| As a place for financing and capital allocation,capital market plays an indispensable role in the economic development.In the process of economic transiton,China's marketization process is speeding up,and the mission of the capital market in the economic development is becoming more and more important.With the continuous scale expansion of the capital market,the wealth effect attracts more and more investors,so that the pricing of portfolio has become the financial research priority.In the problem of portfolio pricing,capital asset pricing model(CAPM)has been affecting investor's investment decisions and capital market's operation since it was put forward.It illustrates the linear relationship between the expected return of portfolios and the systematic risk.As an indicator of systematic risk,the beta coefficient is the key of CAPM and provides investment basis for investors.However,the assumptions that the beta coefficient are too strict in CAPM which limit the effectiveness of the model.At present,China's capital market is in the stage of liberalization reform,and the problems,like investors' composition and imperfect market structure,will lead to the inaccurate measurement of systematic risk.By reviewing the properties and problems of beta coefficient mentioned in existing literatures and combining with the characteristics of the real capital market,this paper revises the calculation of the beta coefficient,in order to provide more accurate methods to measure systemic risk for market participants and regulators.Firstly,the time-varying characteristic of the beta coefficient is analyzed in this paper.The economic situation,policy change and industry cycle will lead to the variation of beta coefficient.Using the constant beta coefficient to estimate systemic risk can cause portfolio pricing bias.The stability of beta coefficients of the 13 industry portfolios in China's stock market from August 22,2001 to March 10,2017 is tested,and the existence of time-varying property of the beta coefficient is verified.Considering the asymmetry,long memory and bias of the portfolio returns fluctuation in China's capital market,this paper introduces a new beta coefficient time-varying path estimation method — score-driven exponential weighted moving average(SD-EWMA).The SD-EWMA time-varying path estimation method reduces the impact of outliers on the beta coefficients,and to the China's industry portfolios,the goodness of fit of the SD-EWMA estimated beta coefficients are better than the rolling window and DCC-GARCH estimated beta coefficients.Moreover,since investors' attitudes towards earnings and losses are different and the volatility of returns in the capital market is asymmetric,it is not accurate to use traditional beta coefficient to measure systematic risks.Taking into account the investors' "loss aversion" psychological and real market characteristics,this paper reviews three typical downside beta coefficient calculation methods,including the beta coefficients proposed by Hogan and Warren(1974),Harlow and Rao(1989)and Estrada(2002),and discusses the related risk areas for each coefficient.Moreover,based on the downside beta coefficient,this paper further considers the autocorrelation of the returns,and then introduces the martingale theory into the calculation of beta coefficients.Compared with the traditional variance,martingale semi-variance and weighted martingale semi-variance can distinguish between the continuous fluctuation and jump,rise and fall trend of portfolio returns,which are more consistent with investors' attitude towards portfolio risk in real capital market.Based on the martingale theory,this paper proposes four new downside beta coefficient calculation methods: the commutative martingale-based semi-variance beta coefficient,the commutative weighted martingale-based semi-variance betas coefficient,the beta coefficient based on Hogan-Warren semi-covariance and martingale theory,the beta coefficient based on mean-lower partial moment and martingale theory.Among the four downside beta coefficients above,the former two betas mainly consider the commutative conditions of the covariance,but the latter two betas are derived from the capital market line.The beta coefficient based on Hogan-Warren semi-covariance martingale theory is obtained under the mean-semivariance framework,while the beta coefficient based on mean-lower partial moment and martingale theory is obtained under a more general mean – lower partial moment framework.Therefore,compared with the first two beta coefficients proposed in this paper,the latter two beta coefficients have financial theoretical bases.By doing the empirical analyses for the latest SFC 13 industry portfolios in China stock market from August 22,2001 to March 10,2017,this paper examines relative performance of several dynamic beta coefficients,including the traditional beta coefficient,three downside beta coefficients proposed by Hogan and Warren(1974),Harlow and Rao(1989),Estrada(2002),the commutative martingale-based semi-variance beta coefficient,the commutative weighted martingale-based semi-variance betas coefficient,the beta coefficient based on Hogan-Warren semi-covariance and martingale theory,the beta coefficient based on mean-lower partial moment and martingale theory.The empirical results show that during the whole sample period,the beta coefficients based on Hogan-Warren semi-covariance and martingale theory,estimated by SD-EWMA,and the beta coefficients based on mean-lower partial moment and martingale theory,estimated by rolling window method,are better than other dynamic betas,and they can better explain the return variation of the China industry portfolios.Therefore,the above two kinds of beta coefficients provide a new method for investors in China's capital market to measure systematic risk.According to the sub-period empirical analyses results,beta coefficients based on Hogan-Warren semi-covariance,estimated by SD-EWMA,can better explain the return variation of the China's industry portfolios during the relative stable period and the 2015 “crash”.Futhermore,this paper tests the idiosyncratic risk of the China's industry portfolios.The results show that the idiosyncratic risk of the industry portfolios is not priced,i.e.the investors will not get extra risk premium by taking the unsystematic risk of the industry portfolios. |
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