The figure 2 is a separate cumulative yield curve for HS300 to compare with the cumulative yield of our portfolio.

Figure 2

3.1.3 Measuring the risk of stock por1tfolio

The figure 3 shows the correlation coefficient of each stock, with values from - 1 to 1. Positive numbers represent positive correlation and negative numbers represent negative correlation.

Figure 3

The table 2 is the covariance matrix for each stock:

The risk of portfolio can be expressed by standard deviation, which is calculated as follows:

Table 2

3.1.4 Building effective portfolio boundariesand confirm the minimum risk weight

The essence of investment is to choose between risk and return, which are depicted in the figure above. Each of these points represents a portfolio situation, the abscissa represents the standard deviation of risk, and the ordinate represents the yield. According to Markowitz's portfolio theory, rational investors always maximize the expected return at a given level of risk, or minimize the expected risk at a given level of return. Reflected in the figure 4 is the peripheral curve of the figure, which is the effective boundary. Only the points on the effective boundary are the most effective portfolio.

Figure 4

The red dot in the figure 5 is the minimum risk portfolio, i.e. the minimum volatility.

Figure 5

Obtain the weight of the minimum risk portfolio as follows:

3.1.5 Building the best portfolio

We first calculate the sharpness ratio corresponding to the above Monte Carlo simulation combination, and take it as the third variable in the profit risk scatter diagram, and use the visual clues of color to express the sharpness ratio, as shown in the figure 6.

Figure 6

We find that the combination of the scattering upper edge has a high sharpness ratio. Then find out the combination with the largest Sharpe ratio, and draw it in the income risk distribution chart. The red dot in Figure 7 is the combination with the largest Sharpe ratio.

Figure 7

Get the weight of the largest combination of Sharpe ratios in the table 3:

Table 3

3.2 Evaluation of volatility of returns using GARCH model.

This paper studies the volatility of portfolio return based on ARMA-GARCH model, but all ARMA models imply the hypothesis of sequence stability. According to the time series observation chart, it can be temporarily determined as a stationary non white noise sequence. ARMA and GARCH models both require the time series data to be stable, so it is necessary to test the unit root of the return series to further judge the stability of the return series. The results show that there is no obvious time trend around the horizontal axis, so the ADF test without intercept and time trend is selected. Meanwhile, in order to prevent the return series from being heteroscedasticity series, PP test is carried out on the series. The results of ADF test and PP test are shown in Table 2. Whether ADF test or PP test yield series R rejects the original hypothesis at 1% significance level and accepts the original hypothesis without unit root, so it can be determined that the yield series is a stable series.

3.2.3.2 Autocorrelation test

After getting a stable sequence, we need to select a suitable model to fit the observed value sequence by examining the properties of the sample autocorrelation coefficient and partial autocorrelation coefficient of the sequence. Figure 9 shows the sample autocorrelation graph and partial autocorrelation graph of the yield sequence.

From Figure 8, we can see that autocorrelation coefficient and partial autocorrelation coefficient show the property of no truncation, so we try to use ARMA (p, q) model to fit the sequence. In this paper, the maximum likelihood estimation is used to estimate the parameters of the mean equation, and the order of the model is determined according to AIC and SBC criteria, so that we can establish the optimal mean equation of GARCH model. When p = 1, 2, q = 1, 2, the parameter estimation results of the mean equation are shown in Table 5. It can be seen from table 3 that ARMA (1, 2) model is significant, and other models are not significant. Formula (3) is ARMA (1,2) model constructed by Eviews software. After determining the order of the model, we need to estimate the parameters of the model and test the model to avoid the lack of validity of the model.

formula 6

Figure 9

3.2.4 Test of conditional heteroscedasticity and GARCH Modeling

3.2.4.1Arch effect test

After using the maximum likelihood estimation to get the mean equation of the model, we also need to test the heteroscedasticity of the square of the return residual sequence, and then get the conditional variance equation. The conditional heteroscedasticity is the arch effect. In this paper, the arch test results of lag order 1 to 5 are selected, as shown in Table 6.It can be seen from table 6 that the P values corresponding to lag terms of order 2 to 5 are all 0, so the original hypothesis is rejected, indicating that arch effect exists in the residual sequence.

After confirming that the equation contains arch effect, try to use GARCH model to fit the heteroscedasticity function with long-term memory. Therefore, the ARMA (1,2) - GARCH (P, q) model is fitted from P = 1, q = 0. After comparison, we can conclude that GARCH (1,1) model is a more suitable model.

formula 7

Then, we test the correlation of residual errors of the model, and the results are shown in Figure 10. It shows that the residual sequence of GARCH (1,1) model is uncorrelated, Both autocorrelation coefficient and partial autocorrelation coefficient are about 0, Q statistic is not significant, which could find that no arch effecthere in the residual sequence.

Figure 10

According to GARCH (1.1) model, the maximum coefficient of GARCH term is 0.988. From the results of significance test, we can see that the model can be regarded as passing the significance test. So we can get that the stock price has the characteristics of "long-term memory". In other words, the price fluctuation of our portfolio in the early stage has a certain impact on the price fluctuation in the later stage; at the same time, we can conclude that the return rate has a high risk premium phenomenon. The equivalent expression is that the greater the portfolio volatility, the greater the risk and the higher the yield. In addition, the coefficients of arch and GARCH terms in the variance equation are significantly positive. It can be concluded that the past volatility has a positive moderating effect on the future volatility, making the portfolio volatility appear "aggregation" phenomenon. The sum of the coefficients of arch and GARCH is 0.987, which is very close to 1. It shows that the conditional variance has the characteristics of long-term memory, that is, the portfolio volatility has a high persistence.

3.3 Forecasting stock prices based on the random walk model.

We selected the closing price data of the portfolio from TheChoice terminal.

The time span is fromJanuary 1, 2017 to April 22, 2020. There are 1033 data. We used 723 data as training sets and the rest 310 data as test sets.

The stock price trend in the last310 days is as follows:

Figure 11

When walking randomly to simulate 5 paths, as shown in the figure 12:

Figure 12

When walking randomly to simulate 15paths, as shown in the figure 13:

Figure 13

When walking randomly to simulate 50paths, as shown in the figure 14:

Figure 14

We can find that in the three Monte Carlo simulation processes, the simulation effect is not very ideal, the actual price of the stock index has the trend of regression mean, which is similar to the characteristics of random walk. However, the price of portfolio does not have the trend of regression mean value, which is quite different from the simulated price.

3.4 Estimate expected stock return using one-, three- and five- factor CAPM models

We use factor data of Fama French in CSMR database.

The factorsare calculated in table7:

We first test the stability of RIF and the results are shown in the table 8:

Table 8

The regression results of the one ,three, five factors are shown in the figure 15,16,17:

Figure 15

Figure 16

Figure 17

The measurement indicators of forecast results are shown in Table 9:

We can conclude that the five factor model has significant explanatory power and the smallest error.

3.5 Findings

1.The yield of our portfolio is higher than that of HS300. So we can show that our investment strategy is effective. Additional expected benefits can be achieved.

2.GARCH model can describe the volatility of portfolio, and its volatility has high sustainability.

3.The effect of random walk to simulate the price trend is not very ideal, and the price of portfolio has no obvious trend of regression mean.

4.CAPM five factor model has significant explanatory power and minimum error.

Conclusion

This paper constructs a portfolio based on three dimensions: core technology, business model and business performance. Then we use GARCH model to capture the risk. Finally, we use random walk model and CAPM one factor three factor five factor model to predict the stock price. The results show that the yield of our stock selection strategy is better than the benchmark index in a given period of time, and we also find that GARCH model can express the volatility of our portfolio. As for the stock price forecasting model, we find that CAPM five factor model has better performance.

The disadvantage of this paper is that our stock selection model is based on the industry research and financial statement analysis of the secondary market, not combined with new tools, such as machine learning. Similarly, our prediction model does not use machine learning model.

Therefore, our future direction will be to use machine learning model to establish transaction strategy and realize automatic transaction behavior.

Reference

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Appendices

the statistical description of the yield series shows in the fogure 18.

Figure 18

ADF PP test shows in the table 10

Table 10

ARMAtest result shows in the table 11

Table 11

Predict result when use CAPM 1 factor shows in the fogure 19

Figure 19

Predict result when use CAPM 1 factor shows in the fogure 20:

Figure 20

Predict result when use CAPM 1 factor shows in the fogure 20.

Figure 21

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