daily closing price of the sprout as the unconventional price series, recorded as P ₁, P ₂, ⋯, P _m . To make the price sequence smoother, we usance the average price serial publication over the past 30 days: \( \overline{P_1},\overline{P_2},\cdots, \overline{P_m} \) (instead of the original price series), to eliminate short-term fluctuations in carry prices. Then, in the second, t can be expressed as follows:

$$ \overline{P_{i,t}}=\frac{1}{30}\total \limits_{j=0}^{29}\overline{P_{i,t-j}},t=1,2,\cdots, n. $$

(8)

First we consider \( \sum {\of import}_i\overline{P_i} \).

Let α personify the weight of the stock in the stock pool, and then get

$$ \Big\{{\displaystyle \begin{array}{l}{\explorative}_i^{+}={\exploratory}_i\left({\of import}_idangt;0,i=1,2,\cdots, n\right)\\ {}-{\alpha}_i^{-}={\alpha}_i\socialistic({\alpha}_idanlt;0,i=1,2,\cdots, n\right)\end{array}}. $$

(9)

Then, we carve up the stock into two groups according to the positive and perverse weights. The stock certificate combination with a positivist weight is called \( {P}_t^{+} \), patc the stock combining with a unfavorable weight is called \( {P}_t^{-} \), so

$$ \Big\{{\displaystyle \begin{array}{l}{P}_t^{+}=\sum {\important}_i^{+}\overline{P_{i,t}}\\ {}{P}_t^{-}=\core {\alpha}_i^{-}\overline{P_{i,t}}\end{array}}. $$

(10)

Accordant to the GGR method acting, every bit sesquipedalian as we are in the formation period n, we bathroom consider that the groups' prices consume to make up a long-term vestibular sense relationship. Therefore, we get the bismuth-objective optimization model American Samoa follows:

$$ \min \sum \limits_{t=1}^n{\left(\sum \limits_{i=1}^m{\alpha}_i\overline{p_{i,t}}\right)}^2. $$

(11)

The volatility of the paired-stock spread is a source of tax income for the pairs-trading strategy. Variances are used to describe the volatility of a time series. Thus, we use the formula below to measure the stock spread:

$$ \max \frac{1}{n}\tot \limits_{t=1}^n{\socialistic(\sum \limits_{i=1}^m{\alpha}_i\overline{p_{i,t}}-\frac{1}{n}\sum \limits_{t=1}^n\sum \limits_{i=1}^m{\alpha}_i\overline{p_{i,t}}\right)}^2. $$

(12)

Avoiding the case that α = 0, we increase the regularity restraint; that is, the second-order modulus is 1, so we can obtain the BQQ model as:

$$ \min \sum \limits_{t=1}^n{\left(\sum \limits_{i=1}^m{\alpha}_i\overline{p_{i,t}}\right)}^2,\easy lay \frac{1}{n}\sum \limits_{t=1}^n{\left(\sum \limits_{i=1}^m{\alpha}_i\overline{p_{i,t}}-\frac{1}{n}\sum of money \limits_{t=1}^n\nitty-gritt \limits_{i=1}^m{\of import}_i\overline{p_{i,t}}\right)}^2. $$

(13)

$$ s.t.\marrow \limits_{i=1}^m{\of import}_i^2=1. $$

(14)

This newspaper publisher uses a linear weighting method by introducing burden λ(λ dangt; 0), transforming the bi-objective optimization job into a single-objective optimization problem. The model is denoted atomic number 3 altered quadratic programming with quadratic constraints (RQQ):

$$ \min \heart and soul \limits_{t=1}^n{\left(\sum \limits_{i=1}^m{\alpha}_i\overline{p_{i,t}}\right)}^2-\lambda \frac{1}{n}\sum \limits_{t=1}^n{\left(\sum \limits_{i=1}^m{\alpha}_i\overline{p_{i,t}}-\frac{1}{n}\tot \limits_{t=1}^n\add together \limits_{i=1}^m{\explorative}_i\overline{p_{i,t}}\right)}^2. $$

(15)

$$ s.t.\sum \limits_{i=1}^m{\alpha}_i^2=1. $$

(16)

Since users of the co-ordinated strategy have different risk preferences, λ can be seen as an important indicant of strategic risk. When λ is large, the good example magnifies the volatility of the opposite-stock spread sequence, and the strategy may prevail high returns, but information technology also raises the risk of divergence in the stock spread. Therefore, users privy adjust λ to match their lay on the line preferences, which increases the usefulness of the sexual unio scheme.

Let \( \overline{p}=\frac{1}{n}\sum \limits_{t=1}^n\overline{p_t} \).

To facilitate the model solution, we execute matrix translation American Samoa follows:

$$ f\left(\alpha \right)=n{\explorative}^T\left(\frac{1}{n}\sum \limits_{t=1}^n\overline{P_t}{\left(\overline{P_t}\reactionary)}^T\right)\explorative -\lambda \left[{\alpha}^T\left(\frac{1}{n}\sum \limits_{t=1}^n\overline{P_t}{\left(\overline{P_t}\right)}^T\right)\explorative -{\alpha}^T\overline{P}{\left(\overline{P}\right)}^T\alpha \right]. $$

(17)

That is,

$$ f\left(\important \right)={\alpha}^T\left[\left(n-\lambda \right)\reactionist(\frac{1}{n}\sum \limits_{i=1}^n\overline{P_t}{\odd(\overline{P_t}\right)}^T+\lambda \overline{P_t}{\left(\overline{P_t}\right)}^T\Big]\alpha . $$

(18)

For a conferred α _k , we arrive the hoagie-job of the model as this:

$$ \min {f}_s\nigh({\of import}_k\right)={d}^TH{\alpha}_k+\frac{1}{2}{d}^T Hd. $$

(19)

$$ s.t.2{d}^T{\alpha}_k+{\alpha_k}^T{\alpha}_k-1=0. $$

(20)

The sequential quadratic programming algorithm

Since the objective and constraints of RQQ are quadratic functions, these are typic nonlinear computer programming problems. Therefore, the sequential quadratic computer programming algorithm can solve the creative problem by solving a series of quadratic programming sub-problems (Jacobs and Ernst Heinrich Weber 2011; Zhang and Liu 2022). The solvent process is as follows:

• Step 1: Give α ₁∈R ^m , ε dangt; 0, μ dangt; 0, δ dangt; 0, k = 1, B ₁∈R ^m ×m .

• Step 2 : Solve sub-question pigboat(α _k ), and we obtain its solution d _k and the Lagrange multiplier factor μ ^k in the case of ∣ d ^k ∣  ≤ε, terminating the iteration; therefore, let s _k ∈ [0,δ] and μ =maxdannbsp;(μ,μ ^k ). By solving this:

$$ P\left({\alpha}_k+{s}_k{d}_k,\mu \right)\le \underset{0\lupus erythematosus s\le \delta }{\mathit{\min}}P\socialist({x}_k+\alpha {d}_k,\mu \decently)+{\varepsilon}_k, $$

(21)

we obtain s _k, where ε _k (k = 1, 2,⋯) satisfies the non-negative discipline and

$$ \sum \limits_{k=1}^{\infty }{\varepsilon}_kdanlt;+\infty . $$

(22)

Equating (21) is the exact penalty officiate.

• Tread 3: Let α _k + 1 =α _k  +s _k d _k , and use the Broyden–John Fletcher–Goldfarb–Shanno algorithm (BFGS, Zhu et al.. 1997) to find B _k + 1, then countenance k =k + 1 and pass away back to Step out 2.

Thence, we discovery the optimal sub-solution d _k . Make d _k the search management and execute a one-dimensional search in direction d _k on the exact penalty function of the first problem; we get the incoming iteration point of the original job every bit α _k + 1. The iteration is terminated when the iteration point satisfies the given accuracy, obtaining the optimum solvent of the original problem.

Coupling strategy empirical analysis

To control the profitability of the BQQ strategy, this wallpaper compares the empirical investment effects of the BQQ scheme and the GGR strategy with the same transaction parameters and applies a profit-risk test for the arbitrage results of the two strategies.

Data selection and preprocessing

We use SSE 50 Index constituent stocks in the Shanghai shopworn market as the sample distribution set for this study. We choose this sample set for its high circulation market price and large market capitalizations. Since the gillyflower-pairing method acting proposed therein paper is supported an improvement of the traditional negligible distance method acting, this is consistent with the GGR fashion mode in the time interval selection of the try out: The paired stocks for trading are selected during the formation period of 12 months, and the stocks are listed in the next 6 months. To verify the effectiveness of the strategy, the paper conducts a plan of action back-test from Jan 2022 to December 2022. Within the period, the broader market experienced a complete set of ups and downs.

Due to the existence of plowshare allotments and contribution issues by catalogued companies, and because the suspension of stocks testament also conduce to a want of market data, the raw information needs to be preprocessed. By reversing the stock price overfamiliar, the stock Leontyne Price changes caused by the allotments and stock offerings are eliminated. In addition, we exclude stocks that ingest been suspended for much 10 days in the formation period. These missing data are replaced by the closing price of the nearest trading sidereal day.

Parameters settings

Transaction parameters setting

The carrying out of a pairs-trading scheme relies on setting trading parameters. To compare this strategy with the time-honored minimum distance method and affirm the cogency of the BQQ scheme, this paper uses the same parameters victimized in the GGR model for setting the trading parameters. We set the period-red ink threshold to 3 to prevent excessive losings due to excessive strategy losings and transaction costs. We arrange the number of paired shares to 10. For convenience, we water parting the stocks into groups according to their weights, positive and disinclined.

Portfolio construction

Later determining the trading parameters and cost parameters, we as wel need to determine the stock opening method; assuming that the final selected pair of stocks is \( \left\{{S}_1^{+},{S}_2^{+},\cdots, {S}_5^{+}\starboard\},\left\{{S}_1^{-},{S}_2^{-},\cdots, {S}_5^{-}\far\} \) (corresponding to two sets of mated stocks), and the corresponding weight is \( \left\{{\alpha}_1^{+},{\alpha}_2^{+},...,{\alpha}_3^{+}\right\} \) and \( \left\{{\alpha}_1^{-},{\alpha}_2^{-},...,{\important}_3^{-}\right\} \). When the trading strategy issues a trading betoken for initiatory, closing, or period-loss, the trading begins. The user necessarily to trade α _i /α ₁(i = 2, 3, 4, …, 10) units of stock \( \left\{{S}_1^{-},{S}_2^{-},\cdots, {S}_5^{-}\right\} \) for each unit of \( \left\{{S}_1^{+},{S}_2^{+},\cdots, {S}_5^{+}\right\} \). Then, the strategy user has a net status, which is the paired-stock spread.

Functioning evaluation

To compare the effects of the GGR model and the proposed BQQ model, we verify the effectiveness of the proposed optimization pairing strategy. This composition selects the income coefficient α, risk coefficient β, and the Sharpe ratio every bit evaluation indicators, and the 2 strategies are back-tested and compared happening the JoinQuant chopine.

Timeworn-duplicate stage

When adopting the GGR model, we select five groups of stocks with the smallest SSD (2 in from each one grouping) from each formation period. There is a small distance between these stocks. The stocks are selected from 50 constituent stocks. The matching results are shown in Tabledannbsp;1. When adopting the BQQ model, since the trend of the regular was screened beforehand, we select two sets of stocks (five in to each one group) for pairing. To research the impact of λ on scheme execution, we perform a stake-test on the optimum matching strategy under different values (when λ is greater than 0.7, the paired-stock spread is relatively poor, resulting in a strategy failure). Therefore, this newspaper is limited to a λ range from 0 to 0.7. The pairing results are shown in Shelvedannbsp;2.

Table 1 GGR model carry matching results

Full size table

Table 2 BQQ model stock matching results

Full size table

Arsenic can be seen in Tabular array 2, when λ changes from 0 to 0.4, the selected blood pairs show a very dramatic work change; when λ changes from 0.4 to 0.6, the hand-picked stock pairs are almost identical. At that time, the change of λ cannot significantly impact the return; when λ changes from 0.6 to 0.7, the elect stock pairs switch less. However, the positives and negatives of the matched-threadbare weights have changed. Therefore, compared with the GGR model, the optimized pairing strategy makes better use of timeworn price selective information and is more flexible.

Stock trading stage

The GGR model and the BQQ model use the same parameters kick in the back-examination. The trading period is 2022.01–2016.12. The results obtained are shown in Proroguedannbsp;3. By comparing the back-prove performance of the BQQ strategy with the GGR model, we reach five findings:

1. (1)

   The ability of the BQQ strategy to obtain revenue is significantly stronger than of the GGR model, which shows that the BQQ strategy is effective in increasing the volatility of the spread to improve the profitability of the pairs-trading scheme.

Postpone 3 BQQ strategy performance

Full sizing table

Estimatedannbsp;1 shows the average annualized rate of restoration of the BQQ strategy and the GGR strategy for different λ values (some in-sampling data and out-of-sample data, severally). For the in-sample rate of return, both strategies were carried out for a total of 32 backwards-tests, with a tally of 31 positive gains. The come back of the BQQ strategy is better than that of the GGR strategy in 87.5% of the cases. For the out-of-sample rate of recall, the recurrence of the BQQ strategy is better than that of the GGR scheme in 68.8% of the cases. To eliminate the deviation of income caused by the diametric ways of opening a position, we also demand to try the coefficient of the deuce strategies and the Sharpe ratio.

FIG. 1

Average annualized charge per unit of return of the two strategies

Full size image

Equally shown in Figs.dannbsp;2 and 3, the BQQ simulation performs significantly better than the GGR mold, both in damage of the coefficient α and the Sharpe ratio. This result indicates that the BQQ framework bears the average return of nonmarket risk during the four trading periods, and the average repay on unit risk is higher than with the GGR model. Therefore, the better perfomance of the BQQ strategy is not from the strategy attractive more commercialize risk; rather, information technology is independent of the way the strategy is opened.

Fig. 2

Coefficient α of the two strategies

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Libyan Fighting Group. 3

Sharpe ratio of the two strategies

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1. (2)

   The BQQ strategy has a strong ability to hedge the market. Tabledannbsp;4 shows the average value of the coefficient β of the BQQ strategy under different values of λ. It can be seen that the absolute value of β is below 0.1, which indicates and proves that the performance of the strategy is not affected by market fluctuations, which in turn proves that the pairs-trading strategy based on the minimum distance method can duck market risk well. Compared with the GGR model, the coefficient β of the BQQ strategy is magnified because the GGR posture uses a capital-neutral border on when in the gap situation, while the BQQ strategy uses a coefficient-neutral approach. Due to the creation of the spread, the BQQ strategy cannot guarantee that the marketplace value of the bought stock will live equal to the market value of the sold stock when the position is opened, which is equal to the fact that some net positions follow market ups and downs and the coefficient will increase.

Table 4 Coefficient β of the two strategies

Full sized table

1. (3)

   Similar to the GGR model, the BQQ strategy performs poorly in out-of-sampling data. In the 32 out-of-sample gage-tests, the annualized issue of the BQQ scheme was overconfident only six times, and the coefficient α was positive only eight times. The main reason for this phenomenon is the lack of rationality in the length of the formation stop used at the line of descent-coordinated stage and the trading parameters used in the neckcloth-trading stage. The yield of the GGR model is affected by trading parameters in many cases, such as the formation period, trading period, and introductory verge. Since this article presents only a methodological improvement for the stock-coupling trading exemplar, it does not provide a more in-depth study of trading parameters.

2. (4)

   Performance of the BQQ strategy is very sensitive to the value of λ. Changeable λ enhances the practicality of the strategy. In the same trading period, the regress of the BQQ strategy does not show a monotonous change with λ. When the value of λ is too large, the stock-matching strategy is unsound because when λ increases, the volatility of the paired-stock spread is increasing, which means that the scheme is in all probability to find higher returns. Conversely, the increase of λ raises the risk of deviation in the spread, devising it easier for the strategy to trigger a stop-loss signal and cause losings. Therefore, λ is a portentous parameter to adapt the risk of the scheme, and the strategy user can adjust λ to match risk preferences, which enhances the usefulness of the strategy.

3. (5)

   The optimal λ respect is time dependent. The profit of the BQQ strategy are non-monotonic changes in λ. Excessive λ forum leads to the invalidation of the stock-matching strategy, which means that for a limited trading period, there is an optimized λ that maximizes the strategy's return. From the perspective of receipts indicators and risk indicators, there are nary obvious rules near the performance of the strategy and the change of λ. That is, the optimal λ valuate varies with the trading full stop and is time dependent.

Tabledannbsp;5 shows the values of coefficient α and the Sharpe ratio from four KO'd-of-sample back-tests. When λ is 0.5, coefficient α and the Sharpe ratio take the maximum esteem at the one fourth dimension.

Table 5 Values of coefficient α and the Sharpe ratio for diametrical λ

Full size of it postpone

The results show that when λ is 0.5, the average matching taxation of the optimized coordinated strategy for non-market risk in the four trading periods and the average return from unit risk are the largest, merely the value needs to be proven aside large data.

Conclusions

Aside introducing multi-target optimization to the GGR model, this newspaper publisher considers the long-term equilibrium of stock prices and the volatility of spreads and establishes a BQQ model. This novel pairs-trading model provides a New perspective for pairs-trading strategy explore. Simultaneously, IT provides investors with a stock-matching method that in effect improves the profitability of the trading strategy. This paper introduces the system of weights λ when solving bi-objective optimization problems, and these problems are transformed into single-objective optimization problems and resolved aside a sequential quadratic programming algorithm. To verify the effectiveness of the optimized coupling strategy, this paper selects the traditional GGR model as modeling for comparison and conducts back-testing on multiple time intervals on the SSE 50 constituents. We find that the BQQ strategy was healthy to obtain significantly higher revenue than the GGR model, and the adjustment of the weight λ increases the flexibility and practicality of the strategy.

This newspaper has any limitations. We used the SSE 50 Indicator as the enquiry target in our empirical analysis. However, this was subject to the limitation of financing and securities loaning; the small add up of stocks may have affected the performance of the trading strategy. To boot, when we performed the cogency break of the optimized pairing strategy, in that location was scarce in-profundity enquiry available on the trading parameters and optimal values of the strategy, and this may have affected the gainfulness of the scheme to few extent. Therefore, subsequent enquiry work should include these aspects. In the future, we volition get ahead the number of stock share pools. In accession, the screening method for the transaction parameter of pairs-trading scheme requires in-profundity research to find the right trading parameters for the BQQ strategy. Finally, we will strain to establish an optimized pairing strategy by attaining the part of endangerment indicator λ through extended falsifiable depth psychology.

Handiness of data and materials

Shanghai Composite Index

Please contact authors for data requests.

Abbreviations

BFGS:

The Broyden–Fletcher–Goldfarb–Shanno algorithm

BQQ:

Bi-objective quadratic programming with quadratic constraints

CAPM:

Capital asset pricing mold

GGR:

The distance approach proposed by Gatev, Goetzmann and Rouwenhorst in 2006

RQQ:

Revised quadratic programming with quadratic constraints

SSD:

Sum of square deviations

SSE:

Shanghai Stock Exchange

References

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Acknowledgements

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Funding

The research is supported by the Fundamental Research Funds for the Central Universities, and the Search Funds of Renmin University of Republic of China (No. 19XNH089).

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1. Patronage School, Renmin University of China, 59 Zhongguancun Street, Beijing, 100872, Mainland China

   Haican Diao,dannbsp;Guoshan Liudannbsp;danA;dannbsp;Zhuangming Zhu

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Diao contributed to the boilersuit writing and the data analysis; Liu planned the idea; Zhu contributed to the data collection and the data analysis. Totally authors read and approved the unalterable manuscript.

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Correspondence to Guoshan Liu.

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Diao, H., Liu, G. danamp; Zhu, Z. Research along a stock-matching trading scheme supported on bi-objective optimization. Foremost. Bus. Res. China 14, 8 (2020). https://doi.org/10.1186/s11782-020-00076-4

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• Received: 09 July 2022

• Accepted: 25 February 2022

• Published: 25 March 2022

• Department of the Interior : https://Department of the Interior.org/10.1186/s11782-020-00076-4

Keywords

• Pairs trading
• Bi-verifiable optimization
• Minimum outstrip method
• Quadratic programming

trading strategies based on bs

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