CN108876106A - A kind of macro Micro dynamic mixing β estimation method merging macro economic policy factor - Google Patents
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Abstract
The invention discloses a kind of macro Micro dynamics for merging macro economic policy factor to mix β estimation method, including：Systematic risk is first divided into prior information part and conventional transaction message part, for priori system risk part, priori system risk is defined as a risk function about macro microcosmic influence factors, then risk function value is calculated to which generation returns by investigating influence of each factor to priori system risk, that is priori system risk, then by contraction method, in conjunction with prior information and stock exchange information, posteriori system risk is calculated, as macro microcosmic mixing β.The method of the present invention combines macroscopical periodic factors and enterprise's microcosmic influence factors with systematic risk, and the noise factors such as removal market unification are to improve estimation accuracy.
Description
Technical Field
The invention relates to the field of economy, in particular to a dynamic mixing β estimation method fusing factors of a macroscopic economy cycle and an enterprise life cycle.
Background
The invention creates a technical basis for a capital asset pricing model CAPM, mainstream literature research based on developed national market shows that the phenomenon that the stock market line is too flat exists in CAPM inspection, namely α (excess risk premium) is obviously positive in a long term, and the regression coefficient (market excess profitability or market risk price) of the systematic risk β is too low, and then a large amount of research is mainly expanded in two aspects to try to accurately measure the systematic risk β, namely the attempt of the angle of the section factor and the expansion of the time dimension (time-variation).
The method is characterized in that the systematic risk estimation result is too low, long-term excess risk premium is positive probably because CAPM omits some risk factors and tries to explain the phenomenon by adding section factors, the development is mainly based on two theoretical dimensions, one dimension of traditional finance is that α is obvious in a long term because some systematic risk factors are leaked, β which is calculated from market indexes simply cannot completely represent systematic risks, so that β coefficients are too low, Zhang et, Zhao Jing (2012) finds that enterprise microscopic characteristic variables are used as causes for causing the variation of β coefficients, particularly β coefficients of stock compositions, and have no convincidences in Zhang Shi, Suzhi and Zhao provinces, and the conclusion is that the macroscopic economic variables in US and English markets have no relationship with time-varying coefficient 2, and the conclusion has no special characteristics of China because the inventor chooses multi-national market to analyze, and has a certain difference with the existing national market conditions, the influence of stock market systematic risk factors on the market risk factors of China is found and found that the market risk system is influenced by the market risk system of national market composition of national market significance, and the market significance of national risk system, and the influence of national risk system of market composition of financial risk (2014) is considered in the market significance, the market significance of market significance, the market significance of significance, significance of.
The other theoretical dimension of increasing the interpretation ability of CAPM by adding the cross-sectional factor is from the perspective of behavioral finance, namely, the emotional factor of an investor is considered to be an important reason for explaining the profitability of stocks, so that the interpretation ability of β factor is too low, the research of any dimension is embodied in mining and supplementing other factors besides β factor, and the subsequent models of three factors, four factors, five factors and the like are developed on the factored interpretation ability of CAPM.
However, the development of the cross-section factors of the traditional financial dimension and the behavioral financial dimension cannot prove that the system risk has an expected explanatory power on the stock profitability, the dynamic and time-varying development research on the CAPM model from the time dimension becomes an increasingly important research focus of the capital asset pricing theory, the time-varying capital asset pricing model research finds that the excessive risk premium factor α (namely the intercept term of the CAPM) and the system risk factor β are time-varying, the time-varying factor is considered to effectively improve the explanatory power of the risk factor on the stock profitability, and on the basis, the research of Adrian et.al (2013, 2015) further indicates that the prices of various types of risks including the system risk premium are time-varying, and relative to the time-varying system risk factor, the time-varying property of the consideration of the risk price has a higher significance on the accuracy of the asset pricing model.
Many researches on the influence mechanism of macroscopic economic factors and microscopic factors on the systematic risk are conducted at home and abroad, and the traditional CAPM is expanded and supplemented by taking one or some market similarities as a starting point. The market heterology discovered by the research at home and abroad mainly comprises: event exceptions (e.g., excess premium in IPO but low long term yield, McDonald and Fisher, 1972); the scale effect, enterprise trait index effect such as enterprise value effect (account-to-market ratio effect), financial leverage effect, etc., which have significant impact on the rate of return of stocks; history presentation, transaction volume, etc. The existing domestic and foreign documents can be summarized and integrated as follows: by adding macroscopic economic cycle factors and enterprise trait index variable factors, the CAPM model can effectively explain the risk price and is suitable for capital markets of developed countries and developing countries. According to the research of the existing documents, no matter the traditional CAPM model, the conditional CAPM model, the three-factor model or other expanded asset pricing models are used, the macroscopic economic cycle factors can be summarized into the increase rate of the currency supply amount, the macroscopic economic risk and the macroscopic market characteristics, and in essence, the macroscopic market characteristics can be measured by using the policy indexes such as financial policy, industrial policy, national investment increase and the like. The enterprise speciality index represents the life cycle of an enterprise, the existing literature has more and more diversified researches on the factor, wherein the scale, the account-market value ratio and the inter-industry difference are representative, and in addition, the momentum effect can also be considered to belong to the enterprise speciality risk index.
The conventional method for measuring the systematic risk β considers the macroscopic economic factors or the microscopic enterprise factors separately, the macroscopic economic factors or the microscopic enterprise factors are not analyzed together to analyze the effect of the systematic risk, the factors are mainly used as control variables for measuring the systematic risk but not used as a part of the systematic risk, Cosemans et.al (2016) comprehensively considers the dynamic influence of other risk factors and an enterprise operation cycle (the macroscopic economic cycle) on the systematic risk factor β, and the macroscopic factor is used as a part of the systematic risk to construct a Hybrid system risk factor (Hybrid β), so that a perfect system risk factor β with the same theoretical expected explanatory power can be obtained, however, the macroscopic economic factors (default) considered by Cosemans et.al (2016) are not suitable for the Chinese market, the macroscopic economic factors (default) are mature in the U.S. capital market, the regulation and control effects of policies are reflected in the microscopic changes of the enterprise mainly due to the fact that the macroscopic factors are difficult to generate policies and stable on the microscopic enterprise under the transferred economy, and the macroscopic factor cannot represent the policy of the Chinese in time, so the macroscopic factor represents the macroscopic policy.
In the case of china, there are two points of need for improvement in the existing literature: firstly, in a time-varying asset pricing model, the lack of investigation on macroscopic economic policy factors can disable the asset pricing model in a transition economic environment; and secondly, an effective method for simultaneously detecting the main structure transition points of the risk factors and the risk price of the system is lacked, so that a solid research support is difficult to provide for relevant policy making. Specifically, if relevant policy measures are to be formulated, the risk of the system is prevented from suddenly rising, and firstly, what policy measures are needed to be known so as to effectively reduce the risk of the system; secondly, whether the system risk is suddenly increased or not can be accurately judged; finally, it is also necessary to be able to determine whether the risk price is also suddenly increased. If the system risk is increased due to the increase of the risk price, the situation that the market is optimistic, the economic environment is rapidly improved at the moment and the urgency of regulation is possibly not strong is probably shown; if an increase in system risk is accompanied by a rapid decrease in risk price, rapid and powerful policy regulation is often required. Conversely, if a decrease in system risk is accompanied by a rapid increase in risk price, that may mean that the market's willingness to withstand the risk is insufficient, the market lacks liquidity, and policy regulation is also required.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a macro-micro dynamic hybrid β estimation method fusing macro-economic policy factors, which combines macro-period factors, enterprise micro factors and systematic risks on the basis of a CAPM model and removes noise factors such as market heterography and the like so as to improve estimation accuracy.
The invention aims to realize the purpose through the following technical scheme that the macro-micro dynamic hybrid β estimation method fusing the macro-economic policy factors comprises the steps of splitting the systematic risk into a prior information part and a traditional transaction information part, defining the prior systematic risk as a risk function related to macro-micro factors for the prior systematic risk part, then obtaining a risk function value, namely the prior systematic risk, by calculating instead through observing the influence of each factor on the prior systematic risk, and then obtaining the posterior systematic risk, namely the macro-micro hybrid β through a contraction method by combining the prior information and the stock transaction information.
Specifically, a macroscopic period factor and an enterprise microscopic factor are introduced on the basis of CAPM, and a priori systemic risk is estimated
Andrespectively the individual stock excess yield and the market excess yield, namely subtracting the risk-free yield from the individual stock/market yield, wherein the variable with the mark represents a prior value; then, the prior systematic risk is determinedDefined as a linear risk function with respect to macrocycle factors and enterprise micro factors:
the method comprises the steps of assuming that sources of prior systematic risks comprise macroscopic period, enterprise life cycle and interactive influence of macroscopic and microscopic factors on systematic risks besides market fluctuation, and assuming that influence of macroscopic period factors on systematic risks of different stocks has heterogeneity but does not change along with time, and influence of enterprise life cycle and interactive influence of macroscopic and microscopic factors are homogeneous in the dimension of each stock and the dimension of time;
substituting the formula (2) into the CAPM model to construct a balance panel data regression model, and estimating and calculating by a Bayesian panel estimation method to obtain an estimation value of prior systematic risk
(2) And (3) wherein X comprises X1And X2Two macro-economic policy factors are introduced: representing the influence of monetary and financial policies, respectively, X1Is the M2 same-ratio growth rate, X2The same-ratio growth rate of the fixed-asset investment ratio for the government; the variable matrix Z contains a total of four variables: z1For the size of the enterprise calculated by taking the logarithm of the total assets of the enterprise, Z2For business account to market ratio, Z3Is the enterprise asset liability rate, Z4The method is characterized in that the method is a momentum factor and adds an industry virtual variable so as to represent the characteristic properties of an enterprise; meanwhile, cross terms of the macro-economic policy and the enterprise micro characteristic variables and cross terms Z of the macro-economic policy and the industry virtual variables are added into the modelit-1Xt-1Controlling these cross-reactions, in particular by X, respectively1And X2And Z1To Z4And industry virtual variable multiplication;
the prior systematic risk is obtained by Bayesian panel estimation and calculationAnd its standard error, combined with the prior distribution of the set macro-micro mix βUsing a contraction method to determine the systematic risk of a priori containing macroscopic factors and microscopic factorsB, rolling estimation under consideration of the information yield rate of stock exchangeitCombined, calculatedIs the systematic risk of the posterior, i.e., the macro-micro hybrid β constructed for this method.
Specifically, Bayesian panel estimation is carried out on the formula (3), a standard Markov chain is selected, repeated for multiple times, and the previous N results are removed, so that the Bayesian estimation result is ensured to be sufficiently converged; handle variableX1、X2Z and Zit-1Xt-1Inputting Bayes model for estimation to obtain coefficient estimation resultγ and δ, γ in this model1i、γ2i、γ3i、δ1、δ2(ii) a After M repeated parameter estimation values gamma and delta are obtained through Bayesian estimation, the parameter estimation result under each repetition is obtained through calculation of formula (2) in a substitution modeFurther calculating to obtain prior systematic riskAnd itVariance, standard error is the arithmetic square root of variance:
wherein L is 1, …, M, L is M.
Further, the mean value, the standard deviation and the t statistic of the parameter estimation value gamma of each repetition obtained by estimation can be calculated to obtain the influence of the macroscopic periodic factors on the prior systematic risk:
preferably, the macro-micro blend β isWhich corresponds to a variance ofWhereinCalculating a shrinkage weight in the method for shrinkage; bitAndboth are coefficients and variances obtained by regression with the traditional rolling window estimation method.
Specifically, the conventional rolling window estimation method includes two methods: 1, day of adoptionPerforming CAPM estimation on each stock according to the degree transaction data to obtain a systematic risk estimation value and a standard error of each stock as bitAnd2, adopting daily transaction data and Fama&The Macbeth regression method distributes the estimated systematic risk estimation value and standard error of each combination to each strand corresponding to the combination as bitAnd
preferably, the macro economic policy factors may further include import and export situations and industrial policy factors.
Preferably, the enterprise micro-factors can also comprise enterprise operation lever and financial lever factors.
Preferably, for the macroeconomic policy variable X, i.e. X1And X2And a momentum factor Z4Selecting values lagging by one month, and for each financial index Z1To Z3A value lagging by one quarter is chosen.
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) the Bayesian estimation method enables the prior systematic risk estimation accuracy to be higher, and the expected estimation error to be minimum.
(2) Based on the CAPM model, the macroscopic period factors and the enterprise microscopic factors are combined with the systematic risk, and noise factors such as market heterography and the like are removed, so that the estimation accuracy is improved.
(3) The combination of the prior systematic risk (including macro-micro factors) with the stock trading information provides consistency and effectiveness to the estimated macro-micro mix β.
Drawings
FIG. 1 shows the intercept and slope estimates (c 0.25) for the CAPM test under the Fama and Macbeth estimation method.
Fig. 2 is an estimate of the intercept and slope of the CAPM test under the macro-micro hybrid β estimation method (c 0.25).
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Example 1
1. A dynamic blending β estimation method fusing macroscopic economic cycle and enterprise lifecycle factors comprises the following steps:
referring to Vasicek (1973), the method combines the systematic risks (i.e., the macro-micro mix of construction β,) Is defined as:) WhereinVasicek (1973) considers that the distribution of the systematic risk on the cross section in the sample can well represent β prior distribution when only stock transaction information but no other information exists, meanwhile, after obtaining the prior distribution of the systematic risk, the prior information and the stock transaction information are weighted and averaged by taking respective estimation accuracy as weights (the step is called shrinkage, shrinkage), so as to obtain the posterior systematic risk, and the method estimates the obtained systematic risk more accuratelyEnterprise micro factors, improving the prior distribution of the systematic risk, and then still contracting the prior information and the stock trading information according to respective estimation accuracy, so as to estimate a more accurate posterior systematic risk, i.e. macro-micro hybrid β,
macro and micro mixingThe specific estimation method is as follows:
firstly, introducing a macroscopic period factor and an enterprise microscopic factor on the basis of CAPM (computer aided design), and estimating prior systemic risk
Andthe individual stock excess yield and the market excess yield are respectively the individual stock/market yield minus the risk-free yield. Where the variables with the "+" signs represent a priori values. Then, the prior systematic risk is determinedDefined as a linear risk function with respect to macrocycle factors and enterprise micro factors:
it is assumed that the sources of a priori systematic risks include, in addition to market fluctuations, the interaction effects of macro-cycles, enterprise life-cycles, and macro-microscopic factors on systematic risks. And it is assumed that the influence of the macrocycle factors on the systematic risk of different stocks is heterogeneous, but does not change with time, and the influence of the enterprise lifecycle and the interaction influence of the macro-micro factors are homogeneous in the dimension of the individual stocks and the dimension of time.
Substituting the formula (2) into the CAPM model to construct a balance panel data regression model, and estimating and calculating by a Bayesian panel estimation method to obtain an estimation value of prior systematic risk
(2) And (3) wherein X comprises X1And X2Two macro-economic policy factors are introduced: representing the impact of monetary and financial policies, respectively. Specifically, X1Is the M2 same-ratio growth rate, X2The same-ratio growth rate of the capital investment proportion is fixed for the government. Similar to the Cosemans et al (2016) study, the variable matrix Z contains a total of four variables: z1For the size of the enterprise calculated by taking the logarithm of the total assets of the enterprise, Z2For business account to market ratio, Z3Is the enterprise asset liability rate, Z4Is a momentum factor and adds an industry virtual variable to represent the characteristic property of the enterprise. Meanwhile, cross terms of the macro-economic policy and the enterprise micro characteristic variables and cross terms Z of the macro-economic policy and the industry virtual variables are added into the modelit-1Xt-1Controlling these cross-reactions, in particular by X, respectively1And X2And Z1To Z4And industry virtual variable multiplication. Besides the variables, the macroeconomic policy factors can also include import and export conditions, industrial policies and other factors, and the enterprise micro-factors can also include enterprise operation levers,Financial leverage, etc. For a macro economic policy variable X (i.e., X)1And X2) And a momentum factor Z4Selecting a value delayed by one month, for each financial index (Z)1To Z3) A value is chosen that lags one quarter, taking into account that the company-on-the-market reports tend to be released in the next quarter.
Then, Bayesian panel estimation is performed on the equation (3), a standard Markov chain is selected, 1250 times of repetition are performed, and the previous 250 times of results (burn-in) are removed, so as to ensure that the Bayesian estimation result is sufficiently converged. Handle variableX1、X2Z and Zit_1Xt_1Inputting Bayes model for estimation to obtain coefficient estimation resultγ and δ (γ in this model)1i、γ2i、γ3i、δ1、δ2). After 1000 repeated parameter estimation values gamma and delta are obtained through Bayesian estimation, the parameter estimation result under each repetition is obtained through calculation of formula (2) in a substitution modeFurther calculating to obtain prior systematic riskAnd its variance, the standard error being the arithmetic square root of the variance:
wherein L is 1., 1000, L is 1000. In addition, the mean value, the standard deviation and the t statistic of the parameter estimation value gamma of each repetition obtained by estimation can be calculated to obtain the influence of the macroscopic periodic factors on the prior systematic risk:
the prior systematic risk is obtained by Bayesian panel estimation and calculationAnd its standard error, combined with the prior distribution of the set macro-micro mix βReference Vasicek (1973) uses the contraction method to calculate the macro-micro-mixing β, i.e.
The macro-micro mixture β is
Which corresponds to a variance ofWhereinThe shrinkage weight (shrinkage weight) in the method is calculated for the shrinkage.
bitAndare all estimated by conventional rolling windowsThe method regresses the resulting coefficients and variances. The conventional rolling window estimation method includes two kinds: 1, performing CAPM estimation on each stock by adopting daily transaction data to obtain a systematic risk estimation value and a standard error of each stock as bitAnd2, adopting daily transaction data and Fama&Macbeth (1973) regression method, the estimated systematic risk estimation value and standard error of each combination (portfolio) are distributed to each strand corresponding to the combination as bitAnd
using a contraction method to determine the systematic risk of a priori containing macroscopic factors and microscopic factorsB, rolling estimation under consideration of the information yield rate of stock exchangeitCombined, calculatedIs the systematic risk of the posterior, i.e., the macro-micro hybrid β constructed for this method.
In general terms, macro-micro mixingBy fusing macro-micro factors in the prior distribution of the systematic risk, the purpose of minimizing the expected estimation error is achieved. Specifically, the systematic risk is firstly split into a prior information part and a traditional transaction information part. For the prior systematic risk part, the prior systematic risk is defined as a risk function related to macro and micro factors, and then a risk function value (prior systematic risk) is obtained by calculating instead by observing the influence of each factor on the prior systematic risk. And calculating to obtain a posterior system by combining the prior information and the stock trading information through a contraction methodSexual risk, i.e. macro-micro mixing
The advantages of the macro-micro hybrid β estimation method are:
(1) bayesian estimation method for making prior systematic riskThe estimation accuracy is higher and the estimation error is expected to be minimum.
The Bayesian estimation method is a classic method of supervised machine learning, which takes learning data distribution from historical data as a target, combines historical information with a sample likelihood function, continuously adjusts the prior distribution according to the historical information to estimate the posterior distribution of parameters, and finally obtains a parameter point estimation value with minimum expected loss caused by estimation error through the posterior distribution of the parameters, namely obtains more accurate prior systematic riskAnd (6) estimating the value. Compared with the traditional estimation method, the Bayesian estimation method is more flexible, more intuitive and more easy to understand, and compared with the classical estimation method, the Bayesian estimation method is not limited to only estimating a plurality of moments (such as parameter values, variances and the like) of the parameters, but inspects the data distribution of the parameters, thereby obtaining a more accurate estimation result. Secondly, after the Bayesian posterior distribution is used for deduction, the loss caused by the first and second errors can be taken into account, so that the method is more practical than a classical estimation method; in addition, on the aspect of processing the redundant parameters, the Bayesian estimation method can directly integrate the redundant parameters in the posterior density, which is much more convenient than the classical estimation method (if the redundant parameters exist in the classical estimation method, some criteria (such as significance, information criteria and the like) are needed to eliminate the redundant parameters, and if the redundant parameters are not processed, the estimation of the classical estimation method can be caused by the possible problems of variable correlation, endogenous property and the likeInaccurate results). Particularly, in the technical method, cross influences of macroscopic factors, microscopic factors and macro-microscopic factors are involved in estimation and calculation of the prior systematic risk, the number of variables is large, the number of parameters to be estimated is large, and the Bayesian estimation method can effectively avoid influences of redundant parameter problems on accuracy of estimation results. Therefore, the bayesian estimation method has an advantage over the conventional estimation method in that the parameter to be estimated is estimated more intuitively and accurately.
(2) Based on the CAPM model, the macroscopic period factors and the enterprise microscopic factors are combined with the systematic risk, and noise factors such as market heterography and the like are removed, so that the estimation accuracy is improved.
The method comprises the steps of splitting the systematic risk into a prior information part and a traditional transaction information part, defining the prior systematic risk as a risk function related to macro and micro factors, and then carrying out back-substitution calculation to obtain a risk function value (prior systematic risk) by observing the influence of each factor on the prior systematic risk.
The systematic risk is inspected by combining the macroscopic period factor and the enterprise microscopic factor, compared with the traditional estimation method only based on market transaction information, the method can effectively reduce misjudgment on the risk caused by market abnormal fluctuation, and can remove noise under market abnormal conditions so as to estimate the systematic risk more accurately. In addition, in a general multi-factor estimation model (such as a Fama-French three-factor model), a factor selection process is a data mining process, whether a certain factor is effective or not is judged according to historical performance after the factor is added into the model, so that whether the factor is added into the model is judged, the effectiveness of the factor in the model is not proved through theoretical derivation, so that economic logic behind the factor is easily ignored, and the effectiveness of the factor cannot be guaranteed to be still established in the future.
The CAPM model is obtained by deducing an investor utility theory on a microscopic level on the basis of a Markowitz investment combination theory; the multi-factor model developed later is essentially the theoretical basis for the data mining process and is not firm. In the method, a risk function is constructed by assuming that the prior systematic risk is influenced by macroscopic risk factors and microscopic risk factors from a CAPM model, and the macroscopic period factors, the enterprise microscopic factors and the interaction thereof are fused with the systematic risk, so that more factors are considered than that of a general multi-factor model, and the problems of model missetting, factor effectiveness instability and the like caused by a data mining process in the general multi-factor model are avoided. Therefore, the factors can be selected more effectively, and the model has more economic meaning and better accords with economic logic. And moreover, a Bayesian estimation method capable of effectively solving the problem of redundant parameters is adopted for estimation, so that the problems of variable correlation, endogenesis and the like which are possibly generated after a large number of factors are considered are avoided.
(3) The combination of the prior systematic risk (including macro-micro factors) with the stock trading information provides consistency and effectiveness to the estimated macro-micro mix β.
Estimating and calculating to obtain prior information part containing macro and micro factors, and fusing the prior information part with the stock exchange information weighted average, wherein the weight is the proportion of the estimation accuracy of each of the two parts to the total accuracy (the sum of the estimation accuracies of the two parts), and finally obtaining the macro and micro mixture β. the calculation process of the macro and micro mixture β is essentially to adjust the optimal prior systematic risk only according to the estimation result of the stock exchange information, and the adjustment distance depends on the estimation accuracy of each of the two parts(the accuracy of the stock exchange information portion,essentially sampling error) and(the accuracy of the a-priori information portion,the essence being Bayesian estimationExpected loss due to medium estimation error), accuracy of the macro-micro hybrid βThe sum of the accuracy is estimated for each of the two parts. Adjusting the distance to the total accuracy of the estimation accuracy of the two partsI.e., the weight of the macro-micro mixture β when the two parts are weighted and averaged.
The stock trading information section represents the systematic risk in the case of fluctuations in individual share and market gains, without considering other factors. The implicit assumption is that systematic risks are only derived from market fluctuations. In actual market operation, the systematic risk of stocks is related to not only market fluctuation, but also factors such as macroscopic risk period, enterprise condition, industry life cycle and the like, and the influence of the factors on the systematic risk is not independent but interactive. It is therefore assumed in the a priori systematic risk section that in addition to market fluctuations, systematic risks also originate from the macro-cycle and enterprise lifecycle.
The combination of the prior systematic risk (including macro and micro factors) and the stock trading information is used for obtaining parameter estimation quantity with consistency and effectiveness, namely macro and micro mixingThe Bayesian method is adopted for estimation, so that the prior systematic risk with the minimum expected error can be estimated, and the model can have theoretical derivation logic and economic logic after macro and micro factors are fused; however, the prior systematic risk estimated by the bayesian method is not unbiased, and the point estimation result b of the stock exchange information part is unbiased without losing important variables (i.e. without problems of endogenesis and the like). Namely, it isThus, a priori systematic risk (including macroscopic microscopic factors) is combined with stock trading information. The main purpose is to mix macro and microWith consistency and effectiveness, i.e.The macro-micro blend β tends to its true value as the sample size tends to infinity;the macro-micro hybrid β has the least estimation error and the highest accuracy, because the point estimation result b of the stock exchange information part has unbiased and consistent,when the amount of samples tends to be infinite,whereby the adjustment distance is reduced, therebyThe effectiveness of the macro-micro hybrid β is necessarily true, the accuracy of the macro-micro hybrid β is the sum of the accuracy of the stock exchange information part and the accuracy of the a priori systematic risk, and the essence of the accuracy of the stock exchange information part is the sampling errorThe sampling error has been controlled to be minimum in the OLS estimation method; likewise, the nature of the accuracy of the prior information part is the estimation errorThe estimation error is also controlled to a minimum in the bayesian estimation method, and thus the accuracy of the macro-micro hybrid β is necessarily maximized.
2. Systematic risk β and risk price structure conversion feature verification method thereof
(1) Structural transformation characteristic checking method for systematic risk β
Whether the systematic risk is time-varying (such as the macro-micro mixture β estimated by the method of the present invention) or the systematic risk estimated by using the rolling window (such as the rolling window OLS estimation, the Fama & Macbeth estimation method, the Fama & French three-factor model, the Carhart four-factor model, etc.), the structural transformation characteristics of the systematic risk can be checked by adopting the classical unit root checking method, and the change of the systematic risk under the change of the time lapse and the market environment in the sample period can be examined.
The specific method for checking the structure transformation time point is to calculate the absolute value of the difference between the two stages of systematic risks β as the systematic risk absolute change amplitude, compare the absolute change amplitudes and find out the largest time points, which are the systematic risk structure transformation time points, and then use different estimation methods (such as the macro-micro hybrid β, the Fama & Macbeth estimation method, etc.) to estimate the systematic risk β, so as to check the systematic risk structure transformation time points under each estimation method.
(2) Risk price structure transformation feature test method (LLDV) for systematic risks
In addition to the structural transformation features for systematic risks, more attention is paid to the examination of the structural transformation features for their risk price. The concept of risk price comes from the examination of the CAPM model, i.e. using the stock market lineChecking the relationship between systematic risk β and stock revenue, where b*The relationship between risk and stock revenue is represented, i.e., the price of the systematic risk β, and a*Then representArbitrage opportunities without systematic risk are essentially the means of other factors that affect the profitability of the stock in addition to systematic risk. According to the CAPM theory, the security market line should be a straight line with an intercept close to 0 and steeper, i.e. there is no significant risk-free arbitrage opportunity in the market in the long term, and the higher the systematic risk, the higher the profit, which means that the stock pricing is the pricing for the systematic risk. However, a great deal of literature shows that the security market line is relatively flat and the intercept is significantly positive through empirical analysis, and the existing literature generally considers that the systematic risk estimation is not accurate enough and the time-varying risk price is ignored. Thus, a large body of literature extends the model for estimation of systemic risk in both the cross-sectional and temporal dimensions in an attempt to more accurately estimate systemic risk; there is also literature that considers risk-free arbitrage opportunities a in the estimation of security market lines*And a risk price b*Time-varying.
In the method of the invention, the risk-free arbitrage opportunity a is taken into account in the estimation of the stock market line*And a risk price b*The time-varying of the risk price is tested by using the established Local Linear Dummy Variable (LLDV) estimation and test method (Chen and Hong, 2012; Chen and Huang, 2016) to test the structure transformation characteristics of the risk price. The method is essentially a semi-parametric estimation method with the introduction of smooth structure transformation. The method is roughly characterized in that a sample is divided into small time window widths, a kernel function is introduced to perform local linear regression, then an estimated value is compared with an estimated value of global regression, and statistics are measured through generalized Hausman testAnd judging whether time-varying and structure conversion characteristics of intercept and slope exist or not, and if the time-varying and structure conversion characteristics of intercept and slope exist, further checking the time point of occurrence of the most main structure conversion. The specific method of the actual test is as follows:
consider a time-varying coefficient panel model with fixed effects:
in checking the risk price, the literature typically groups stocks according to a certain method to construct an investment portfolio, and then checks the portfolio profitability and the systematic risk of the portfolio β.Representing the combined excess rate of return,represents an estimate of the combined systematic risk under each estimation method. Lambda [ alpha ]pIn order to combine the fixing effect with each other,the chance of arbitrage for a time-fixed effect, i.e. no risk, essentially derives from factors that change only with time, in addition to the systematic risk. Here, the time-varying property of risk-free arbitrage opportunities and risk prices are considered, so that the corresponding letters all have time subscripts, which will be found at each time point in the LLDV estimationAndthe value is obtained.
Firstly, the parameter to be estimated is assumed to be a function relative to time, and the model is changed into the following model:
whereinAndis an unknown smoothing functionNumber (smooth function). The model allows lambdapThere is some unknown form of correlation with the explanatory variables, so the time-varying coefficient panel model includes both fixed and random effects models.
Suppose thatLet τ be T/T and θ (τ) be [ a*(τ) b*(τ)]TThe LLDV estimation is done by a two-step algorithm.
First, solve λpAs a function of theta. For any given τ ∈ (0,1), the following optimization problem is solved:
wherein λ ═ λ2,...,λN)T，θ′(τ)＝dθ(τ)/dτ，
k (·) is a kernel function, h ≡ h (nt) cNT-1/5Is the bandwidth (bandwidth),
the first derivative is obtained for λ for equation (6):
second step, processing lambdapThe functional relation with theta is substituted back to the model, originalIs λpBecomes a model of the relationship with thetaOnly a model of the theta functional relationship. In the formula (7)Substitution of formula (5) for λpAnd based on taylor expansion θ (t) ═ θ (τ) + θ' (τ) (t τ) + omicron ((t τ)2) Solving the weighted least squares equation (8) to obtain the local linear estimator of θ (τ):
wherein W (τ) ═ WT(τ)κ(τ)W(τ)，W(τ)＝INT-D[DTκ(τ)D]-1DTκ (τ). Then calculates to obtain LLDV estimator of theta (tau)
This is one(can also be made as) Is thatI.e. time-varying risk-free arbitrage opportunities and time-varying risk price estimates. The structure transformation characteristics are then verified by two verifications. Firstly, checking 1 to check whether the intercept and the slope have structural transformation characteristics at the same time, and thenTest 2 determines whether this structural change originates from a structural transformation characteristic of the slope. Two tests were detailed as follows:
and (3) test 1:
the original assumption is that: h0:b*(·)＝b*&a*(·)＝a*
Alternative hypothesis H1:b*(·)≠b*Or a*(·)≠a*. Under the original assumption that the following formula (5) becomes
Namely, the model is a traditional individual fixed effect model, and can be estimated by adopting a traditional Least Square Dummy Variable method (LSDV) to obtain an estimation resultUnder the original assumption, LSDV estimatorAnd LLDV estimatorConverge to the same probability limit but differ under alternative assumptions, so a Wald-type test was designed to compare the two estimators:
wherein the weight matrixWhile the more generalized hausman test (Hausmantest) is its standard form:
wherein,
on the correlation hypothesis and the original hypothesis H0It is true that, when T → ∞ and N → ∞ are present,however, the preset significance level can have a great influenceThe probability of making the first type of error (false positive), calculating the p-value by only a standard normal distribution is not robust enough, so this effect is eliminated by bootstrapping the residual. The bootstrap method comprises the following steps: firstly, LSDV regression is carried out to obtainThen LLDV regression is carried out to obtainAnd non-parametric residualRandomly sampling nonparametric residual errors and then carrying out mean value removing treatment to obtain bootstrap residual errorsCalculating by back-substitution according to bootstrap residualFor the bootstrap samplePerforming LLDV regression and according toObtained by a calculation methodRepeating random sampling and calculating for B times to obtain B bootstrap statisticsThe bootstrap p value is
And (3) checking:
if test 1 passes, it indicates that there is a significant structural transformation feature between the intercept and the slope, and then test 2 determines whether the structural change originates from the slope. In the presence of an allowed intercept term a*(T/T) time-varying tendency, whether structural change in the test is from b*Time variation of (T/T).
The original assumption is that:
alternative assumptionsIs composed ofIs erroneous. Under the original assumption that the following formula (5) becomes
Adopts PSPDV (pooldedemaarametric profile dummy) estimation method proposed by Chen et al (2012)Estimating to obtain an estimated value of the slopeAs with the idea of test 1, a generalized hausmann test statistic was constructed for testing:
wherein:
on the correlation premise hypothesis and the original hypothesisIt is true that, when T → ∞ and N → ∞ are present,similar to the test, the predetermined significance level will have a great influenceThe probability of making the first type of error (false positive) is not robust enough to compute the p-value by only a standard normal distribution, so it is necessary to eliminate this effect by bootstrapping the residual, a method similar to the test.
If the test 1 and the test 2 both pass, the non-risk arbitrage opportunity and the risk price have obvious structural transformation characteristics. The point in time when the most prominent structural transformation occurred was further examined. The inspection thought is as follows: for any time point, observing whether the difference between the LLDV regression value within the extremely short window width from the left and the LLDV regression value within the extremely short window width from the right is maximum in the sample period, if so, indicating that the maximum difference exists in the sample period.
The method for estimating the risk price transformation conversion point specifically comprises the following steps: selecting two different kernel functions kleft(. o) and krightReplacing kernel function k (·) in original LLDV (which can be regarded as weights approaching arbitrary time points from left and right sides respectively), and estimating to obtain LLDV estimation quantity under two kernel functions by using LLDV-like estimation method (namely, only replacing kernel function respectively, and other estimation steps are not changed)Andconstruction ofEstimating the distance of two LLDV The time point corresponding to the maximum value is the most important structure conversion point. The two kernel functions are:
the Local Linear Dummy Variable (LLDV) estimation and inspection method has the advantages that:
(1) the generalized time-varying characteristics of risk-free arbitrage opportunities and risk prices are innovatively characterized by introducing a semi-parameter estimation method under smooth structure transformation.
Compared with the detection method, the general time-varying detection method of Local Linear Dummy Variable (LLDV) estimation can better describe the time variation of the parameter to be estimated. The LLDV method can check the characteristic that the parameter to be estimated generates structural transformation for a plurality of times in a sample period, can also check the time-varying characteristic under the condition that the approximate time point of the structural transformation is unknown, and can check the structural transformation characteristic that the parameter is smooth in the sample period. LLDV can therefore characterize the generalized time-varying nature of risk-free arbitrage opportunities and risk prices.
The conventional CAPM inspection (namely risk price inspection) method ignores the time variation of risk price, and specifically, the time variation neglects the conventional inspection model only statically inspecting the relationship between systematic risk and income, and the estimation result of coefficient, namely the risk price, is static, the ② conventional CSR (cross section regression) inspection method regresses the time-point-by-time section yield and the time-point systematic risk to obtain the time-point risk price, but the inspection method cannot guarantee the consistency and the effectiveness of the estimation coefficient in the section dimension, and the inspection method is difficult to inspect the time point of occurrence of main structure conversion, so that the inaccurate estimation of the risk price by the CSR inspection method can be called as the factor of ignoring the time variation, the ③ conventional CAPM inspection method often needs a priori information (such as Chow Test, etc.) about the approximate time point of occurrence of the structure conversion, the inaccuracy of the information 196and the requirement for the sample amount can cause the inspection to be inaccurate and the inspection of the sample amount to be capable of verifying the time variation of verifying the structure price, but the time variation of the conventional CAPM inspection method is likely to be a lot of the occurrence of the conventional structural conversion, the time variation, the conventional CSR inspection model is likely to be an economic characteristic that the time variation, the initial stage conversion of the conventional sample amount is likely to be ignored, and the initial stage, such as the initial stage, the initial stage of the conventional method is likely to be the initial stage of the occurrence of the conventional structural conversion, the conventional economic conversion, the initial stage of the.
In addition, LLDV can more accurately characterize the time-varying nature of risk-free arbitrage opportunities and risk prices. The parameters to be estimated, which are estimated by the LLDV method, have consistency and effectiveness, namely, the time-varying risk-free arbitrage opportunity can be more accurately estimatedAnd the price of the riskThe value of (c). In contrast, the conventional method (such as the CSR inspection method) cannot guarantee the consistency and validity of the estimation result.
(2) Innovatively investigating accurate time point of occurrence of main structure conversion under consideration of generalized time-varying characteristics
The LLDV method can estimate the risk-free arbitrage opportunity of obtaining accurate time-varying propertyAnd the price of the riskThis provides a basis for finding exactly the point in time at which the structural transformation of the risk price takes place. Meanwhile, the structure conversion time point is considered under the condition of considering the generalized time-varying characteristic of the parameter, and the conversion point of the risk price can be found more accurately. In addition, the technical method of finding the structure conversion point by adopting two kernel functions to approach from the left side and the right side can simultaneously inspect the abrupt structure conversion and the smooth structure conversion, and most of the traditional methods can only inspect the abrupt structure conversion.
3. Result comparison and application prospect of the technical method and other technical methods
(1) Comparison of results from macro-micro hybrid β with conventional systematic risk assessment methods
Table 1: macro and micro mixingAccuracy of estimation and explanatory power of
Note: in Panel A, the method for calculating Implied SD is as follows:i.e., the variance of all the estimated beta for the full sample, and the square root of the difference between the mean of the variance of the estimated beta for each combination. The patch B time points are returned back to brackets, which are the average of absolute t values calculated after adjustment by the method of Shanken (1992). In the mixed OLS regression, the absolute value of the t value is in parentheses.
Comparing the estimation result of the macro-micro hybrid β estimation model proposed by the method with the estimation result of the traditional estimation model, and further adopting a traditional CSR (cross Sectional regression) test method to compare the interpretability of the systematic risk estimated by each method to the income (namely CAPM test), the result shows that the traditional systematic risk estimation model underestimates the systematic risk of the stock, and the macro-micro hybrid β proposed by the method has higher interpretability compared with the systematic risk estimated by the traditional method.
(2) Comparison of results of macro-micro mixing β with traditional systematic risk assessment method under LLDV test method
Aiming at the LLDV inspection method, two estimation models of systematic risks are adopted, and the time-varying risk-free arbitrage opportunities and risk prices (respectively marked asAnd) And (6) obtaining the result. The results of fig. 1 and 2 show that, under the Fama and Macbeth estimation method,long term positive, the market has long-term no risk arbitrage opportunities, which deviate from theoretical and practical results, while macro-micro hybrid β estimates,fluctuating around 0 or so, and fluctuating around 0,the results show that the macro-micro mixing β can estimate systematic risks more accurately, and on the basis, the LLDV estimation and inspection method can accurately grasp the structure transformation characteristics of risk-free arbitrage opportunities and risk prices.
(3) Application prospect of the technical method
The technical method can more accurately estimate the systematic risk and the structural transformation characteristics thereof, and can more accurately grasp the time-varying characteristics of risk-free arbitrage opportunities and systematic risk prices. Investors and capital market monitoring departments can perform early warning on systematic risk according to the technical method result and perform prejudgment on the relationship between risk and income according to the risk price structure conversion characteristics, so that more effective investment decisions and monitoring decisions can be made. The method is beneficial for capital market managers to reform a systematic risk management mechanism of the capital market in China, effectively controls risks, and simultaneously improves the information feedback efficiency of the capital market and the support efficiency of innovative enterprises; the method can also provide basis for government departments to perform macroscopic economic intervention, financial currency policy, industry development decision, capital market management and stock market intervention, and can also provide theoretical and empirical help for investors to invest in marketing enterprises. Thereby driving the healthy development of the capital market and further promoting the technological innovation of new normal economy to be effectively supported by the capital market while managing economic risks more effectively.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (9)
1. A macro-micro dynamic hybrid β estimation method fusing macro-economic policy factors is characterized by comprising the steps of splitting systematic risks into a prior information part and a traditional transaction information part, defining the prior systematic risks as a risk function related to macro-micro factors for the prior systematic risk part, then obtaining a risk function value, namely a prior systematic risk, by calculating instead through considering the influence of each factor on the prior systematic risk, and then obtaining a posterior systematic risk, namely macro-micro hybrid β, by calculating through a contraction method in combination with the prior information and stock transaction information.
2. The method of claim 1 for estimating macro-micro dynamic blending β that incorporates macro-economic policy factors, comprising the steps of:
firstly, introducing a macroscopic period factor and an enterprise microscopic factor on the basis of CAPM (computer aided design), and estimating prior systemic risk
Andrespectively the individual stock excess yield and the market excess yield, namely subtracting the risk-free yield from the individual stock/market yield, wherein the variable with the mark represents a prior value; then, the prior systematic risk is determinedDefined as a linear risk function with respect to macrocycle factors and enterprise micro factors:
the method comprises the steps of assuming that sources of prior systematic risks comprise macroscopic period, enterprise life cycle and interactive influence of macroscopic and microscopic factors on systematic risks besides market fluctuation, and assuming that influence of macroscopic period factors on systematic risks of different stocks has heterogeneity but does not change along with time, and influence of enterprise life cycle and interactive influence of macroscopic and microscopic factors are homogeneous in the dimension of each stock and the dimension of time;
substituting the formula (2) into the CAPM model to construct a balance panel data regression model, and estimating and calculating by a Bayesian panel estimation method to obtain an estimation value of prior systematic risk
(2) And (3) wherein X comprises X1And X2Two macro-economic policy factors are introduced: representing the influence of monetary and financial policies, respectively, X1Is the M2 same-ratio growth rate, X2The same-ratio growth rate of the fixed-asset investment ratio for the government; the variable matrix Z contains a total of four variables: z1For the size of the enterprise calculated by taking the logarithm of the total assets of the enterprise, Z2For business account to market ratio, Z3Is the enterprise asset liability rate, Z4The method is characterized in that the method is a momentum factor and adds an industry virtual variable so as to represent the characteristic properties of an enterprise; meanwhile, cross terms of the macro-economic policy and the enterprise micro characteristic variables and cross terms Z of the macro-economic policy and the industry virtual variables are added into the modelit-1Xt-1Controlling these cross-reactions, in particular by X, respectively1And X2And Z1To Z4And industry virtual variable multiplication;
the prior systematic risk is obtained by Bayesian panel estimation and calculationAnd its standard error, combined with the prior distribution of the set macro-micro mix βUsing a contraction method to determine the systematic risk of a priori containing macroscopic factors and microscopic factorsB, rolling estimation under consideration of the information yield rate of stock exchangeitCombined, calculatedIs the systematic risk of the posterior, i.e., the macro-micro hybrid β constructed for this method.
3. The macro-micro dynamic blending β estimation method fusing macro-economic policy factors according to claim 2, wherein for macro-economic policy variable X, namely X1And X2And a momentum factor Z4Selecting values lagging by one month, and for each financial index Z1To Z3A value lagging by one quarter is chosen.
4. The method of claim 2, wherein Bayesian panel estimation is performed on equation (3), a standard Markov chain is selected, and the result is repeated for a plurality of times and removed for the previous N times to ensure sufficient convergence of the Bayesian estimation result, and variables are variedX1、X2Z and Zit-1Xt-1Inputting Bayes model for estimation to obtain coefficient estimation resultGamma and delta, gamma in the present process1i、γ2i、γ3i、δ1、δ2(ii) a After M repeated parameter estimation values gamma and delta are obtained through Bayesian estimation, the parameter estimation result under each repetition is obtained through calculation of formula (2) in a substitution modeFurther calculation yields a prioriSystemic riskAnd its variance, the standard error being the arithmetic square root of the variance:
wherein L is 1, …, M, L is M.
5. The method for estimating the macro-micro dynamic hybrid β fused with the macro-economic policy factors according to claim 4, wherein the method comprises the steps of calculating the mean value, the standard deviation and the t statistic of the parameter estimation value γ obtained by estimation for each repetition to obtain the influence of macro-periodic factors on the prior systematic risk:
6. the method of claim 2, wherein the macro-micro dynamic blending β of the macro-economic policy factor is βWhich corresponds to a variance ofWhereinCalculating a shrinkage weight in the method for shrinkage; bitAndboth are coefficients and variances obtained by regression with the traditional rolling window estimation method.
7. The macro-micro dynamic hybrid β estimation method fusing macro-economic policy factors according to claim 6, wherein the traditional rolling window estimation method includes two methods, 1, using daily transaction data to perform CAPM estimation on each stock, and obtaining the systematic risk estimation value and standard error of each stock as bitAnd2, adopting daily transaction data and Fama&The Macbeth regression method distributes the estimated systematic risk estimation value and standard error of each combination to each strand corresponding to the combination as bitAnd
8. the macro-micro dynamic blending β method of claim 2, wherein the macro-economic policy factors further include import and export conditions and industry policy factors.
9. The macro-micro dynamic blending β estimation method fusing macro-economic policy factors according to claim 2, wherein the enterprise micro factors further include enterprise business leverage and financial leverage factors.
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