Finance Market Efficiency and Adaptive Market Hypothesis

This study examines the Adaptive Market Hypothesis is appropriate for the Chinese Stock Market by carrying out descriptive statistics and validating GS test, AQ test, AVR test including dynamic and static comparison, BDS test, and rolling window approach. In this study, the Chinese stock market daily and weekly data of Shanghai Composite Index and Shenzhen Stock Index are regarded as our research objects, deeply inquiring the adaptability characteristics of China's stock market and analyze the uncertainty of stock market effectiveness indicators. Further, based on the test result, we verify the balance of stock market returns and risks, and then select the typical factor as a market environment indicator to measure the impact of changes in market conditions on stock market returns and measurability. The empirical result shows that the effectiveness of China's stock market and the relationship between income and risk are time-varying. In addition, the impact of market environment on risk premium is not obvious while it has a significant impact on the predictability of income. Therefore, according to this, the development trends of the stock market can be judged and it is a good way to adjust the direction of investment strategy and risk management in a timely manner.

Since 1970, Professor Fama of the University of Chicago proposed EMH (Efficient Market hypothesis), then EMH theory has become the cornerstone of modern financial research with its rigorous theoretical system and empirical model(Sam,2013). However, the effective market theory still cannot provide a reasonable explanation for the many financial market visions discovered since the 1980s. In the early 21st century, some scholars which were based on the differences and debates between EMH and behavioral finance theory, and borrowed the ideas from biological evolution theory to propose adaptation from the perspective of adaptive evolution, called as AMD (adaptive markets hypothesis). In fact, this hypothesis does not deny the EMH's analytical model but also introduce Darwin's theory of biological evolution, emphasizing that rationality is a relative concept, associated with the external environment and changing rationality, the behavior of participants. It will show irrationality due to changes in the environment, and it will gradually disappear due to constant adaptation to the environment.

More specifically, AMH regards the market as an ecosystem in which different groups or species compete for scarce resources. AMH believes that the changing market environment determines key market characteristics such as revenue predictability, so it is impossible to evaluate market efficiency from reality. In addition, market efficiency is highly environmentally dependent and dynamic, which means the predictability of profits will follow the statistical characteristics of investors. Changes in the financial system and market environment often occur. AMH also believes that the relationship between risk and return cannot be stabilized with time since the relationship is determined by market ecology and institutions.

According to the adaptive market hypothesis, market effectiveness and market inefficiency are specific manifestations of adaptive behavior in the securities market. More precisely, when investors' investment decisions are adapted to the investment environment, the market is effective. On the contrary, when investors' investment decisions and the investment environment are not suitable, the market will have behavioral deviations and behave ineffective(Andrew,2018). Based on this hypothesis, this article empirically analyzes the adaptability characteristics of China's stock market. The market adaptability test mainly proceeds from the following aspects: (1) The effectiveness of the market and its stability (2) The stability of the relationship between income and risk (3) The relationship between risk premium and stock market measurability and the environment in which it is located. Its research characteristics are: (1) Taking the representative indices of China's stock market: Shanghai Composite Index and Shenzhen Stock Index as the research object, discussing the applicability of AHM in emerging markets; (2) Analyzing the uncertainty of stock market effectiveness indicators, verifying stock market returns and risks The time-varying relationship is explained by the ecological evolutionary viewpoint; (3) The relevant indicators are used to represent the financial market environment variables, and the impact of market conditions changes on stock market returns and measurability is measured to validate the natural selection viewpoint emphasized by AHM.

As a rapidly developing emerging market, China's stock market has unlimited prospects for its future development. Therefore, verifying the applicability of AHM theory in China's stock market is crucial to its universal applicability. At the same time, the research work in this study will help to further discover the AMH evidence in emerging markets, providing a strong factual basis for the improvement of AHM's theoretical system as well as provide new empirical evidence and ways for China's stock market investment and risk management policies in the future.

Empirical research models and methods analysis

Time interval: 1995.01~2018.07

Data pre-processing: In the daily data, the Shenzhen Stock index is actually duplicated on 2010.12.01, and the data needs to be removed. In addition, the timeline of Shanghai Composite Index and Shenzhen Stock index is matched and processed in Excel. The required data is finally compiled into data_daily_1995.csv. And data_weekly_1995.csv.

Automatic mixing test AQ test (automatic portmanteau Box-Pierce test)

Hybrid testing is widely used to test the zero hypothesis of the yield series.

Among them, it is the autocorrelation coefficient of the j-order lag term of the rate of return. Escanciano and Lotabo propose an automatic test whose optimal value is determined by the degree of complete data dependence. More specifically,pi is the optimal lag term determined by the AIC (Akaike's information criterion) criterion and the BIC (Bayesian information criterion) criterion.

It is the i-order auto-covariance estimator of the yield Y_t, τ ̅_i^2 is the auto-covariance of Y_t^2, T is the number of observations. The AQ statistic progressively obeys the chi-square distribution with a degree of freedom of 1. If the AQ value is greater than 3.84 or the accompanying p value is less than 0.05, the null hypothesis of the no-revenue autocorrelation is rejected at the 5% significance level.

AVR and WBAVR test (Wild boot-strapped automatic variance ratio test)

The null hypothesis is the same as AQ test.

We consider the variance of an asset's return when the holding period is k, as V_k. Then we define the variance ratio VR(k) as the ratio of the variance of the k-period to the variance of the first-period:

Where ρ_j is the autocorrelation coefficient of the j-order lag term of the yield. The null hypothesis of the variance ratio is VR(k) = 1 (or equivalent to, given all k, ρ_j = 0). In this test, the choice of holding period k is arbitrary and there is no statistical judgment as a basis. Choi proposes a full data-dependent estimation method for the optimal estimate of k. Given all j, T is the number of observations, under the null hypothesis, Choi proposes that the assumption of independent and identical stock market returns is as followings:

When the benefits belong to the unknown form of conditional heteroskedasticity, Kim proposes the original self-help method of statistics to improve the small sample characteristics. Let the income for the moment t. It can be derived in the following three steps:

1. A self-service sample of a T observation,
2. where η_t is a random sequence.
3. Calculate AVR^* (k^* ), and the AVR statistic can be obtained from AVR statistics can be obtained.
4. Repeat (i) and (ii)B times to gain self-distribution.

The value of the AVR statistic and the p value are calculated in the case of satisfying the standard normal distribution. Here the p value needs to be compared with the 5% significance level. If it is less than 5%, the zero correlation hypothesis is rejected, and the window is considered to have profit predictability.

GS test (generalized spectral test)

Let the income for the moment t. Assuming that the stationary time series obeys the difference sequence, the null hypothesis is that μ is a real number. The above null hypothesis is equivalent to the following conditions:

Y_j (x) is an autocovariance in the nonlinear framework, x is any real number, 1 ≤ j ≤ T and is an integer. Escanciano and Velasco propose a generalized spectral distribution function( Khuntia & Pattanayak,2018).Under the null hypothesis, the statistic of the test is constructed as follows:

Λ is any real number in [0,1]. The sample of the above distribution function is estimated as:

In this formula, Under the null hypothesis, H(λ, x) = γ_0(x) λ, the statistic for checking H_0 is constructed as follows:

Escanciano and Velasco finally came up with GS statistics:

The GS test given above does not have a standard progressive distribution. In order to use this test for a limited sample, Escanciano and Velasco used the original self-help method, that is to say, the p-value of the test can be derived from the original self-service distribution as described by the AVR test. If the p-value is less than 5%, then this window is considered to have revenue predictability.

BDS test (Brock, Dechert and Scheinkman test)

The BDS test is a nonparametric test method used to test the independent and identical distribution hypothesis of a time series( Wolff,1994). The BDS test statistic is based on the concept of integrals. More specifically, Let Y_t be the gain at time t, (t=1,...,T), let m-dimensional vector Y_t^m=(Y_t,Y_(t+1),...,Y_(i+m-1) )^', It is called m-dimensional history. The associated points are defined as follows:

In the formula,

This is quivalent to an indicative function. The associated integral mainly measures the probability that the distance between any two embedded vectors Y_t^m and Y_s^m in the embedded space is less than δ. The null hypothesis: H_0: {Y_t } is independent and identically distributed. Brock proposed BDS statistics under the null hypothesis H_0 in 1996:

Where σ ̂_m (δ) is an estimate of the asymptotic standard deviation of C(N, m, δ) - C(N, 1, δ)^m. When H_0 is established, it can be obtained from statistical conclusions that the asymptotic distribution of BDS(m, δ) statistic is a standard normal distribution. On the contrary, when H_0 is not established, the BDS(m, δ) statistic has a tendency to stay away from zero. In general, the embedding dimension m is limited to between 2 and 5.

In the rolling subsample window method, our aim is to track the predictability of stock market returns. Based on the simulations of Escanciano and Lobato and Kim, the combination of China's stock market opening time is only about recent 20 years, and related to more major domestic or international events. In order to better reveal the predictability of stock market returns and meet the sample size requirements, we select 260 observations for the weekly data,that is, 5 years totally. As for the daily data, we select 252 observations, that is, 1 year.

The steps of the rolling subsample window test are as follows: After the first subsample is checked, the window scrolls forward one observation value, recalculates the test statistic, and through the rolling calculation, finally calculates the p value of the test statistic as a function of time. The daily data p value is the calculation result of the current time t to t - 1 year period, and the weekly data p value is the calculation result of the current time t to t - 5 year period. If the p-value is less than 0.05, then the revenue predictability of this window is significant at the 5% significant level. In this way, a statistically significant period of revenue predictability can be identified, and this period may be related to a corresponding significant event.

The daily data provides more detailed information than the weekly data, so there may be deviations in the capture of the daily and weekly data over certain time periods, and the weekly data response will be relatively insensitive.

From the top left corner, through the AQ test of the Shanghai Composite Index Weekly data, we can see that the AQ statistic is greater than 3.84 around 2008, capturing the predictability of the Chinese stock market. For the Shanghai Composite Index and Shenzhen Component Index, the AQ statistics captured the predictability of earnings around 1998, around 2008, and around 2016.

AVR test

Drawing time series chart: The two figures below show the time series of the yield of the Shanghai Composite Index and Shenzhen Component Index. It can be clearly seen that the fluctuations in yields around 2008 and 2016 are more severe and obvious than in other time periods.

Drawing a histogram: The two images below show the histogram of the yield series for the two major indices. As can be easily seen from the distribution map, the distribution of the two indices is roughly the same as the normal distribution.

Due to the fact that the daily data volume is too large, thus we only performed the WBAVR test on the weekly data, and the results were basically consistent with the AQ test. Revenue predictability can be captured around 2008 and around 2016. The chart clearly illustrates the time-varying characteristics of stock market return predictability. Although China's stock market returns are unpredictable during most sample periods, there is still significant partial predictability.

Results

Overall, in the early stage of stock market development, since the development model has not yet formed, participants have a wait-and-see attitude or learn from the theory of mature foreign markets. Therefore, the relationship between stock market returns and risks is not much.