An Empirical Study on the Non-Linear Relationship between the Performance of Funds and the Cash Flows of Funds

This article takes 152 open-ended stock funds and partial stock funds established before the second quarter of 2015 as samples. Using the regression model of the non-balanced panel data fixed-effect model, this paper discussed the specific impact of the historical performance and other influencing factors on the purchase and redemption of investors from the first quarter of 2013 to the second quarter of 2017. And the nonlinear relationship between fund performance and capital flow is investigated by piecewise linear regression. The empirical results reveal that the fund’s lagging quarterly performance has a positive impact on the funds flow in the next quarter. Investors generally chase performance rather than “reverse selection”, and find that the relationship between historical performance and capital flow is non-linear. The fund flow has different sensitivity to outstanding performance fund, medium performance fund and poor performance fund. Fund flow is most sensitive to outstanding performance funds, followed by the medium performance fund, and insensitive to the poor performance funds. Finally, this paper uses the theory of “principal-agent” to analyze the results, and puts forward suggestions to improve the performance incentive mechanism of China’s fund market.

In the fund market, investors will refer to the fund's historical performance to make a purchase or redemption fund decision. The fund's performance will play a signal role in the market competition. China's open-end funds have a free purchase and redemption mechanism. Rational investors can evaluate fund managers' ability according to fund performance, buy funds with good performance, and redeem funds with poor performance. The "pursuit of performance" rational behavior of investors can enable funds with good performance to obtain capital inflows, increase in scale, and increase management fee income. Funds with poor performance will encounter outflows of funds, scale reduction, and decline in management fee income. The positive feedback between fund performance and capital inflow can generate implicit incentives for fund managers.
The effectiveness of this positive feedback also relates to fund governance and investor interest protection. On the contrary, if the negative relationship between "fund flow-performance" exists, the "paradox of fund redemption" exists.
This will "incentivize" fund managers to pursue the maximization of management fees at the expense of the fund's return on investment, thus seriously damaging the interests of investors. It will seriously damage the interests of investors and cause the "Bad money drives out good money" in fund market, which ultimately has a major negative impact on the sound development of China's fund market [1].
The main contributions of this article are as follows. First, this article uses normative research methods to enrich the research literature on the relationship between capital flow and fund performance, revealing that there is no "paradox DOI: 10 The sixth part is conclusions and advice.

Literature Review
The Western market economy developed earlier and the capital market is highly better performance funds is faster than the fund outflow rate of poor performance funds [5]. Sirri & Tufano (1998) also confirmed the positive correlation between historical fund performance and capital inflows and PFR non-linearity.
Funds with outstanding performance will be sought after by investors and will receive more capital inflows in the next period. However, funds with poor performance will not suffer the same degree of investor abandonment. The outflow of funds in the next period is not obvious [6]. Brown, Harlow & Starks (1996) believe that investors are optimistic about the follow-up performance of poor funds. The PFR mechanism was similar to the call option, which was a convex function [7]. Fant & O'Neal (2000) analyzes the more apparent PFR asymmetry in subsamples of US mutual funds of the market from 1978 to 1987 and from 1988 to 1997. This paper uses the raw return and Jensen Alpha as performance indicators to perform a piecewise linear regression. And establish an elastic indicator of fund flow on fund performance. The study found that the flow of funds does not increase the elasticity of the pursuit of fund performance. A large amount of capital inflows is merely due to the increase in the total funds in the fund market, and not to the increase in investor interest in the fund. In summary, foreign scholars have a more consistent view of the fund's PFR, and generally believe that the graph between them shows a positive convex curve [8].
There are also pointed out that the non-linearities of the fund PFR include as a sample, and regressed monthly panel data. It was empirically found that the "paradox of fund redemption" had fund current performance, but it does not exist for historical performance. The better the fund's historical performance, the more it can attract capital inflows, and the SVAR analysis indicates that there is no disposal effect for investors to redeem. The "paradox of fund redemption" is due to the abnormal behavior of investors' purchase [17]. In the Chinese market, Liu Zhiyuan et al. (2005) have pointed out that the more dividends the more the fund redemption rate is lower, the less obvious the outflow [12]. Lu Rong et al. (2007) found that the stability of returns, fund size, and dividends all affect investors' choices. It is found that investors tend to redeem funds with large returns, low dividends, and large scale [14]. Xiao Jun et al.
where TNA i,t is the total net asset value of fund i in season t, R i,t is the return rate of fund i in season t, and dividend reinvestment is included.
Explanatory variables: The fund performance indicators selected in this paper R i,,t-1 : Lag of a quarter of the raw return (including dividend reinvestment) where P i,t is the net asset value of the fund i at the end of period t, and divident t is the unit equity dividend of fund i at t period At the same time, the market model adjusted return Jensen Alpha as a robustness test, the calculation method is: , , For each fund, using its historical data in the study, estimate β i,,RMRF according to Equation (3), and find that

Control variables:
Fund size-ln(TNA i,t-1 ). The same amount of fund flow affects the small fund much more than the big fund, so it is similar to Sirri and Tufano (1998) [6]. The natural capital of the fund at the end of the previous quarter was ln(TNA i,t-1 ) as the control variable of the fund size.
Fund age-ln(Age i,t-1 ). DelGuercio and Tkac (2001) have found that the number of years of fund establishment is negatively related to financial flows [9]. Therefore, referring to DelGuercio and Tkac (2001), the natural logarithm ln(Age i,t-1 ) of the fund's life span is used as a control variable to control the potential impact of fund age differences on financial flows [9].
Fund family size-ln(FamilySize i,t-1 ). Funds from the big family are more susceptible to investor attention, making it easier to attract capital. This is evidenced by Sirri and Tufano (1998) [6]. Therefore, we use the natural logarithm ln(FamilySize i,t-1 ) manage the total assets to measure the family size.
Standard deviation of fund returns-Std i,t-1 . Foreign research shows that the greater the fund's risk, the smaller the net inflow of funds, in order to control the impact of fund risk on investors' behavior.
Return on Market- The summary statitics of the main variables is shown in Table 2. The ordinal measure is defined as: In each period, the sample fund is sorted by the performance of the lag quarter from small to large, The lowest performance

Preliminary Exploration of the Relationship between Fund Performance and Capital Flow
It can be seen from Table 3   This table examines the overall relationship between fund performance and capital flow, based on the fixed-effect model. The result of the Hausman test is zero, which supports the fixed effect model and negates the stochastic effect model. The explanatory variable is the rank of the raw return of the fund lagging one quarter, while the rank of Jensen Alpha as a robustness test. The first number in each cell is the regression coefficient and the value in parentheses is the associated t-value. ***indicates p < 0.01 **indicates < 0.05 *indicates p < 0.10.

Further Analysis of PFR
According to the literature Feng Xunan (2013) pointed out that the performance of China's fund market poor funds, performance of general funds, and merit funds have a non-linear impact on investors [2]. In order to further analyze the performance of funds and the sensitivity of fund flow, we divide the performance of each quarter (raw return including dividend reinvestment) into 20 groups from the largest to the smallest. The ordinate is the net fund of the corresponding group in the next quarter. The ordinate is the average of the net flow of funds in the next quarter.
It can be seen that the reaction of fund flow to the previous quarter's performance varies according to the performance. In the fund with excellent performance (10%) in the previous quarter, the flow of funds in the next quarter increased significantly. When the performance is poor and the performance is normal, the financial flow is not sensitive to the performance. The findings in  According to Model (6), the following is a further study of the relationship between fund performance and fund flow, based on piecewise linear regression.
The model examines the impact of ranking bottom funds, ranking medium funds, and ranking top funds on the capital flow of funds.
The regression results of Model (6), as shown in Table 4, can be found that the coefficients of Rank Top and Rank Middle are positive, while the rank bottom coefficients are negative but not significant, which shows that the sensitivity of PFR is characterized by stages. Combining Chart 1 and Table 2, we can see that the pre-performance of the merit fund and the middle performance fund has a positive impact on the next-period flow, while the performance of the ranking bottom fund's previous period has no obvious effect on investors. Among them, Rank Top coefficient is the largest and Rank Middle coefficient is the second. This shows that investors are most sensitive to the ranking top funds, while the sensitivity to the funds with ranking medium funds is second, and the performance of the fund is not sensitive to ranking bottom funds. This shows that the PFR in the Chinese fund market also appears asymmetric. Therefore, this article can draw the following conclusion: When the fund's performance is good, the slight increase in the previous period's performance can bring more capital inflows; when the fund's performance is normal, it needs a large increase in performance to bring in capital inflows. However, when the performance of the fund is poor, investors are not sensitive to the performance. Interestingly, this finding is different from the fact that Feng Xunan et al. (2013) found that poor performance Capital Inflow

Rank
The Rank and Capital Inflow This table uses the results of a fixed-effects panel regression .The first number in each cell is the regression coefficient and the value in parentheses is the associated t-value. ***indicates p < 0.01 **indicates < 0.05 *indicates p < 0.10.
funds are subject to strong investor selling [2]. Consistent with the evidence from markets in the United States of Sirri and Tufano (1998), in their sample, the merit fund caused over-subscription of investors, and the poor performance fund did not receive the same degree of redemption [6].
From Table 4, it can be found that the fund size has a significant negative

Robustness Check
In the empirical part above, the raw return and Jensen's excess return were selected as metrics of the fund's performance, which significantly improved the reliability and robustness of the paper.
Considering that the past fund flow of the fund may have an impact on the future fund flow, we added one lagging period's Flow i,t-1 as one of the explanatory variables in the basic model (6). Build a Dynamic Panel Regression Model for Robustness Testing. In order to solve the endogeneity problem of explanatory variables in the dynamic model, we adopt a two-step systematic generalized moment estimation method. The results are shown in Table 5. The P value of Sargan test is greater than 0.10, indicating that the overall construction of the instrument variable is effective. The p-values of AR(1) and AR (2) indicate that there are only first-order correlations and no second-order correlations for the residuals after difference, and there is no sequence correlation in the original model error term. The first number in each cell is the regression coefficient and the value in parentheses is the associated t-value. ***indicates p < 0.01 **indicates < 0.05 *indicates p < 0.10.
In Table 5, the sign and significance of the key variables Rank Bottom , Rank Middle and Rank Top have not changed, indicating that the conclusions in this paper have good robustness. At the same time, the regression coefficient of Flow i,t-1 is minimal and not significant, indicating that the dynamic panel model is not better than the fixed effect model. This also proves that there is no missing variable problem in the fixed effect model used above, and the model setting is reasonable. Chinese investors have shown overall performance in purchasing funds instead of "opposite choices", which shows that the overall trend of investors in China is rational and conducive to the stable and healthy development of China's financial market. Second, this paper finds that there is also a non-linear relationship between the performance of funds and the cash flow of funds in China's fund market. That is to say, the "star fund" that ranks high in performance can attract excessive capital inflows. At the same time, the investors prefer small-scale funds, and pay more attention to the performance of funds but ignore the risks of funds.

Conclusions and Advice
Based on the above conclusions, this study provides the following implications and practical significance: First of all, China's Securities Investment fund is based on modern trust relationship on the basis of the contract (contract type) fund. As the main parties of the Fund contract, there is a "principal-agent" cooperative relationship between the Fund investor (client) and the fund Management Company (agent), which is behind the fund assets "ownership" and "management rights". Similar to the separation of "ownership" and "operation right" of the stock company, and the "principal-agent" problem of shareholders and management, the separation of "ownership" and "management power" of fund assets may lead to potential conflict of interest between fund investors and fund management companies. In other words, the objective functions of the "ownership" and "management power" are not naturally consistent: the investor pursues the maximization of wealth (or utility), and the fund management company pursues the maximization of management fee income.
Under the agent investment model of the fund industry, for the purpose of maximizing self-interest, the goal of maximizing the income of the fund management company may be above the target of maximizing investor wealth, which means that the income growth of the fund management company may be the loss of investor wealth which is at the expense of the investor. It should be pointed out that since the management fees of China's securities investment F. Chen et al.
funds generally adopt a fixed-rate payment model, the goal of maximizing the interests of fund management companies can be regarded as maximizing the scale of assets pursuing management.
According to the "consignment-agent" theory, only by establishing an effective incentive mechanism and motivating the fund management company to take actions aimed at maximizing the interests of investors, can we minimize the conflict of interest between the fund investor and the fund management company. According to the empirical results of this paper, we can infer that the combination of the "pursuit of performance" behavior of fund investors and the goal of maximizing asset size by fund management companies can generate positive incentive mechanisms that effectively reduce the conflict of interest between the two theories.
This endogenous positive incentive mechanism can be described as follows: Fund performance is significantly positively correlated with the net fund flow, which means that investors will "reward and punish" according to the performance of fund, and rising fund performance will attract incremental capital inflows. The expansion of the size of fund assets will lead the increase in management fee income; conversely, a decline in the fund's performance will lead to shrinking asset size and decrease in management fee income. This implies a positive feedback relationship between fund performance and fund management company income. Obviously, this positive feedback relationship will motivate fund management companies to work hard to increase the return on investment of funds in order to pursue the growth of fund assets. It can be inferred that the fund management company can achieve the goal of maximizing the scale of assets while maximizing the investor's wealth. In other words, investors and fund management companies can achieve a win-win situation. There is no doubt that this endogenous positive incentive mechanism can not only reduce the conflict of interest between fund investors and fund management companies, but also promote the survival of the fittest in China's fund market, and can be an important "base stone" for the sound development of the fund market.
Secondly, securities regulatory authorities should strengthen the supervision of high-risk investment behaviors of funds, and help investors establish risk-matching investment ideas by strengthening investor education, so as to effectively limit the moral risk behavior of fund management companies (fund managers). Compared with the U.S. mutual fund market, China's fund market has a short history of development. Individual investors with immature investment ideas occupy the largest share of the market. Our research shows that domestic investors tend to pay more attention to rewards and relatively ignore risks. This irrational investment behavior "incentivizes" fund management companies (fund managers) to adopt high-risk radical investment strategies to pursue high returns. Therefore, supervisory authorities should strengthen the supervision of high-risk investment activities of the fund. For example, the frequency of fund short-term trading can be reduced by setting the upper limit of the turnover rate. Furthermore, the supervisory authority should also vigorously promote the education of fund investors, help fund investors establish investment concepts that match risk and return, change only the inherent thinking of rewards regardless of risk, and restrict the moral risk behavior of fund managers from the source, promoting the performance of incentive mechanism.
Finally, for fund management companies, it is necessary to strengthen internal governance of the company and strive to improve the performance of the fund so as to attract more investors to purchase. Fund management companies should strengthen the level of investment and research, create long-term star brands by increasing the sustainability of the performance of star funds, and stimulate the "star funds" effect of the fund market, so as to more effectively exert the positive incentive effect of performance incentives.